Excellent Trading School - 21 - Pricing of Options Contracts

Understanding Option Pricing

You might have had success beating the market by trading stocks using a disciplined process that anticipates a nice move either up or down. Many traders have also gained the confidence to make money in the stock market by identifying one or two good stocks that may make a big move soon. But if you don't know how to take advantage of that movement, you might be left in the dust. If this sounds like you, then maybe it's time to consider using options to play your next move. This article will explore some simple factors that you must consider if you plan to trade options to take advantage of stock movements.

Option Pricing

Before venturing into the world of trading options, investors should have a good understanding of the factors that determine the value of an option. These include the current stock price, the intrinsic value, time to expiration or the time value, volatility, interest rates and cash dividends paid.

There are several options pricing models that use these parameters to determine the fair market value of the option. Of these, the Black-Scholes model is the most widely used. In many ways, options are just like any other investment in that you need to understand what determines their price in order to use them to take advantage of moves the market.

Main Drivers of an Option's Price

Let's start with the primary drivers of the price of an option: current stock price, intrinsic value, time to expiration or time value, and volatility. The current stock price is fairly obvious. The movement of the price of the stock up or down has a direct - although not equal - effect on the price of the option. As the price of a stock rises, the more likely the price of a call option will rise and the price of a put option will fall. If the stock price goes down, then the reverse will most likely happen to the price of the calls and puts.

Intrinsic Value

Intrinsic value is the value that any given option would have if it were exercised today. Basically, the intrinsic value is the amount by which the strike price of an option is in the money. It is the portion of an option's price that is not lost due to the passage of time. The following equations can be used to calculate the intrinsic value of a call or put option:

Call Option Intrinsic Value = Underlying Stock's Current Price – Call Strike Price

Put Option Intrinsic Value = Put Strike Price – Underlying Stock's Current Price

The intrinsic value of an option reflects the effective financial advantage that would result from the immediate exercise of that option. Basically, it is an option's minimum value. Options trading at the money or out of the money have no intrinsic value.

Time Value
The time value of options is the amount by which the price of any option exceeds the intrinsic value. It is directly related to how much time an option has until it expires as well as the volatility of the stock. The formula for calculating the time value of an option is:

Time Value = Option Price – Intrinsic Value

The more time an option has until it expires, the greater the chance it will end up in the money. The time component of an option decays exponentially. The actual derivation of the time value of an option is a fairly complex equation. As a general rule, an option will lose one-third of its value during the first half of its life and two-thirds during the second half of its life. This is an important concept for securities investors because the closer you get to expiration, the more of a move in the underlying security is needed to impact the price of the option. Time value is often referred to as extrinsic value.

Time value is basically the risk premium that the option seller requires to provide the option buyer the right to buy/sell the stock up to the date the option expires. It is like an insurance premium of the option; the higher the risk, the higher the cost to buy the option.

An option's time value is also highly dependent on the volatility in that the market expects the stock will display up to expiration. For stocks where the market does not expect the stock to move much, the option's time value will be relatively low. The opposite is true for more volatile stocks or those with a high beta, due primarily to the uncertainty of the price of the stock before the option expires.

Basically, when the market believes a stock will be very volatile, the time value of the option rises. On the other hand, when the market believes a stock will be less volatile, the time value of the option falls. It is this expectation by the market of a stock's future volatility that is key to the price of options.

The effect of volatility is mostly subjective and it is difficult to quantify. Fortunately, there are several calculators that can be used to help estimate volatility. To make this even more interesting, there are also several types of volatility - with implied and historical being the most noted. When investors look at the volatility in the past, it is called either historical volatility or statistical volatility. Historical Volatility helps you determine the possible magnitude of future moves of the underlying stock. Statistically, two-thirds of all occurrences of a stock price will happen within plus or minus one standard deviation of the stocks' move over a set time period. Historical volatility looks back in time to show how volatile the market has been. This helps options investors to determine which exercise price is most appropriate to choose for the particular strategy they have in mind.

 
Implied volatility is what is implied by the current market prices and is used with the theoretical models. It helps to set the current price of an existing option and assists option players to assess the potential of an option trade. Implied volatility measures what option traders expect future volatility will be. As such, implied volatility is an indicator of the current sentiment of the market. This sentiment will be reflected in the price of the options helping options traders to assess the future volatility of the option and the stock based on current option prices.

Summary
A stock investor who is interested in using options to capture a potential move in a stock must understand how options are priced. Besides the underlying price of the stock, the key determinates of the price of an option are its intrinsic value - the amount by which the strike price of an option is in-the-money - and its time value. Time value is related to how much time an option has until it expires and the option's volatility. Volatility is of particular interest to a stock trader wishing to use options to gain an added advantage. Historical volatility provides the investor a relative perspective of how volatility impacts options prices, while current option pricing provides the implied volatility that the market currently expects in the future. Knowing the current and expected volatility that is in the price of an option is essential for any investor that wants to take advantage of the movement of a stock's price.

Options Pricing: Factors That Influence Option Price

Six factors that affect option prices are shown above. As indicated, the underlying price and strike price determine the intrinsic value; the time until expiration and volatility determine the probability of a profitable move; the interest rates determine the cost of money; and dividends can cause an adjustment to share price.

