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Essential Options Trading Guide
Options trading may seem overwhelming at first, but it’s easy to understand if you know a few key points. Investor portfolios are usually constructed with several asset classes. These may be stocks, bonds, ETFs, and even mutual funds. Options are another asset class, and when used correctly, they offer many advantages that trading stocks and ETFs alone cannot.
Key Takeaways
 An option is a contract giving the buyer the right, but not the obligation, to buy (in the case of a call) or sell (in the case of a put) the underlying asset at a specific price on or before a certain date.
 People use options for income, to speculate, and to hedge risk.
 Options are known as derivatives because they derive their value from an underlying asset.
 A stock option contract typically represents 100 shares of the underlying stock, but options may be written on any sort of underlying asset from bonds to currencies to commodities.
Option
What Are Options?
Options are contracts that give the bearer the right, but not the obligation, to either buy or sell an amount of some underlying asset at a predetermined price at or before the contract expires. Options can be purchased like most other asset classes with brokerage investment accounts.
Options are powerful because they can enhance an individual’s portfolio. They do this through added income, protection, and even leverage. Depending on the situation, there is usually an option scenario appropriate for an investor’s goal. A popular example would be using options as an effective hedge against a declining stock market to limit downside losses. Options can also be used to generate recurring income. Additionally, they are often used for speculative purposes such as wagering on the direction of a stock.
There is no free lunch with stocks and bonds. Options are no different. Options trading involves certain risks that the investor must be aware of before making a trade. This is why, when trading options with a broker, you usually see a disclaimer similar to the following:
Options involve risks and are not suitable for everyone. Options trading can be speculative in nature and carry substantial risk of loss.
Options as Derivatives
Options belong to the larger group of securities known as derivatives. A derivative’s price is dependent on or derived from the price of something else. As an example, wine is a derivative of grapes ketchup is a derivative of tomatoes, and a stock option is a derivative of a stock. Options are derivatives of financial securities—their value depends on the price of some other asset. Examples of derivatives include calls, puts, futures, forwards, swaps, and mortgagebacked securities, among others.
Call and Put Options
Options are a type of derivative security. An option is a derivative because its price is intrinsically linked to the price of something else. If you buy an options contract, it grants you the right, but not the obligation to buy or sell an underlying asset at a set price on or before a certain date.
A call option gives the holder the right to buy a stock and a put option gives the holder the right to sell a stock. Think of a call option as a downpayment for a future purpose.
Call Option Example
A potential homeowner sees a new development going up. That person may want the right to purchase a home in the future, but will only want to exercise that right once certain developments around the area are built.
The potential home buyer would benefit from the option of buying or not. Imagine they can buy a call option from the developer to buy the home at say $400,000 at any point in the next three years. Well, they can—you know it as a nonrefundable deposit. Naturally, the developer wouldn’t grant such an option for free. The potential home buyer needs to contribute a downpayment to lock in that right.

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With respect to an option, this cost is known as the premium. It is the price of the option contract. In our home example, the deposit might be $20,000 that the buyer pays the developer. Let’s say two years have passed, and now the developments are built and zoning has been approved. The home buyer exercises the option and buys the home for $400,000 because that is the contract purchased.
The market value of that home may have doubled to $800,000. But because the down payment locked in a predetermined price, the buyer pays $400,000. Now, in an alternate scenario, say the zoning approval doesn’t come through until year four. This is one year past the expiration of this option. Now the home buyer must pay the market price because the contract has expired. In either case, the developer keeps the original $20,000 collected.
Call Option Basics
Put Option Example
Now, think of a put option as an insurance policy. If you own your home, you are likely familiar with purchasing homeowner’s insurance. A homeowner buys a homeowner’s policy to protect their home from damage. They pay an amount called the premium, for some amount of time, let’s say a year. The policy has a face value and gives the insurance holder protection in the event the home is damaged.
What if, instead of a home, your asset was a stock or index investment? Similarly, if an investor wants insurance on his/her S&P 500 index portfolio, they can purchase put options. An investor may fear that a bear market is near and may be unwilling to lose more than 10% of their long position in the S&P 500 index. If the S&P 500 is currently trading at $2500, he/she can purchase a put option giving the right to sell the index at $2250, for example, at any point in the next two years.
If in six months the market crashes by 20% (500 points on the index), he or she has made 250 points by being able to sell the index at $2250 when it is trading at $2000—a combined loss of just 10%. In fact, even if the market drops to zero, the loss would only be 10% if this put option is held. Again, purchasing the option will carry a cost (the premium), and if the market doesn’t drop during that period, the maximum loss on the option is just the premium spent.
Put Option Basics
Buying, Selling Calls/Puts
There are four things you can do with options:
 Buy calls
 Sell calls
 Buy puts
 Sell puts
Buying stock gives you a long position. Buying a call option gives you a potential long position in the underlying stock. Shortselling a stock gives you a short position. Selling a naked or uncovered call gives you a potential short position in the underlying stock.
Buying a put option gives you a potential short position in the underlying stock. Selling a naked, or unmarried, put gives you a potential long position in the underlying stock. Keeping these four scenarios straight is crucial.
People who buy options are called holders and those who sell options are called writers of options. Here is the important distinction between holders and writers:
 Call holders and put holders (buyers) are not obligated to buy or sell. They have the choice to exercise their rights. This limits the risk of buyers of options to only the premium spent.
 Call writers and put writers (sellers), however, are obligated to buy or sell if the option expires inthemoney (more on that below). This means that a seller may be required to make good on a promise to buy or sell. It also implies that option sellers have exposure to more, and in some cases, unlimited, risks. This means writers can lose much more than the price of the options premium.
Why Use Options
Speculation
Speculation is a wager on future price direction. A speculator might think the price of a stock will go up, perhaps based on fundamental analysis or technical analysis. A speculator might buy the stock or buy a call option on the stock. Speculating with a call option—instead of buying the stock outright—is attractive to some traders since options provide leverage. An outofthemoney call option may only cost a few dollars or even cents compared to the full price of a $100 stock.
Hedging
Options were really invented for hedging purposes. Hedging with options is meant to reduce risk at a reasonable cost. Here, we can think of using options like an insurance policy. Just as you insure your house or car, options can be used to insure your investments against a downturn.
Imagine that you want to buy technology stocks. But you also want to limit losses. By using put options, you could limit your downside risk and enjoy all the upside in a costeffective way. For short sellers, call options can be used to limit losses if wrong—especially during a short squeeze.
How Options Work
In terms of valuing option contracts, it is essentially all about determining the probabilities of future price events. The more likely something is to occur, the more expensive an option would be that profits from that event. For instance, a call value goes up as the stock (underlying) goes up. This is the key to understanding the relative value of options.
The less time there is until expiry, the less value an option will have. This is because the chances of a price move in the underlying stock diminish as we draw closer to expiry. This is why an option is a wasting asset. If you buy a onemonth option that is out of the money, and the stock doesn’t move, the option becomes less valuable with each passing day. Since time is a component to the price of an option, a onemonth option is going to be less valuable than a threemonth option. This is because with more time available, the probability of a price move in your favor increases, and vice versa.
Accordingly, the same option strike that expires in a year will cost more than the same strike for one month. This wasting feature of options is a result of time decay. The same option will be worth less tomorrow than it is today if the price of the stock doesn’t move.
Volatility also increases the price of an option. This is because uncertainty pushes the odds of an outcome higher. If the volatility of the underlying asset increases, larger price swings increase the possibilities of substantial moves both up and down. Greater price swings will increase the chances of an event occurring. Therefore, the greater the volatility, the greater the price of the option. Options trading and volatility are intrinsically linked to each other in this way.
On most U.S. exchanges, a stock option contract is the option to buy or sell 100 shares; that’s why you must multiply the contract premium by 100 to get the total amount you’ll have to spend to buy the call.
What happened to our option investment  

May 1  May 21  Expiry Date  
Stock Price  $67  $78  $62 
Option Price  $3.15  $8.25  worthless 
Contract Value  $315  $825  $0 
Paper Gain/Loss  $0  $510  $315 
The majority of the time, holders choose to take their profits by trading out (closing out) their position. This means that option holders sell their options in the market, and writers buy their positions back to close. Only about 10% of options are exercised, 60% are traded (closed) out, and 30% expire worthlessly.
