02 May 2008

More On Options Pricing

In an earlier section, I outlined the six inputs into the option pricing model that are required to calculate an option premium:

1/ The price of the underlying
2/ The strike price
3/ The time till expiry
4/ Risk free interest rates
5/ Dividends, if any
6/ Volatility

Note that “premium” is not a term I’ve used before, but is interchangeable with “price”.

In this section I want to cover in more detail the first two inputs, the price of the underlying asset and strike price as it is important how these to relate to each other.

Both of these inputs are unequivocally known at any point is time, the strike price of course is constant, whereas the price of the underlying will fluctuate from day to day and minute to minute.

It is in the relationship of these two inputs that we derive 3 new terms, which I will introduce now:

• Intrinsic value
• Extrinsic value
• Moneyness

Moneyness is further divided into three terms of relevance:

• At the money
• In the money
• Out of the money

Let’s cover the moneyness terminology first. An option is said to be “at the money” (ATM), if the underlying stock is trading at or near the option strike price. This is fairly self-explanatory and is the same for both call options and put options. For example, if we have a \$50 call or put option where the underlying is trading at \$50.00, that option is trading ATM.

A call option where the underlying is trading higher than the strike price is said to be “in the money” (ITM). For example, if we have a \$20 call option where the underlying is trading at \$22.30, that call option is ITM.

It therefore stands to reason that a call option where the underlying is trading lower than the strike price is said to be “out of the money” (OTM). For example, if we have a \$30 call option where the underlying is trading at \$27.90, that call option is OTM.

Put options on the other hand are precisely the opposite to call options.

A put option where the underlying is trading lower than the strike price is said to be “in the money” (ITM). For example, if we have a \$50 put option where the underlying is trading at \$46.70, that put option is ITM.

It therefore stands to reason that a put option where the underlying is trading higher than the strike price is said to be “out of the money” (OTM). For example, if we have an \$80 put option where the underlying is trading at \$83.90, that call option is OTM.

In practice, the nearest strike to the price of the underlying is often referred to as ATM, even though it may be a little bit ITM or OTM.

Intrinsic and Extrinsic Value

If an option is ITM, is has intrinsic value. Why? Let’s look at an example. Let’s say we own a \$50 call option with the underlying trading a \$55.00. That option is \$5.00 ITM.

A \$50 call option gives you the right to buy those shares at \$50, so if you exercise the option you can buy the stock for \$50 and immediately sell for \$55.00, a \$5.00 profit. Therefore that option is worth at least \$5.00.

So “intrinsic value” is simply the amount by which an option is ITM.

Remember that put options are the reverse. A put option is ITM if the underlying is trading below the exercise price, because you can exercise to sell stock and buy back with an immediate profit.

ATM and OTM options have no intrinsic value at all. Yet in most cases, they still have value; it costs money to buy them. Also in most cases, ITM options have value in excess of their intrinsic value. This is referred to as “extrinsic value” or “time value”.

I prefer the term extrinsic value over time value, because extrinsic value also considers volatility, not just time until expiry.

Have a look at the diagram below of the value of an ATM call option some time before expiry. (All of the following diagrams are for ATM options) The purple area represents intrinsic value and the light blue area represents extrinsic value.

Put options have intrinsic value below the strike price. (See below)

You will note that extrinsic value is greatest when ATM. If we plot the extrinsic value only without intrinsic value, this concept becomes very obvious, an important point for when we get into the Greeks. (See below).

This is the graph of extrinsic value for a call option, but has a similar shape for calls and puts . Note that in this instance the extrinsic value is greater when underlying prices are higher, than when they are lower. This applies to stock options and won’t be seen on futures options. This relates to “cost of carry” because a stock is an actual tangible and will be discussed later in the section on risk free rates.

Next - Time & Time Decay