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# Introduction to Options: Understanding Implied Volatility

Understanding how the options market works and how to trade within this market can add value to any financial firm. Whether you are a long-term investor or a day trader, options can bring a new degree of diversification to a portfolio, as well as give insight into market psychology. This article is an introduction to a series discussing what can be learned from the options market and associated volatility products.

The options market differs in practice than what the theory states. Before we examine the practice of options trading, we must first understand the underlying theory.

An option gives a buyer the right, but not the obligation, to buy or sell a specific amount of stock at a specific price at any point in time before the contract expires. The seller of the contract has the obligation to provide shares to the buyer should the contract be â€˜exercisedâ€™ before the expiration date. The buyer pays a premium to the seller for this right. An option that has the right to buy stock is a call and an option that has the right to sell stock is a put.

The terminology of an options contract must be understood before advancing any further. A single options contract is for the purchase (calls) or sale (puts) of 100 units of stock. The underlying price is the price at which the stock associated with the option is currently trading for. The strike price, or exercise price, is the price at which the underlying stock will be bought or sold at if the option is exercised.

An option is exercised if the buyer â€˜exercisesâ€™ the right to buy or sell stock at the specified price. An option must be â€˜in-the-moneyâ€™ to be exercised. A call option is said to be in-the-money (ITM) if the strike price is less than the underlying price. A call option is out-the-money (OTM) if the strike price is greater than the underlying price. The reverse holds true of put options.

Options have two kinds of value, intrinsic value and time value. All options have time value prior to expiration, but as expiration nears, time value will decay. Only ITM options have intrinsic value. This is because you can potentially exercise ITM options for a profit, but not OTM. Given this, only ITM options have value at expiration. OTM options expire worthless. Below you will find a labeled options chain. Use this to gain a better understanding for the terminology.

This is an option chain for the SPY. In the top left corner, you will find the underlying price. Right below that are the expiration dates inside the amber box. Dec14 expiration is selected. The blue circles represent OTM calls on the left and OTM puts on the right.

To illustrate the use of options, lets say that IBM is trading at $160.00 (underlying price) on November 15th, 2014. Quinn wants to purchase 100 shares, but is unsure about the short-term outlook for the market. He decides to buy one call option with a strike price of 165 that expires on January 14th, 2015. For this right, Quinn pays a premium of $2.00 (100 shares * $2.00 = total cost of $200.00). Since the call strike price is less than the underlying, this option is OTM. On December 20th, 2014, IBM is trading for $170.00. This means that Quinnâ€™s call option is now ITM and can be exercised. Quinn decides to exercise his right and buy 100 shares at IBM at $165.00, immediately making $5 a share.

Now, you might be asking why Quinn did not simply purchase shares when they were trading at $160.00. By purchasing the call, his loss on the trade is limited to the premium paid of $200. If he bought 100 shares at $160.00, his potential loss is $16,000. This is where the benefit of trading options becomes apparent. Options give the buyer the ability to limit losses and increase the profitability of a trade.

Lets not forget about the seller of the option. In an alternative reality, lets say that on January 14th, 2015, IBM is trading for $155.00. This means that Quinnâ€™s option is OTM and has expired worthless. Since OTM options are not exercised, the seller will be credited the premium of $2.00 that the buyer paid. Selling an option comes with significant risk. Since the underlying price can theoretically rise to infinity, the seller may have to deliver stock at a much higher price.

Lets move away from how options are theoretically used to how they are actually used. In practice, about 82% of all options are not exercised. To show why, lets continue with the story of IBM and Quinn. It is December 20th, 2014 and IBM is trading at $170.00. Instead of exercising the option and buying shares of IBM at $165.00, Quinn closes out his options contract by selling it. Call options will increase in value as the price of the underlying stock increases. Quinnâ€™s 165 January 14 call option was purchased for $2.00 when the underlying price was $160, but now that the price of IBM has risen to $170.00, that call option is now worth $5.50. Since Quinn has now decided to exit his position without exercising, he will make $350.00 ([5.50 â€“ 2.00] *100) as opposed to only $300 with exercising ([170-165] â€“ 200).