Fluctuations in option prices can be explained by intrinsic value and extrinsic value, which is also known as time value. An option’s premium is the combination of its intrinsic value and time value. Intrinsic value is the inthemoney amount of an options contract, which, for a call option, is the amount above the strike price that the stock is trading. Time value represents the added value an investor has to pay for an option above the intrinsic value. This is the extrinsic value or time value. So, the price of the option in our example can be thought of as the following:
Premium =  Intrinsic Value +  Time Value 
$8.25  $8.00  $0.25 
In real life, options almost always trade at some level above their intrinsic value, because the probability of an event occurring is never absolutely zero, even if it is highly unlikely.
Types of Options
American and European Options
American options can be exercised at any time between the date of purchase and the expiration date. European options are different from American options in that they can only be exercised at the end of their lives on their expiration date. The distinction between American and European options has nothing to do with geography, only with early exercise. Many options on stock indexes are of the European type. Because the right to exercise early has some value, an American option typically carries a higher premium than an otherwise identical European option. This is because the early exercise feature is desirable and commands a premium.
There are also exotic options, which are exotic because there might be a variation on the payoff profiles from the plain vanilla options. Or they can become totally different products all together with “optionality” embedded in them. For example, binary options have a simple payoff structure that is determined if the payoff event happens regardless of the degree. Other types of exotic options include knockout, knockin, barrier options, lookback options, Asian options, and Bermudan options. Again, exotic options are typically for professional derivatives traders.
Options Expiration & Liquidity
Options can also be categorized by their duration. Shortterm options are those that expire generally within a year. Longterm options with expirations greater than a year are classified as longterm equity anticipation securities or LEAPs. LEAPS are identical to regular options, they just have longer durations.
Options can also be distinguished by when their expiration date falls. Sets of options now expire weekly on each Friday, at the end of the month, or even on a daily basis. Index and ETF options also sometimes offer quarterly expiries.
Reading Options Tables
More and more traders are finding option data through online sources. (For related reading, see “Best Online Stock Brokers for Options Trading 2020”) While each source has its own format for presenting the data, the key components generally include the following variables:
 Volume (VLM) simply tells you how many contracts of a particular option were traded during the latest session.
 The “bid” price is the latest price level at which a market participant wishes to buy a particular option.
 The “ask” price is the latest price offered by a market participant to sell a particular option.
 Implied Bid Volatility (IMPL BID VOL) can be thought of as the future uncertainty of price direction and speed. This value is calculated by an optionpricing model such as the BlackScholes model and represents the level of expected future volatility based on the current price of the option.
 Open Interest (OPTN OP) number indicates the total number of contracts of a particular option that have been opened. Open interest decreases as open trades are closed.
 Delta can be thought of as a probability. For instance, a 30delta option has roughly a 30% chance of expiring inthemoney.
 Gamma (GMM) is the speed the option is moving in or outofthemoney. Gamma can also be thought of as the movement of the delta.
 Vega is a Greek value that indicates the amount by which the price of the option would be expected to change based on a onepoint change in implied volatility.
 Theta is the Greek value that indicates how much value an option will lose with the passage of one day’s time.
 The “strike price” is the price at which the buyer of the option can buy or sell the underlying security if he/she chooses to exercise the option.
Buying at the bid and selling at the ask is how market makers make their living.
Long Calls/Puts
The simplest options position is a long call (or put) by itself. This position profits if the price of the underlying rises (falls), and your downside is limited to loss of the option premium spent. If you simultaneously buy a call and put option with the same strike and expiration, you’ve created a straddle.
This position pays off if the underlying price rises or falls dramatically; however, if the price remains relatively stable, you lose premium on both the call and the put. You would enter this strategy if you expect a large move in the stock but are not sure which direction.
Basically, you need the stock to have a move outside of a range. A similar strategy betting on an outsized move in the securities when you expect high volatility (uncertainty) is to buy a call and buy a put with different strikes and the same expiration—known as a strangle. A strangle requires larger price moves in either direction to profit but is also less expensive than a straddle. On the other hand, being short either a straddle or a strangle (selling both options) would profit from a market that doesn’t move much.
Below is an explanation of straddles from my Options for Beginners course:
Straddles Academy
And here’s a description of strangles:
How to use Straddle Strategies
Spreads & Combinations
Spreads use two or more options positions of the same class. They combine having a market opinion (speculation) with limiting losses (hedging). Spreads often limit potential upside as well. Yet these strategies can still be desirable since they usually cost less when compared to a single options leg. Vertical spreads involve selling one option to buy another. Generally, the second option is the same type and same expiration, but a different strike.
A bull call spread, or bull call vertical spread, is created by buying a call and simultaneously selling another call with a higher strike price and the same expiration. The spread is profitable if the underlying asset increases in price, but the upside is limited due to the short call strike. The benefit, however, is that selling the higher strike call reduces the cost of buying the lower one. Similarly, a bear put spread, or bear put vertical spread, involves buying a put and selling a second put with a lower strike and the same expiration. If you buy and sell options with different expirations, it is known as a calendar spread or time spread.
Spread
Combinations are trades constructed with both a call and a put. There is a special type of combination known as a “synthetic.” The point of a synthetic is to create an options position that behaves like an underlying asset, but without actually controlling the asset. Why not just buy the stock? Maybe some legal or regulatory reason restricts you from owning it. But you may be allowed to create a synthetic position using options.
Butterflies
A butterfly consists of options at three strikes, equally spaced apart, where all options are of the same type (either all calls or all puts) and have the same expiration. In a long butterfly, the middle strike option is sold and the outside strikes are bought in a ratio of 1:2:1 (buy one, sell two, buy one).
If this ratio does not hold, it is not a butterfly. The outside strikes are commonly referred to as the wings of the butterfly, and the inside strike as the body. The value of a butterfly can never fall below zero. Closely related to the butterfly is the condor – the difference is that the middle options are not at the same strike price.
Options Risks
Because options prices can be modeled mathematically with a model such as the BlackScholes, many of the risks associated with options can also be modeled and understood. This particular feature of options actually makes them arguably less risky than other asset classes, or at least allows the risks associated with options to be understood and evaluated. Individual risks have been assigned Greek letter names, and are sometimes referred to simply as “the Greeks.”
Below is a very basic way to begin thinking about the concepts of Greeks:
What Is Options Trading? Examples and Strategies
If you hadn’t noticed by now, there are a lot of choices when it comes to investing in securities.
Whether you prefer to play the stock market or invest in an Exchange Traded Fund (ETF) or two, you probably know the basics of a variety of securities. But what exactly are options, and what is options trading?
What Are Options?
An option is a contract that allows (but doesn’t require) an investor to buy or sell an underlying instrument like a security, ETF or even index at a predetermined price over a certain period of time. Buying and selling options is done on the options market, which trades contracts based on securities. Buying an option that allows you to buy shares at a later time is called a “call option,” whereas buying an option that allows you to sell shares at a later time is called a “put option.”
However, options are not the same thing as stocks because they do not represent ownership in a company. And, although futures use contracts just like options do, options are considered lower risk due to the fact that you can withdraw (or walk away from) an options contract at any point. The price of the option (its premium) is thus a percentage of the underlying asset or security.
When buying or selling options, the investor or trader has the right to exercise that option at any point up until the expiration date – so simply buying or selling an option doesn’t mean you actually have to exercise it at the buy/sell point. Because of this system, options are considered derivative securities – which means their price is derived from something else (in this case, from the value of assets like the market, securities or other underlying instruments). For this reason, options are often considered less risky than stocks (if used correctly).
But why would an investor use options? Well, buying options is basically betting on stocks to go up, down or to hedge a trading position in the market.
The price at which you agree to buy the underlying security via the option is called the “strike price,” and the fee you pay for buying that option contract is called the “premium.” When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price. The price you are paying for that bet is the premium, which is a percentage of the value of that asset.
