# Options Pricing

Summary

Options prices are made up of intrinsic and extrinsic value.

Intrinsic value is the amount the stock price is above the strike price.

Extrinsic value is also known as time value and the most important component is implied volatility.

Implied volatility is derived from the options price and tells the trader the demand for the option as well as the market's forecast for the real volatility of the stock.

Changes in implied volatility can have a dramatic affect on an option's price.

Time decay is against option buyers and works for option sellers.

Option buyers want to buy low and sell high, ideally supported by increasing implied volatility.

So you bought a call option prior to earnings, with the expectation that the stock price would go up. And go up it did! But your call option didn't gain in value. Now, as you hold onto it and ponder what could have happened, you start losing money. What is going on? What you are seeing is the result of the various factors - other than the price of the underlying - that help determine an options price. Foremost are implied volatility and time decay.

## Factors in Options Pricing

There are several factors that determine the price of an options contract. Most traders are trying to take advantage of directional moves in the underlying stock, and that is the primary driver of the price of an options contract, especially its intrinsic value. But the extrinsic value of an option, also known as its time value, is affected by time left before expiry, as well as the option's implied volatility. And there are several other factors. Traders must understand all of the things that can influence the price of an option in order to understand their risks as well as have the highest probability of profit.

The following, known as option "greeks," are used to measure the sensitivity of options price:

Options are influenced by the underlying price (delta)

• Delta gives the change in the options price given a \$1 change in the underlying. An option with a delta of .5 will change \$.50 for a \$1 change in the underlying.
• Example: You buy an XYZ \$40 call for \$1.00 with a delta of .5 and XYZ at \$40. If the stock price goes up to \$41, the call should be worth roughly \$1.50.

Options are influenced by time decay (theta)

• As options are expiring assets, the entire extrinsic value is exposed to time decay, which will, all else held equal, eat away at the value of an option every day.
• The amount of time decay will increase as the option approaches expiration.
• An option has no time value at expiration and is only worth its intrinsic value.
• Theta is negative for long options, as they lose value due to time decay.

Options are influenced by implied volatility (vega)

• Vega gives us an approximation of the amount that the options price will change given a 1% move in implied volatility.
• Implied volatility is the most misunderstood and the most important component of time value. For example, most options traders have had the experience of buying an option, being right on the direction of the underlying stock, and still losing money.

Options are also influenced by interest rates (rho) and the sensitivity to the change in the delta (gamma). Gamma, which is derived from delta, tells the amount that the delta will change given a \$1 change in the underlying stock.

## Option Price and Value

For the right to either buy (call) or sell (put) the underlying security on or before the expiration date, the buyer of an option will pay a premium, the options price. This is known as the debit, and is the maximum risk. As the seller of the option you will receive a premium as net credit, but you will be obligated to buy (when short a put) or sell (when short a call) the underlying shares if the options contract is exercised. Cash will be held as a margin on a short position.

In the money (ITM), At the money (ATM), Out of the Money (OTM)

The strike price, or exercise price, of an option determines whether that contract is "in the money," "at the money", or "out of the money." If the strike price of a call option is less than the current market price of the underlying security, the call is said to be in the money, because the holder of this call has the right to buy the stock at a price which is less than the price he would have to pay to buy the stock in the marketplace. Likewise, if a put option has a strike price that is greater than the current market price of the underlying security, it is also said to be in the money because the holder of this put has the right to sell the stock at a price which is greater than the price he would receive selling the stock in the market. The converse of in the money is, not surprisingly, out of the money. If the strike price equals the current market price, the option is said to be at the money.

 Call Put In the money (ITM) Strike price < Stock price Strike price > Stock price At the money (ATM) Strike price = Stock price Strike price = Stock price Out of the money (OTM) Strike price > Stock price Strike price < Stock price

The premium for an option has two components: the intrinsic value and time value.

The intrinsic value is the amount the stock price is above the strike price (for calls) or below the strike price for puts. It is also the value if at expiration. Therefore by definition the amount by which an option is in the money is defined as intrinsic value.

Time value is the option premium minus the intrinsic value. It is the amount that you pay for the possibility that it will be worth more in the future. Therefore an at-the-money or out-of-the-money option has no intrinsic value and only time value.