Underlying Price
The most influential factor on an option premium is the current market price of the underlying asset. In general, as the price of the underlying increases, call prices increase and put prices decrease. Conversely, as the price of the underlying decreases, call prices decrease and put prices increase.

If underlying prices ...	Call prices will ...	Put prices will ...
Increase	Increase	Decrease
Decrease	Decrease	Increase

Expected Volatility

Volatility is the degree to which price moves, regardless of direction. It is a measure of the speed and magnitude of the underlying's price changes. Historical volatility refers to the actual price changes that have been observed over a specified time period. Option traders can evaluate historical volatility to determine possible volatility in the future. Implied volatility, on the other hand, is a forecast of future volatility and acts as an indicator of the current market sentiment. While implied volatility is often difficult to quantify, option premiums will generally be higher if the underlying exhibits higher volatility, because it will have higher expected price fluctuations.

The greater the expected volatility, the higher the option value

Strike Price
The strike price determines if the option has any intrinsic value. Remember, intrinsic value is the difference between the strike price of the option and the current price of the underlying. The premium typically increases as the option becomes further in-the-money (where the strike price becomes more favorable in relation to the current underlying price). The premium generally decreases as the option becomes more out-of-the-money (when the strike price is less favorable in relation to the underlying).

Premiums increase as options become further in-the-money

Time Until Expiration
The longer an option has until expiration, the greater the chance that it will end up in-the-money, or profitable. As expiration approaches, the option's time value decreases. In general, an option loses one-third of its time value during the first half of its life and two-thirds of its value during the second half. The underlying's volatility is a factor in time value; if the underlying is highly volatile, one could reasonably expect a greater degree of price movement before expiration. The opposite holds true where the underlying typically exhibits low volatility; the time value will be lower if the underlying price is not expected to move much.

The longer the time until expiration, the higher the option price

The shorter the time until expiration, the lower the option price

Interest Rate and Dividends
Interest rates and dividends also have small, but measurable, effects on option prices. In general, as interest rates rise, call premiums will increase and put premiums will decrease. This is because of the costs associated with owning the underlying; the purchase will incur either interest expense (if the money is borrowed) or lost interest income (if existing funds are used to purchase the shares). In either case, the buyer will have interest costs.

If interest rates ...	Call prices will ...	Put prices will ...
Rise	Increase	Decrease
Fall	Decrease	Increase

Dividends can affect option prices because the underlying stock's price typically drops by the amount of any cash dividend on the ex-dividend date. As a result, if the underlying's dividend increases, call prices will decrease and put prices will increase. Conversely, if the underlying's dividend decreases, call prices will increase and put prices will decrease.

If dividends ...	Call prices will ...	Put prices will ...
Rise	Decrease	Increase
Fall	Increase	Decrease

 Pricing of Options Contracts

An option buyer has the right but not the obligation to exercise on the seller. The worst that can happen to a buyer is the loss of the premium paid by him. His downside is limited to this premium, but his upside is potentially unlimited. This optionality is precious and has a value, which is expressed in terms of the option price. Just like in other free markets, it is the supply and demand in the secondary market that drives the price of an option.

There are various models, which help us get close to the true price of an option. Most popular among them are the binomial option-pricing model and the much-celebrated Black-Scholes model. Today most calculators and spread-sheets come with a built-in Black-Scholes options pricing formula so to price options we don’t really need to memorize the formula.

Variables affecting Option Pricing

Option prices are affected by six factors.

These are Spot Price (S), Strike Price (X), Volatility of spot price, Time for expiration of contract (T) risk free rate of return (r) and Dividend on the asset (D).

The price of a call option rises with rise in spot price as due to rise in prices the option becomes more likely to exercise. It however falls with the rise in strike price as the payoff (S-X) falls. The opposite is true for the price of put options. The rise in volatility levels of the stock price however leads to increase in price of both call and put options.

The option price is higher for an option, which has a longer period to expire. Option prices tend to fall as contracts are close to expiry. This is because longer the term of an option higher is the likelihood or probability that it would be exercised. It should be noted that the time factor is applicable only for American options and not European types. The rise in risk free rate tends to increase the value of call options and decrease the value of put options. Similarly price of a call option is negatively related with size of anticipated dividends. Price of put option positively related with size of anticipated dividends.

All option contracts have price limits. This implies that one would pay maximum or a definite minimum price for acquiring an option. The limits can be defined as follows:

(i) The maximum price of a call option can be the price of underlying asset. In case of stocks a call option on it can never be larger than its spot price. This is true for both European and American call options.

(ii) The minimum price for a European call option would always be the difference in the spot price (S) and present value of the strike price (x). Symbolically it can be written as equal to S - Xe –rt. Here X has been discounted at the risk free rate. This is true only for European options.

(iii) The maximun price for a put option can never be more than the present value of the strike price X (discounted at risk free rate r). This is true for both types of options European and American.

(iv) The minimum price of the European put option would always be equal to difference between present value of strike price and the spot price of the asset. This can be symbolically expressed as Xe –rt –S.

For the sake of simplicity the above relationships have been written for options on non dividend paying stocks. In practice a minor adjustment is done to the formula to calculate the price limits for options on dividend paying stocks.