There are two different kinds of options – call and put options – which give the investor the right (but not obligation) to sell or buy securities.
Call Options
A call option is a contract that gives the investor the right to buy a certain amount of shares (typically 100 per contract) of a certain security or commodity at a specified price over a certain amount of time. For example, a call option would allow a trader to buy a certain amount of shares of either stocks, bonds, or even other instruments like ETFs or indexes at a future time (by the expiration of the contract).
If you’re buying a call option, it means you want the stock (or other security) to go up in price so that you can make a profit off of your contract by exercising your right to buy those stocks (and usually immediately sell them to cash in on the profit).
The fee you are paying to buy the call option is called the premium (it’s essentially the cost of buying the contract which will allow you to eventually buy the stock or security). In this sense, the premium of the call option is sort of like a downpayment like you would place on a house or car. When purchasing a call option, you agree with the seller on a strike price and are given the option to buy the security at a predetermined price (which doesn’t change until the contract expires).
So, call options are also much like insurance – you are paying for a contract that expires at a set time but allows you to purchase a security (like a stock) at a predetermined price (which won’t go up even if the price of the stock on the market does). However, you will have to renew your option (typically on a weekly, monthly or quarterly basis). For this reason, options are always experiencing what’s called time decay – meaning their value decays over time.
For call options, the lower the strike price, the more intrinsic value the call option has.
Put Options
Conversely, a put option is a contract that gives the investor the right to sell a certain amount of shares (again, typically 100 per contract) of a certain security or commodity at a specified price over a certain amount of time. Just like call options, a put option allows the trader the right (but not obligation) to sell a security by the contract’s expiration date.
Just like call options, the price at which you agree to sell the stock is called the strike price, and the premium is the fee you are paying for the put option.
Put options operate in a similar fashion to calls, except you want the security to drop in price if you are buying a put option in order to make a profit (or sell the put option if you think the price will go up).
On the contrary to call options, with put options, the higher the strike price, the more intrinsic value the put option has.
Long vs. Short Options
Unlike other securities like futures contracts, options trading is typically a “long” – meaning you are buying the option with the hopes of the price going up (in which case you would buy a call option). However, even if you buy a put option (right to sell the security), you are still buying a long option.
Shorting an option is selling that option, but the profits of the sale are limited to the premium of the option – and, the risk is unlimited.
For both call and put options, the more time left on the contract, the higher the premiums are going to be.
What Is Options Trading?
Well, you’ve guessed it — options trading is simply trading options, and is typically done with securities on the stock or bond market (as well as ETFs and the like).
For starters, you can only buy or sell options through a brokerage like E*Trade (ETFC) – Get Report or Fidelity (FNF) – Get Report .
When buying a call option, the strike price of an option for a stock, for example, will be determined based on the current price of that stock. For example, if a share of a given stock (like Amazon (AMZN) – Get Report ) is $1,748, any strike price (price of the call option) that is above that share price is considered to be “out of the money.” Conversely, if the strike price is under the current share price of the stock, it’s considered “in the money.”
However, for put options (right to sell), the opposite is true – with strike prices below the current share price being considered “out of the money” and vice versa. And, what’s more important – any “out of the money” options (whether call or put options) are worthless at expiration (so you really want to have an “in the money” option when trading on the stock market).
Another way to think of it is that call options are generally bullish, while put options are generally bearish.
Options typically expire on Fridays with different time frames (for example, monthly, bimonthly, quarterly, etc.). Many options contracts are six months.
Trading Call vs. Put Options
Purchasing a call option is essentially betting that the price of the share of security (like a stock or index) will go up over the course of a predetermined amount of time. For instance, if you buy a call option for Alphabet (GOOG) – Get Report at, say, $1,500 and are feeling bullish about the stock, you are predicting that the share price for Alphabet will increase.
When purchasing put options, you are expecting the price of the underlying security to go down over time (so, you’re bearish on the stock). For example, if you are purchasing a put option on the S&P 500 I:GSPC index with a current value of $2,100 per share, you are being bearish about the stock market and are assuming the S&P 500 will decline in value over a given period of time (maybe to sit at $1,700). In this case, because you purchased the put option when the index was at $2,100 per share (assuming the strike price was at or in the money), you would be able to sell the option at that same price (not the new, lower price). This would equal a nice “chaching” for you as an investor.
Options trading (especially in the stock market) is affected primarily by the price of the underlying security, time until the expiration of the option, and the volatility of the underlying security.
The premium of the option (its price) is determined by intrinsic value plus its time value (extrinsic value).
Historical vs. Implied Volatility
Volatility in options trading refers to how large the price swings are for a given stock.
Just as you would imagine, high volatility with securities (like stocks) means higher risk – and conversely, low volatility means lower risk.
When trading options on the stock market, stocks with high volatility (ones whose share prices fluctuate a lot) are more expensive than those with low volatility (although due to the erratic nature of the stock market, even low volatility stocks can become high volatility ones eventually).
Historical volatility is a good measure of volatility since it measures how much a stock fluctuated daytoday over a oneyear period of time. On the other hand, implied volatility is an estimation of the volatility of a stock (or security) in the future based on the market over the time of the option contract.
Value: Time Value and in/at/out of the Money
If you are buying an option that is already “in the money” (meaning the option will immediately be in profit), its premium will have an extra cost because you can sell it immediately for a profit. On the other hand, if you have an option that is “at the money,” the option is equal to the current stock price. And, as you may have guessed, an option that is “out of the money” is one that won’t have additional value because it is currently not in profit.
For call options, “in the money” contracts will be those whose underlying asset’s price (stock, ETF, etc.) is above the strike price. For put options, the contract will be “in the money” if the strike price is below the current price of the underlying asset (stock, ETF, etc.).
The time value, which is also called the extrinsic value, is the value of the option above the intrinsic value (or, above the “in the money” area).
If an option (whether a put or call option) is going to be “out of the money” by its expiration date, you can sell options in order to collect a time premium.
The longer an option has before its expiration date, the more time it has to actually make a profit, so its premium (price) is going to be higher because its time value is higher. Conversely, the less time an options contract has before it expires, the less its time value will be (the less additional time value will be added to the premium).
So, in other words, if an option has a lot of time before it expires, the more additional time value will be added to the premium (price) – and the less time it has before expiration, the less time value will be added to the premium.
Pros and Cons
Some of the major pros of options trading revolve around their supposed safety.
According to Nasdaq’s options trading tips, options are often more resilient to changes (and downturns) in market prices, can help increase income on current and future investments, can often get you better deals on a variety of equities and, perhaps most importantly, can help you capitalize on that equity rising or dropping over time without having to invest in it directly.
Of course, there are cons to trading options – including risk.
There are a variety of ways to interpret risks associated with options trading, but these risks primarily revolve around the levels of volatility or uncertainty of the market. For example, expensive options are those whose uncertainty is high – meaning the market is volatile for that particular asset, and it is more risky to trade it.
Options Trading Strategies
When trading options, the contracts will typically take this form:
Stock ticker (name of the stock), date of expiration (typically in mm/dd/yyyy, although sometimes dates are flipped with the year first, month second and day last), the strike price, call or put, and the premium price (for example, $3). So an example of a call option for Apple stock would look something like this: APPL 01/15/2020 200 Call @ 3.
Still, depending on what platform you are trading on, the option trade will look very different.
There are numerous strategies you can employ when options trading – all of which vary on risk, reward and other factors. And while there are dozens of strategies (most of them fairly complicated), here are a few main strategies that have been recommended for beginners.
Straddles and strangles
With straddles (long in this example), you as a trader are expecting the asset (like a stock) to be highly volatile, but don’t know the direction in which it will go (up or down). When using a straddle strategy, you as the trader are buying a call and put option at the same strike price, underlying price and expiry date. This strategy is often used when a trader is expecting the stock of a particular company to plummet or skyrocket, usually following an event like an earnings report. For example, when a company like Apple (AAPL) – Get Report is getting ready to release their third quarter earnings on July 31st, an options trader could use a straddle strategy to buy a call option to expire on that date at the current Apple stock price, and also buy a put option to expire on the same day for the same price.