Trading in the options market this way is generally more profitable that exercising the contract. One very important factor to keep in mind is time value. As mentioned earlier, all options have time value. Time value will decreases the closer expiration gets. Sometimes, the decrease in an options time value will make exercising the option more attractive than closing out of the position.

The above scenario is just one of many ways options can be used. By combining options of different strikes, expirations, and types (calls and puts), one can create different payoff structures to be profitable in any market condition. One quick example is simultaneously purchasing an equal amount of calls and puts at the same expiration and at the same strike price. This position will profit if the underlying stock makes a large moves in either direction.

Now that we know the basics of the options market, we can begin to examine how the price of an option is determined. Options are financial derivatives, meaning that their price is dependent upon other variables. Options are dependent upon the underlying price, time to expiration, volatility, and interest rates. In mathematics, a derivative is defined as the rate at which a variable is changing at an instantaneous point in time. Although this is not the direct interpretation of an options price, this definition will come into play when discussing how an option is priced.

The Black-Scholes model is widely accepted and used by the financial community to price an option. There are 5 factors produced by the model and one independent variable that ultimately will determine the price. Referring back to the mathematical definition of a derivative, you will find that the 5 factors used in pricing an option is where the term â€˜financial derivativeâ€™ comes from. These 5 factors are called the 'greeks', and you will soon see why.

The first factor is delta, or how much an options price will change given a $1 change in the underlying price. For example, assume that the underlying price of IBM is $160, a call option with a strike price of 162 is $0.65 and delta is .05. Holding all else constant, if the price of IBM increase to $161, the call option would increase by $0.05 (delta) to $0.70.

The next factor is gamma, or how much delta will change given a $1 change in the underlying. Delta and gamma are how an options price is reflective of the underlying stock price.

As an option nears expiration, it will lose value as time passes. This is measured by theta, or time decay. Specifically, it says how much value the option will lose over the course of one day.

The next measure is vega, or the options sensitivity to volatility. Vega, by definition, is how much the option price will change given a 1% move in volatility. The more volatile the underlying stock is, the more valuable the option. This intuitively makes sense because there is a greater chance of an OTM option being pulled ITM due to potential swings in the underlying stock.

The last factor produced by the model is rho. Although not extremely important in determining the price, rho is how much the option price will change given a 1% per annum risk-free rate rise. Refer to the index to see a graphical representation of the option greeks.

Greeks will affect the price of an option in different ways, depending on the type of option and the position taken. A plus sign indicates that the greek is working in favor of the position, and a negative sign shows that it is working against the position.

The last factor to be discussed is the independent variable that will ultimately determine the price of an option. It is called implied volatility. Implied Volatility, or IVOL, is the expected future volatility of the underlying, as expressed though options. This measure is not determined by Black-Scholes, but by investors buying and selling in the options market. You might have begun to see how this measure can be used to gain incredible insights into the markets. As investors buy into options, implied volatility will rise.

On a top level, implied volatility is a measure of demand.

We have barely begun to scratch the surface of what options offer. When used properly, one can begin to discover great things about the behavior of investors and gain insight into the future direction of the market. To truly understand what the options market has to offer, we must dive deep into the subject.

This article should be used as a starting point and reference tool for your own research into the topic. The world of finance is an extremely competitive industry, and the knowledge that is soon to be shared is not widely dispersed. The following articles should be read multiple times and be accompanied by your own independent research.

Here at Blackpier, we want to start a conversation. We encourage you to reach out to us with questions so that we may both grow and bring this valuable information to light.

-TM

**INDEX**

**DELTA**

Delta, the change in the option price given a $1 move in the underlying price, changes as the option becomes further ITM or more OTM. Buying an option with a delta of 1 is the same thing as holding the underlying stock.

**THETA**

At first, time decay does not affect an option too much, but as the option approaches expiration, the value will start decaying quickly. Generally, an option will loose 60% of its value in the last 3 months of its remaining life.

**VEGA**

Vega, or the sensitivity to volatility, is greatest for ATM options that are further dated. This is because further dated options have a greater chance of becoming ITM if volatility is elevated.

**GAMMA**

Gamma measures how much delta will change given a $1 change in the underlying stock price. This graph shows that delta will change quickly on shorter dated options that are ATM. This means that the value of ATM, short dated options will increase rapidly for a given price change.