CallsPuts
Intrinsic Value = Stock Price - Strike PriceIntrinsic Value = Strike Price - Stock Price
Time Value = Option Price - Intrinsic ValueTime Value = Option Price - Intrinsic Value

Intrinsic value is only affected by moves in the underlying contract. Time value is subject to several factors, primarily time to expiration and implied volatility. Implied volatility is the market's expectations of the future volatility of the underlying stock. It is derived from the option's price, and represents the demand for the option. The higher the implied volatility, the more expectation there is that the underlying stock will make big moves. This also means that option premiums (time values) are higher, and therefore time decay is higher. That time decay increases dramatically in the last 30 days as expiration approaches.

Example:

If Google (GOOG) were trading at \$500 when you bought a 490 call for \$25, then \$10 of the option would be intrinsic value. The other \$15 would be time value. A 500 call purchased when GOOG was trading for 500 is all time value. It has no intrinsic value.

If the stock were at 500 when you bought a 500 call it would be the at-the-money (ATM) option. Buying the same 500 call with the stock at 510 makes it in the money (ITM), because the strike price is below the stock price. If the strike price is above the stock price, say at 510, then the call is out of the money (OTM). Only in-the-money options have any intrinsic value. Out-of-the-money options are all time value.

 Strike Price Stock Price = \$500 490 call = \$25 500 call = \$18 510 call = \$10 In-the-money At-the-money Out-of-the-money \$10 Intrinsic \$0 Intrinsic \$0 Intrinsic \$15 time value \$18 time value \$10 time value

## Isolating Implied Volatility and Time

We can isolate implied volatility to look at the affect that changes just in this one factor have on the price of an option.

With Cisco (CSCO) trading at \$23, the impact of implied volatility on premium can be demonstrated with the two examples:

 Implied volatility = 30% 30 days to expiration CSCO Call = \$1.12 Implied volatility = 50% 30 days to expiration CSCO Call = \$1.63

As you can see, the rise in implied volatility from 30% to 50% is a 46% gain in the options price. A decline from 50% to 30% implied volatility is a 31% loss.

We can also look at isolating time. Let's consider a QQQQ 45 call option with QQQQ at \$45 and implied volatility held constant at 25 percent:

• 90 days until expiration, call = \$2.48
• 60 days until expiration, call = \$1.98
• 30 days until expiration, call = \$1.37
• 15 days until expiration, call = \$0.95
•  5 days until expiration, call = \$0.54
• At expiration, call = \$0

## Option Price Changes

What you want (Rewards)

• Call buyers want the price to rise and implied volatility to rise in as short a time as possible - to limit time decay.
• Put buyers want the price to fall and implied volatility to rise in as short a time as possible.
• Call sellers want the price to fall or stay flat, implied volatility to fall, and time to pass (since time decay is on their side).
• Put sellers want the price to rise or stay flat, implied volatility to fall, and time to pass.

What can happen (Risks)

• You buy a call and the underlying goes up, but implied volatility goes down and/or time decay eats away at your premium and so you lose.
• You buy a put and the underlying falls, but implied volatility goes down and/or time decay eats away at your premium and so you lose.
• You sell a call or put and the underlying stays flat, but implied volatility goes up, producing losses. Time decay will reduce these losses.

## Examples

Example 1:

 Now: CSCO @ \$28.5 60 days out, IV 30% 27.5 put trading at \$.84 27.5/25 spread at \$.64 In 16 days: CSCO @ 24 IV to 45% Put now trading at \$3.84 Spread is trading at \$1.84

Here the underlying price has fallen and implied volatility has risen, making time decay a negligible factor and producing significant returns.

Example 2:

 Now: CSCO @ \$23 60 days out, IV 50% 22.5 call trading at \$2.20 22.5/25 spread at \$1.04 In 7 days: CSCO @ 24 IV to 30% Call now trading at \$2.15 Spread is trading at \$1.33

Here the underlying has risen, but the implied volatility has fallen and that combined with the time decay has produced a small loss for the outright call. The spread has a gain, however, and this is one reason the option spreads can be beneficial, especially when implied volatility is high.

Options involve risk and are not suitable for all investors. For more information, please read the Characteristics and Risks of Standardized Options. Copies may be obtained from The Options Clearing Corporation, One North Wacker Drive, Suite 500, Chicago, IL 60606 or call 1-888-OPTIONS or visit www.888options.com.

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