For strangles (long in this example), an investor will buy an “out of the money” call and an “out of the money” put simultaneously for the same expiry date for the same underlying asset. Investors who use this strategy are assuming the underlying asset (like a stock) will have a dramatic price movement but don’t know in which direction. What makes a long strangle a somewhat safe trade is that the investor only needs the stock to move greater than the total premium paid, but it doesn’t matter in which direction.
The upside of a strangle strategy is that there is less risk of loss, since the premiums are less expensive due to how the options are “out of the money” – meaning they’re cheaper to buy.
Covered Call
If you have long asset investments (like stocks for example), a covered call is a great option for you. This strategy is typically good for investors who are only neutral or slightly bullish on a stock.
A covered call works by buying 100 shares of a regular stock and selling one call option per 100 shares of that stock. This kind of strategy can help reduce the risk of your current stock investments but also provides you an opportunity to make profit with the option.
Covered calls can make you money when the stock price increases or stays pretty constant over the time of the option contract. However, you could lose money with this kind of trade if the stock price falls too much (but can actually still make money if it only falls a little bit). But by using this strategy, you are actually protecting your investment from decreases in share price while giving yourself the opportunity to make money while the stock price is flat.
Selling Iron Condors
With this strategy, the trader’s risk can either be conservative or risky depending on their preference (which is a definite plus). For iron condors, the position of the trade is nondirectional, which means the asset (like a stock) can either go up or down – so, there is profit potential for a fairly wide range. To use this kind of strategy, sell a put and buy another put at a lower strike price (essentially, a put spread), and combine it by buying a call and selling a call at a higher strike price (a call spread). These calls and puts are short.
When the stock price stays between the two puts or calls, you make a profit (so, when the price fluctuates somewhat, you’re making money). But the strategy loses money when the stock price either increases drastically above or drops drastically below the spreads. For this reason, the iron condor is considered a market neutral position.
Options Trading Examples
There are lots of examples of options trading that largely depend on which strategy you are using. However, as a basic idea of what a typical call or put option would be, let’s consider a trader buying a call and put option on Microsoft (MSFT) – Get Report .
For example, if you bought a long call option (remember, a call option is a contract that gives you the right to buy shares later on) for 100 shares of Microsoft stock at $110 per share for December 1, you would have the right to buy 100 shares of that stock at $110 per share regardless of if the stock price changed or not by December 1. For this long call option, you would be expecting the price of Microsoft to increase, thereby letting you reap the profits when you are able to buy it at a cheaper cost than its market value. However, if you decide not to exercise that right to buy the shares, you would only be losing the premium you paid for the option since you aren’t obligated to buy any shares.
If you were buying a long put option for Microsoft, you would be betting that the price of Microsoft shares would decrease up until your contract expires, so that, if you chose to exercise your right to sell those shares, you’d be selling them at a higher price than their market value.
Another example involves buying a long call option for a $2 premium (so for the 100 shares per contract, that would equal $200 for the whole contract). You buy an option for 100 shares of Oracle (ORCL) – Get Report for a strike price of $40 per share which expires in two months, expecting stock to go to $50 by that time. You’ve spent $200 on the contract (the $2 premium times 100 shares for the contract). When the stock price hits $50 as you bet it would, your call option to buy at $40 per share will be $10 “in the money” (the contract is now worth $1,000, since you have 100 shares of the stock) – since the difference between 40 and 50 is 10. At this point, you can exercise your call option and buy the stock at $40 per share instead of the $50 it is now worth – making your $200 original contract now worth $1,000 – which is an $800 profit and a 400% return.
Common Options Trading Mistakes
There are plenty of mistakes even seasoned traders can make when trading options.
One common mistake for traders to make is that they think they need to hold on to their call or put option until the expiration date. If your option’s underlying stock goes way up over night (doubling your call or put option’s value), you can exercise the contract immediately to reap the gains (even if you have, say, 29 days left for the option).
Another common mistake for options traders (especially beginners) is to fail to create a good exit plan for your option. For example, you may want to plan to exit your option when you either suffer a loss or when you’ve reached a profit that is to your liking (instead of holding out in your contract until the expiration date).
Still other traders can make the mistake of thinking that cheaper is better. For options, this isn’t necessarily true. The cheaper an option’s premium is, the more “out of the money” the option typically is, which can be a riskier investment with less profit potential if it goes wrong. Buying “out of the money” call or put options means you want the underlying security to drastically change in value, which isn’t always predictable.
And while there are plenty of other options faux pas, be sure to do your research before getting into the options trading game.
(Editor’s Pick. Originally published Nov. 9.)
Options Transactions
Unlike stock trading, the contractual nature of options offer four different ways for entering and exiting positions. There is an options seller (writer) and an options buyer (holder). The option seller can enter or exit a transaction, and so can an option buyer.
Opening Transactions
BuytoOpen
This is the transaction the options buyer make to enter a long position on an option. For example, if you want to buy a call option, you would enter a “buytoopen” transaction.
SelltoOpen
This is the transaction the options seller make when he wish to enter a short position on an option. For example, if you are writing call options to earn premiums, you would enter a “selltoopen” transaction.
Closing Transactions
BuytoClose
This is the transaction the options writer make when he wish to exit a short position on an option. For example, if you wish to buy back the calls you had previously sold, you would enter a “buytoclose” transaction.
SelltoClose
This is the transaction the options holder make to exit a long position on an option. For example, if you want to sell a previously purchased call option, you would enter a “selltoclose” transaction.
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Writing Puts to Purchase Stocks
If you are very bullish on a particular stock for the long term and is looking to purchase the stock but feels that it is slightly overvalued at the moment, then you may want to consider writing put options on the stock as a means to acquire it at a discount. [Read on. ]
What are Binary Options and How to Trade Them?
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Investing in Growth Stocks using LEAPSÂ® options
If you are investing the Peter Lynch style, trying to predict the next multibagger, then you would want to find out more about LEAPSÂ® and why I consider them to be a great option for investing in the next MicrosoftÂ®. [Read on. ]
Effect of Dividends on Option Pricing
Cash dividends issued by stocks have big impact on their option prices. This is because the underlying stock price is expected to drop by the dividend amount on the exdividend date. [Read on. ]
Bull Call Spread: An Alternative to the Covered Call
As an alternative to writing covered calls, one can enter a bull call spread for a similar profit potential but with significantly less capital requirement. In place of holding the underlying stock in the covered call strategy, the alternative. [Read on. ]
Dividend Capture using Covered Calls
Some stocks pay generous dividends every quarter. You qualify for the dividend if you are holding on the shares before the exdividend date. [Read on. ]
Leverage using Calls, Not Margin Calls
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Day Trading using Options
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What is the Put Call Ratio and How to Use It
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Understanding PutCall Parity
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Understanding the Greeks
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Valuing Common Stock using Discounted Cash Flow Analysis
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What is an Option? Put Option and Call Option Explained
The Chicago Board Options Exchange defines an “option” as follows: There are many ways a stockbroker can violate legal and ethical obligations to a customer, and in most cases, the broker’s
An option is a contract giving the buyer the right, but not the obligation, to buy or sell an underlying asset (a stock or index) at a specific price on or before a certain date (listed options are all for 100 shares of the particular underlying asset). An option is a security, just like a stock or bond, and constitutes a binding contract with strictly defined terms and properties.
For most casual investors, that definition may as well be written in ancient Greek. And yet brokers sometimes buy and sell options for investors who don’t understand what they are, can’t appreciate or afford their risk, and may not even know that the option transactions are occurring.
Put Options and Call Options
Perhaps we can explain options a bit more clearly.
There are only two kinds of options: “put” options and “call” options. You’re likely to hear these referred to as “puts” and “calls.” One option contract controls 100 shares of stock, but you can buy or sell as many contracts as you want.
