# Chapter 4-1 Factors in Option Pricing

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 did not 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 effect of the various factors, other than the price of the underlying asset, that help determine an options price. Of these other factors, foremost are implied volatility and time decay.

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; this 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. However, there are several other factors. Traders must understand all of the factors 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 will roughly be worth $1.50.

Options are influenced by time decay (**Theta**)

- Options are expiring assets. The entire extrinsic value is exposed to time decay which will, all else equal, eat away at the value of an option every day.
- The rate 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 option positions 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 important, and often most misunderstood component of time value. This is why 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 sensitivity to changes 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.

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**Option Price and Value**

**Premium**

The buyer of an option pays a premium for the right to either buy (call) or sell (put) the underlying asset on or before the expiration date; this is the option’s price. The premium is known as a debit, and represents the maximum risk. As the seller of the option you receive a premium as net credit. Option sellers are obligated to buy (when short a put) or sell (when short a call) the underlying shares if the options contract is exercised. Cash is held as a margin on a short position.

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**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 asset, 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 pay in the open market. Likewise, if a put option has a strike price that is greater than the current market price of the underlying asset 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 in the open 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.

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**For Calls and Puts:**

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**In the money (ITM) **Strike price < Stock price Strike price > Stock price

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**At the money (ATM) **Strike price + Stock price Strike price + Stock price

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**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 of the option 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, only time value.

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**For Calls and Puts:**

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**Intrinsic Value** = Stock Price – Strike Price Intrinsic Value = Strike Price – Stock Price

**Time Value** = Option Price – Intrinsic Value Time Value = Option Price – Intrinsic Value

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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 future volatility in 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.

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Consider the following example:

Google (GOOG) is trading at $500 and you bought a 490 call for $25. $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 intrinsic value. Out-of-the-money options are all time value.

Stock Price: $500

Strike Price: 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

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**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:

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.

- Implied volatility = 30%
- 30 days to expiration
- CSCO Call =
**$1.12**

- Implied volatility = 50%
- 30 days to expiration
- CSCO Call =
**$1.63**

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

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**Option Price Changes**

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What options traders want (Rewards?)

- Call buyers want the price 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. Implied volatility goes down and/or time decay eats away at your premium and you lose.
- You buy a put and the underlying falls. Implied volatility goes down and/or time decay eats away at your premium and 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.

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**Examples**

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Example 1:

Now: In 16 days:

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

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

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Example 2

Now: In 7 days:

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.

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

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**Summary**

Therefore, to review the focal points of this lesson:

- 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 is 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 works against option buyers and thus works for option sellers.
- Option buyers want to buy low and sell high, ideally supported by increasing implied volatility.