Call Options
When you buy a call option, you’re buying the right to purchase from the seller of that option 100 shares of a particular stock at a predetermined price, which is called the “strike price.” You have to exercise your call by a certain date or it expires. To purchase a call option, you pay the seller of the call a fee, known as a “premium.” When you hold a call option, you hope the market price of the stock associated with it will increase in the near future. Why? If the stock price increases enough to exceed the strike price, you can exercise your call and buy that stock from the call’s seller at the strike price, or in other words, at a price below the stock’s market value. Then you can either keep the shares (which you obtained at a bargain price) or sell them for a profit. But what happens if the price of the stock goes down, rather than up? You let the call option expire and your loss is limited to the cost of the premium.
Put Options
When you buy a put option, you’re buying the right to force the person who sells you the put to purchase 100 shares of a particular stock from you at the strike price. When you hold put options, you want the stock price to drop below the strike price. If it does, the seller of the put will have to buy shares from you at the strike price, which will be higher than the market price. Because you can force the seller of the option to buy your shares at a price above market value, the put option is like an insurance policy against your shares losing too much value. If the market price instead goes up rather than down, your shares will have increased in value and you can simply let the option expire because all you’ll lose is the cost of the premium you paid for the put.
Purchasing options can give you a hedge against losses, and in that sense, they can be used conservatively. But there are many options strategies that amount to little more than gambling and can increase your risk to a frightening degree. One simple example is the sale of “uncovered” calls. Remember, when a call is exercised, stock must be delivered by the seller of the call. If you’ve sold that call on stock you already own, the call is “covered” by those shares and your cost has already been incurred. If the option is exercised, you’ll simply deliver those shares to the option holder. But if you sell an “uncovered” call, meaning you don’t yet own the stock, your potential for loss is unlimited. If the option is exercised, you’ll have to buy those shares on the open market to cover your obligation, no matter how high the price may be at that time. If a strong market advance or a major announcement by the issuer has driven the share price up sharply, your losses could be enormous.
As indicated, many option strategies involve great complexity and risk. For this reason, not all options strategies will be suitable for all investors. In fact, with the exception of sophisticated, high net worth individuals who can afford and are willing to incur substantial losses, the writing of puts or uncovered calls would be unsuitable for just about everyone. Nevertheless, brokers sometimes engage in inappropriate options trading on behalf of customers who do not understand the risks.
If you have lost assets because your stockbroker was engaging in options trading, please contact us today.
Basics Of Options Trading Explained
Before we delve deep into the world of options trading, let’s take a moment to understand why do we need options at all. If you are thinking it is just another way to make money and was created by some fancy guys in suits working in Wall Street, well, you are wrong. The options world predates the modern stock exchanges by a large margin.
While some credit the Samurai for giving us the foundation on which options contracts were based, some actually acknowledge the Greeks for giving us an idea on how to speculate on a commodity, in this case, the harvest of olives. In both cases, humans were trying to guess the price of a food item and trade accordingly (rice in the case of samurais), long before the modern world put in various rules and set up exchanges.
With this in mind, let us try to answer the first question in your mind.
What is options trading?
Let’s take a very simple example to understand options trading. Consider that you are buying a stock for Rs. 3000. But the broker tells you about an exciting offer, that you can buy it now for Rs. 3000 or you can give a token amount of Rs. 30 and reserve the right to buy it at Rs. 3000 after a month, even if the stock increases in value at that time. But that token amount is nonrefundable!
You realise that there is a high chance that the stock would cross Rs. 3030 and thus, you can breakeven at least. Since you have to pay only Rs. 30 now, the remaining amount can be used elsewhere for a month. You wait for a month and then look at the stock price.
Now, depending on the stock price, you have the option to buy the stock from the broker or not. Of course, this is an oversimplification but this is options trading in a gist.In the world of trading, options are instruments that belong to the derivatives family, which means its price is derived from something else, mostly stocks. The price of an option is intrinsically linked to the price of the underlying stock.
A formal definition is given below:
A stock option is a contract between two parties in which the stock option buyer (holder) purchases the right (but not the obligation) to buy/sell shares of an underlying stock at a predetermined price from/to the option seller (writer) within a fixed period of time.
We are going to make sure that by the end of this article you are well versed with the options trading world along with trying out a few options trading strategies as well. We will cover the following points in this article. If you feel that you want to skip the basics of options, then head straight to the options trading strategies.
Let’s start now, shall we!
Options trading vs. Stock trading
There must be a doubt in your mind that why do we even have options trading if it is just another way of trading. Well, here are a few points which make it different from trading stocks
 The Options contract has an expiration date, unlike stocks. The expiration can vary from weeks, months to years depending upon the regulations and the type of Options that you are practising. Stocks, on the other hand, do not have an expiration date.
 Unlike Stocks, Options derive their value from something else and that’s why they fall under the derivatives category
 Options are not definite by numbers like Stocks
 Options owners have no right (voting or dividend) in a company unlike Stock owners
It is quite often that some people find the Option’s concept difficult to understand though they have already followed it in their other transactions, for e.g. car insurance or mortgages. In this part of the article, we will take you through some of the most important aspects of Options trading before we get down to the world of options trading.
Options terminologies
Strike Price
The Strike Price is the price at which the underlying stocks can be bought or sold as per the contract. In options trading, the Strike Price for a Call Option indicates the price at which the Stock can be bought (on or before its expiration) and for Put Options trading it refers to the price at which the seller can exercise its right to sell the underlying stocks (on or before its expiration)
Premium
Since the Options themselves don’t have an underlying value, the Options premium is the price that you have to pay in order to purchase an Option. The premium is determined by multiple factors including the underlying stock price, volatility in the market and the days until the Option’s expiration. In options trading, choosing the premium is one of the most important components.
Underlying Asset
In options trading, the underlying asset can be stocks, futures, index, commodity or currency. The price of Options is derived from its underlying asset. For the purpose of this article, we will be considering the underlying asset as the stock. The Option of stock gives the right to buy or sell the stock at a specific price and date to the holder. Hence its all about the underlying asset or stocks when it comes to Stock in Options Trading.
Expiration Date
In options trading, all stock options have an expiration date. The expiration date is also the last date on which the Options holder can exercise the right to buy or sell the Options that are in holding. In Options Trading, the expiration of Options can vary from weeks to months to years depending upon the market and the regulations.
Options Style
There are two major types of Options that are practised in most of the options trading markets.
 American Options which can be exercised anytime before its expiration date
 European Options which can only be exercised on the day of its expiration
Moneyness (ITM, OTM & ATM)
It is very important to understand the Options Moneyness before you start trading in Stock Options. A lot of options trading strategies are played around the Moneyness of an Option.
It basically defines the relationship between the strike price of an Option and the current price of the underlying Stocks. We will examine each term in detail below.
When is an Option inthemoney?
 Call Option – when the underlying stock price is higher than the strike price
 Put Option – when the underlying stock price is lower than the strike price
When is an Option outofthemoney?
 Call Option – when the underlying stock price is lower than the strike price
 Put Option – when the underlying stock price is higher than the strike price
When is an Option atthemoney?
 When the underlying stock price is equal to the strike price.
Take a break here to ponder over the different terms as we will find it extremely useful later when we go through the types of options as well as a few options trading strategies.
Type of options
In the true sense, there are only two types of Options i.e Call & Put Options. We will understand them in more detail.
To Call or Put
A Call Option is an option to buy an underlying Stock on or before its expiration date. At the time of buying a Call Option, you pay a certain amount of premium to the seller which grants you the right (but not the obligation) to buy the underlying stock at a specified price (strike price).
Purchasing a call option means that you are bullish about the market and hoping that the price of the underlying stock may go up. In order for you to make a profit, the price of the stock should go higher than the strike price plus the premium of the call option that you have purchased before or at the time of its expiration.
In contrast, a Put Option is an option to sell an underlying Stock on or before its expiration date. Purchasing a Put Option means that you are bearish about the market and hoping that the price of the underlying stock may go down. In order for you to make a profit, the price of the stock should go down from the strike price plus the premium of the Put Option that you have purchased before or at the time of its expiration.
In this manner, both Put and Call option buyer’s loss is limited to the premium paid but profit is unlimited. The above explanations were from the buyer’s point of view. We will now understand the putcall options from the seller’s point of view, ie options writers. The Put option seller, in return for the premium charged, is obligated to buy the underlying asset at the strike price.
Similarly, the Call option seller, in return for the premium charged, is obligated to sell the underlying asset at the strike price. Is there a way to visualise the potential profit/loss of an option buyer or seller? Actually, there is. An option payoff diagram is a graphical representation of the net Profit/Loss made by the option buyers and sellers.
Before we go through the diagrams, let’s understand what the four terms mean. As we know that going short means selling and going long means buying the asset, the same principle applies to options. Keeping this in mind, we will go through the four terms.
 Short call – Here we are betting that the prices will fall and hence, a short call means you are selling calls.
 Short put – Here the short put means we are selling a put option
 Long call – it means that we are buying a call option since we are optimistic about the underlying asset’s share price
 Long put – Here we are buying a put option.
S = Underlying Price
X = Strike Price
Breakeven point is that point at which you make no profit or no loss.
The long call holder makes a profit equal to the stock price at expiration minus strike price minus premium if the option is in the money. Call option holder makes a loss equal to the amount of premium if the option expires out of money and the writer of the option makes a flat profit equal to the option premium.
Similarly, for the put option buyer, profit is made when the option is in the money and is equal to the strike price minus the stock price at expiration minus premium. And, the put writer makes a profit equal to the premium for the option.
All right, until now we have been going through a lot of theory. Let’s switch gears for a minute and come to the real world. How do options look like? Well, let’s find out.
What does an options trading quote consist of?
If you were to look for an options quote on Apple stock, it would look something like this:
When this was recorded, the stock price of Apple Inc. was $196. Now let’s take one line from the list and break it down further.
Eg.
In a typical options chain, you will have a list of call and put options with different strike prices and corresponding premiums. The call option details are on the left and the put option details are on the right with the strike price in the middle.
 The symbol and option number is the first column.
 The “last” column signifies the amount at which the last time the option was bought.
 “Change” indicates the variance between the last two trades of the said options
 “Bid” column indicates the bid submitted for the option.
 “Ask” indicates the asking price sought by the option seller.
 “Volume” indicates the number of options traded. Here the volume is 0.
 “Open Interest” indicates the number of options which can be bought for that strike price.
The columns are the same for the put options as well. In some cases, the data provider signifies whether the option is in the money, at the money or out of money as well. Of course, we need an example to really help our understanding of options trading. Thus, let’s go through one now.
Options Trading Example
We will go through two cases to better understand the call and put options.
For simplicity’s sake, let us assume the following:
 Price of Stock when the option is written: $100
 Premium: $5
 Expiration date: 1 month after the option is bought
Case 1:
The current price of stock: $110. Strike price: $120
Case 2:
The current price of stock: $120. Strike price: $110
Considering that we have gone through the detailed scenario of each option, how about we combine a few options together. Let’s understand an important concept which many professionals use in options trading.
What is PutCall Parity In Python?
Putcall parity is a concept that anyone who is interested in options trading needs to understand. By gaining an understanding of putcall parity you can understand how the value of call option, put option and the stock are related to each other. This enables you to create other synthetic position using various option and stock combination.
The principle of putcall parity
Putcall parity principle defines the relationship between the price of a European Put option and European Call option, both having the same underlying asset, strike price and expiration date. If there is a deviation from putcall parity, then it would result in an arbitrage opportunity. Traders would take advantage of this opportunity to make riskless profits till the time the putcall parity is established again.
The putcall parity principle can be used to validate an option pricing model. If the option prices as computed by the model violate the putcall parity rule, such a model can be considered to be incorrect.
Understanding PutCall Parity
To understand putcall parity, consider a portfolio “A” comprising of a call option and cash. The amount of cash held equals the call strike price. Consider another portfolio “B” comprising of a put option and the underlying asset.
S0 is the initial price of the underlying asset and ST is its price at expiration.
Let “r” be the riskfree rate and “T” be the time for expiration.
In time “T” the Zerocoupon bond will be worth K (strike price) given the riskfree rate of “r”.
Portfolio A = Call option + Zerocoupon bond
Portfolio B = Put option + Underlying Asset
If the share price is higher than X the call option will be exercised. Else, cash will be retained. Hence, at “T” portfolio A’s worth will be given by max(ST, X).
If the share price is lower than X, the put option will be exercised. Else, the underlying asset will be retained. Hence, at “T”, portfolio B’s worth will be given by max (ST, X).
If the two portfolios are equal at time, “T”, then they should be equal at any time. This gives us the putcall parity equation.
Equation for putcall parity:
C + XerT = P + S0
In this equation,
 C is the premium on European Call Option
 P is the premium of European Put Option
 S0 is the spot price of the underlying stock
 And, XerT is the current value (discounted value) of Zerocoupon bond (X)
We can summarize the payoffs of both the portfolios under different conditions as shown in the table below.
From the above table, we can see that under both scenarios, the payoffs from both the portfolios are equal.
Required Conditions For Putcall Parity
For putcall parity to hold, the following conditions should be met. However, in the real world, they hardly hold true and putcall parity equation may need some modifications accordingly. For the purpose of this blog, we have assumed that these conditions are met.
 The underlying stock doesn’t pay any dividend during the life of the European options
 There are no transaction costs
 There are no taxes
 Shorting is allowed and there are no borrow charges
Hence, putcall parity will hold in a frictionless market with the underlying stock paying no dividends.
Arbitrage Opportunity
In options trading, when the putcall parity principle gets violated, traders will try to take advantage of the arbitrage opportunity. An arbitrage trader will go long on the undervalued portfolio and short the overvalued portfolio to make a riskfree profit.
How to take advantage of arbitrage opportunity
Let us now consider an example with some numbers to see how trade can take advantage of arbitrage opportunities. Let’s assume that the spot price of a stock is $31, the riskfree interest rate is 10% per annum, the premium on threemonth European call and put are $3 and $2.25 respectively and the exercise price is $30.
In this case, the value of portfolio A will be,
C+XerT = 3+30e0.1 * 3/12 = $32.26
The value of portfolio B will be,
P + S0 = 2.25 + 31 = $33.25
Portfolio B is overvalued and hence an arbitrageur can earn by going long on portfolio A and short on portfolio B. The following steps can be followed to earn arbitrage profits.
 Short the stock. This will generate a cash inflow of $31.
 Short the put option. This will generate a cash inflow of $2.25.
 Purchase the call option. This will generate cash outflow of $3.
 Total cash inflow is 3 + 2.25 + 31 = $30.25.
 Invest $30.25 in a zerocoupon bond with 3 months maturity with a yield of 10% per annum.
Return from the zero coupon bond after three months will be 30.25e 0.1 * 3/12 = $31.02.
If the stock price at maturity is above $30, the call option will be exercised and if the stock price is less than $30, the put option will be exercised. In both the scenarios, the arbitrageur will buy one stock at $30. This stock will be used to cover the short.
Total profit from the arbitrage = $31.02 – $30 = $1.02
Well, shouldn’t we look at some codes now?
Python Codes Used For Plotting The Charts
The below code can be used to plot the payoffs of the portfolios.
So far, we have gone through the basic concepts in options trading and looked at an options trading strategy as well. At this juncture, let’s look at the world of options trading and try to answer a simple question.
Why is Options Trading attractive?
Options are attractive instruments to trade in because of the higher returns. An option gives the right to the holder to do something, with the ‘option’ of not to exercise that right. This way, the holder can restrict his losses and multiply his returns.
While it is true that one options contract is for 100 shares, it is thus less risky to pay the premium and not risk the total amount which would have to be used if we had bought the shares instead. Thus your risk exposure is significantly reduced.However, in reality, options trading is very complex and that is because options pricing models are quite mathematical and complex.
So, how can you evaluate if the option is really worth buying? Let’s find out.
The key requirement in successful options trading strategies involves understanding and implementing options pricing models. In this section, we will get a brief understanding of Greeks in options which will help in creating and understanding the pricing models.
Options Pricing
Options Pricing is based on two types of values
Intrinsic Value of an option
Recall the moneyness concept that we had gone through a few sections ago. When the call option stock price is above the strike price or when put option stock price is below the strike price, the option is said to be “InTheMoney (ITM)”, i.e. it has an intrinsic value. On the other hand, “Out of the money (OTM)” options have no intrinsic value. For OTM call options, the stock price is below the strike price and for OTM put options; stock price is above the strike price. The price of these options consists entirely of time value.
Time Value of an option
If you subtract the amount of intrinsic value from an options price, you’re left with the time value. It is based on the time to expiration. You can enroll for this free online options trading python course on Quantra and understand basic terminologies and concepts that will help you in options trading. We know what is intrinsic and the time value of an option. We even looked at the moneyness of an option. But how do we know that one option is better than the other, and how to measure the changes in option pricing. Well, let’s take the help of the greeks then.
Options Greeks
Greeks are the risk measures associated with various positions in options trading. The common ones are delta, gamma, theta and vega. With the change in prices or volatility of the underlying stock, you need to know how your options pricing would be affected. Greeks in options help us understand how the various factors such as prices, time to expiry, volatility affect the options pricing.
Delta measures the sensitivity of an option’s price to a change in the price of the underlying stock. Simply put, delta is that options greek which tells you how much money a stock option will rise or drop in value with a $1 rise or drop in the underlying stock. Delta is dependent on underlying price, time to expiry and volatility. While the formula for calculating delta is on the basis of the BlackScholes option pricing model, we can write it simply as,
Delta = [Expected change in Premium] / [Change in the price of the underlying stock]
Let’s understand this with an example for a call option:
We will create a table of historical prices to use as sample data. Let’s assume that the option will expire on 5th March and the strike price agreed upon is $140.
Thus, if we had to calculate the delta for the option on 2nd March, it would be $5/$10 = 0.5.
Here, we should add that since an option derives its value from the underlying stock, the delta option value will be between 0 and 1. Usually, the delta options creeps towards 1 as the option moves towards “inthemoney”.
While the delta for a call option increases as the price increases, it is the inverse for a put option. Think about it, as the stock price approaches the strike price, the value of the option would decrease. Thus, the delta put option is always ranging between 0 and 1.
Gamma measures the exposure of the options delta to the movement of the underlying stock price. Just like delta is the rate of change of options price with respect to underlying stock’s price; gamma is the rate of change of delta with respect to underlying stock’s price. Hence, gamma is called the secondorder derivative.
Gamma = [Change in an options delta] / [Unit change in price of underlying asset]
Let’s see an example of how delta changes with respect to Gamma. Consider a call option of stock at a strike price of $300 for a premium of $15.
 Strike price: $300
 Initial Stock price: $150
 Delta: 0.2
 Gamma: 0.005
 Premium: $15
 New stock price: $180
 Change in stock price: $180 – $150 = $30
Thus, Change in Premium = Delta * Change in price of stock = 0.2 * 30 = 6.
Thus, new premium = $15 + $6 = $21
Change in delta = Gamma * Change in stock price = 0.005 * 30 = 0.15
Thus, new delta = 0.2 + 0.15 = 0.35.
Let us take things a step further and assume the stock price increases another 30 points, to $210.
Now,
New stock price: $210
Change in stock price: $210 – $180 = $30
Change in premium = Delta *Change in 0.35*30 = $10.5
Thus, new premium = $21 + $10.5 = $31.5
Change in delta = Gamma * Change in stock price = 0.005 * 30 = 0.15
Thus, new delta = 0.35 + 0.15 = 0.5.
In this way, delta and gamma of an option changes with the change in the stock price. We should note that Gamma is the highest for a stock call option when the delta of an option is at the money. Since a slight change in the underlying stock leads to a dramatic increase in the delta. Similarly, the gamma is low for options which are either out of the money or in the money as the delta of stock changes marginally with changes in the stock option.
Highest Gamma for Atthemoney (ATM) option
Among the three instruments, atthemoney (ATM), outofthemoney (OTM) and inthemoney (ITM); at the money (ATM) has the highest gamma. You can watch this video to understand it in more detail.
Theta measures the exposure of the options price to the passage of time. It measures the rate at which options price, especially in terms of the time value, changes or decreases as the time to expiry is approached.
Vega measures the exposure of the option price to changes in the volatility of the underlying. Generally, options are more expensive for higher volatility. So, if the volatility goes up, the price of the option might go up to and viceversa.
Vega increases or decreases with respect to the time to expiry?
What do you think? You can confirm your answer by watching this video.
One of the popular options pricing model is Black Scholes, which helps us to understand the options greeks of an option.
BlackScholes options pricing model
The formula for the BlackScholes options pricing model is given as:
C is the price of the call option
P represents the price of a put option.
S0 is the underlying price,
X is the strike price,
σ represents volatility,
r is the continuously compounded riskfree interest rate,
t is the time to expiration, and
q is the continuously compounded dividend yield.
N(x) is the standard normal cumulative distribution function.
The formulas for d1 and d2 are given as:
To calculate the Greeks in options we use the BlackScholes options pricing model.
Delta and Gamma are calculated as:
In the example below, we have used the determinants of the BS model to compute the Greeks in options.
At an underlying price of 1615.45, the price of a call option is 21.6332.
If we were to increase the price of the underlying by Rs. 1, the change in the price of the call, put and values of the Greeks in the option is as given below.
As can be observed, the Delta of the call option in the first table was 0.5579. Hence, given the definition of the delta, we can expect the price of the call option to increase approximately by this value when the price of the underlying increases by Rs.1. The new price of the call option is 22.1954 which is
22.1954
22.1911
Let’s move to Gamma, another Greek in option.
If you observe the value of Gamma in both the tables, it is the same for both call and put options contracts since it has the same formula for both options types. If you are going long on the options, then you would prefer having a higher gamma and if you are short, then you would be looking for a low gamma. Thus, if an options trader is having a netlong options position then he will aim to maximize the gamma, whereas in case of a netshort position he will try to minimize the gamma value.
The third Greek, Theta has different formulas for both call and put options. These are given below:
In the first table on the LHS, there are 30 days remaining for the options contract to expire. We have a negative theta value of 0.4975 for a long call option position which means that the options trader is running against time.
He has to be sure about his analysis in order to profit from trade as time decay will affect this position. This impact of time decay is evident in the table on the RHS where the time left to expiry is now 21 days with other factors remaining the same. As a result, the value of the call option has fallen from 21.6332 to 16.9 behaviour 319. If an options trader wants to profit from the time decay property, he can sell options instead of going long which will result in a positive theta.
We have just discussed how some of the individual Greeks in options impact option pricing. However, it is very essential to understand the combined behaviour of Greeks in an options position to truly profit from your options position. If you want to work on options greeks in Excel, you can refer to this blog.
Let us now look at a Python package which is used to implement the Black Scholes Model.
Python Library – Mibian
What is Mibian?
Mibian is an options pricing Python library implementing the BlackScholes along with a couple other models for European options on currencies and stocks. In the context of this article, we are going to look at the BlackScholes part of this library. Mibian is compatible with python 2.7 and 3.x. This library requires scipy to work properly.
How to use Mibian for BS Model?
The function which builds the BlackScholes model in this library is the BS() function. The syntax for this function is as follows:
The first input is a list containing the underlying price, strike price, interest rate and days to expiration. This list has to be specified each time the function is being called. Next, we input the volatility, if we are interested in computing the price of options and the option greeks. The BS function will only contain two arguments.
If we are interested in computing the implied volatility, we will not input the volatility but instead will input either the call price or the put price. In case we are interested in computing the putcall parity, we will enter both the put price and call price after the list. The value returned would be:
(call price + price of the bond worth the strike price at maturity) – (put price + underlying asset price)
The syntax for returning the various desired outputs are mentioned below along with the usage of the BS function. The syntax for BS function with the input as volatility along with the list storing underlying price, strike price, interest rate and days to expiration:
Attributes of the returned value from the abovementioned BS function:
The syntax for BS function with the input as callPrice along with the list storing underlying price, strike price, interest rate and days to expiration:
Attributes of the returned value from the abovementioned BS function:
The syntax for BS function with the input as putPrice along with the list storing underlying price, strike price, interest rate and days to expiration:
Attributes of the returned value from the abovementioned BS function:
The syntax for BS function with the inputs as callPrice and putPrice along with the list storing underlying price, strike price, interest rate and days to expiration:
Attributes of the returned value from the abovementioned BS function:
While BlackScholes is a relatively robust model, one of its shortcomings is its inability to predict the volatility smile. We will learn more about this as we move to the next pricing model.
Derman Kani Model
The Derman Kani model was developed to overcome the longstanding issue with the Black Scholes model, which is the volatility smile. One of the underlying assumptions of Black Scholes model is that the underlying follows a random walk with constant volatility. However, on calculating the implied volatility for different strikes, it is seen that the volatility curve is not a constant straight line as we would expect, but instead has the shape of a smile. This curve of implied volatility against the strike price is known as the volatility smile.
If the Black Scholes model is correct, it would mean that the underlying follows a lognormal distribution and the implied volatility curve would have been flat, but a volatility smile indicates that traders are implicitly attributing a unique nonlognormal distribution to the underlying. This nonlognormal distribution can be attributed to the underlying following a modified random walk, in the sense that the volatility is not constant and changes with both stock price and time. In order to correctly value the options, we would need to know the exact form of the modified random walk.
The Derman Kani model shows how to take the implied volatilities as inputs to deduce the form of the underlying’s random walk. More specifically a unique binomial tree is extracted from the smile corresponding to the random walk of the underlying, this tree is called the implied tree. This tree can be used to value other derivatives whose prices are not readily available from the market – for example, it can be used in standard but illiquid European options, American options, and exotic options.
What is the Heston Model?
Steven Heston provided a closedform solution for the price of a European call option on an asset with stochastic volatility. This model was also developed to take into consideration the volatility smile, which could not be explained using the Black Scholes model.
The basic assumption of the Heston model is that volatility is a random variable. Therefore there are two random variables, one for the underlying and one for the volatility. Generally, when the variance of the underlying has been made stochastic, closedform solutions will no longer exist.
But this is a major advantage of the Heston model, that closedform solutions do exist for European plain vanilla options. This feature also makes calibration of the model feasible. If you are interested in learning about these models in more detail, you may go through the following research papers,
 Derman Kani Model – “The Volatility Smile and Its Implied Tree” by Emanuel Derman and Iraj Kani.
 Heston Model – “A ClosedForm Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options”
So far, you have understood options trading and how to analyse an option as well as the pricing models used. Now, to apply this knowledge, you will need access to the markets, and this is where the role of a broker comes in.
Opening an options trading account
How to choose a broker for Options Trading?
Before we open an options trading account with a broker, let’s go over a few points to take into consideration when we choose a broker.
 Understand your aim when you tread the options trading waters, whether it is a way of hedging risk, as a speculative instrument, for income generation etc.
 Does the broker provide option evaluation tools of their own? It is always beneficial to have access to a plethora of tools when you are selecting the right option.
 Enquire the transaction costs or the commission charged by the broker as this will eat into your investment gains.
 Some brokers give access to research materials in various areas of the stock market. You can always check with the broker about access to research as well as subscriptions etc.
 Check the payment options provided by the broker to make sure it is compatible with your convenience.
Searching for the right broker
Once the required background research is done, you can choose the right broker as per your need and convenience. In the global market, a list of the top brokers is provided below:
List of Top International Brokers (Options Trading)
The list of top international options brokers is given below:
 Etrade ($0.65 per options contract)
 Ally Invest ($0.5 per contract traded)
 TD Ameritrade ($0.65 fee per contract)
 Interactive Brokers (starts at $0.25 per options contract)
 Schwab Brokerage ($0.65 per options contract)
List of Top Indian Brokers (Options Trading)
The list of top Indian options brokers is given below:
 Zerodha
 ICICI Direct
 HDFC Securites
 ShareKhan
 Kotak Securities
 Angel Broking
 Axis Direct
Great! Now we look at some options trading strategies which can be used in the real world.
Options Trading Strategies
There are quite a few options trading strategies which can be used in today’s trading landscape. One of the most popular options trading strategies is based on Spreads and Butterflies. Let’s look at them in detail.
Spreads and Butterflies
Spreads or rather spread trading is simultaneously buying and selling the same option class but with different expiration date and strike price. Spread options trading is used to limit the risk but on the other hand, it also limits the reward for the person who indulges in spread trading.
Thus, if we are only interested in buying and selling call options of security, we will call it a call spread, and if it is only puts, then it will be called a put spread.
Depending on the changing factor, spreads can be categorised as:
 Horizontal Spread – Different expiration date, Same Strike price
 Vertical Spread – Same Expiration date, Different Strike price
 Diagonal Spread – Different expiration date, Different Strike price
Remember that an option’s value is based on the underlying security (in this case, stock price). Thus, we can also distinguish an option spread on whether we want the price to go up (Bull spread) or go down (Bear spread).
Bull call spread
In a bull call spread, we buy more than one option to offset the potential loss if the trade does not go our way.
Let’s try to understand this with the help of an example.
The following is a table of the available options for the same underlying stock and same expiry date:
Normally, if we have done the analysis and think that the stock can rise to $200, one way would be to buy a call stock option with a strike price of $180 for a premium of $15. Thus, if we are right and the stock reaches $200 on expiry, we buy it at the strike price of $180 and pocket a profit of ($20 $15) = $5 since we paid the premium of $15.
But if we were not right and the stock price reaches $180 or less, we will not exercise the option resulting in a loss of the premium of $15. One workaround is to buy a call option at $180 and sell a call option for $200 at $10.
Thus, when the stock’s price reaches $200 on expiry, we exercise the call option for a profit of $5 (as seen above) and also pocket a profit of the premium of $10 since it will not be exercised by the owner. Thus, in this way, the total profit is ($5 + $10) = $15.
If the stock price goes above $200 and the put option is exercised by the owner, the increase in the profit from bought call option at $180 will be the same as the loss accumulated from the sold call option at $200 and thus, the profit would always be $15 no matter the increase in the stock price above $200 at expiry date.
Let’s construct a table to understand the various scenarios.
You can go through this informative blog to understand how to implement it in Python.
Bear put spread
The bull call spread was executed when we thought the stock would be increasing, but what if we analyse and find the stock price would decrease. In that case, we use the bear put spread.
Let’s assume that we are looking at the different strike prices of the same stock with the same expiry date.
One way to go about it is to buy the put option for the strike price of 160 at a premium of $15 while selling a put option for the strike price of $140 for the strike price of $10.
Thus, we create a scenario table as follows:
In this way, we can minimize our losses by simultaneously buying and selling options. You can go through this informative blog to understand how to implement it in Python.
Butterfly Spread
A butterfly spread is actually a combination of bull and bear spreads. One example of the Butterfly Options Strategy consists of a Body (the middle double option position) and Wings (2 opposite end positions).
 Its properties are listed as follows:
 It is a threeleg strategy
 Involves buying or selling of Call/Put options (unlike Covered Call Strategy where a stock is bought and an OTM call option is sold)
 Can be constructed using Calls or Puts
 4 options contracts at the same expiry date
 Have the same underlying asset
 3 different Strike Prices are involved (2 have the same strike price)
 Create 2 Trades with these calls
Other Trading Strategies
We will list down a few more options trading strategies below:
Summary
We have covered all the basics of options trading which include the different Option terminologies as well as types. We also went through an options trading example and the option greeks. We understood various options trading strategies and things to consider before opening an options trading account.
If you have always been interested in automated trading and don’t know where to start, we have created a learning track for you at Quantra, which includes the. “Trading using Option Sentiment Indicators” course.
Disclaimer: All data and information provided in this article are for informational purposes only. QuantInsti ® makes no representations as to accuracy, completeness, currentness, suitability, or validity of any information in this article and will not be liable for any errors, omissions, or delays in this information or any losses, injuries, or damages arising from its display or use. All information is provided on an asis basis.

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