Mar 22

Option Pricing Models (OPM). Part 1: Option Mechanics

by David Harper, CFA, FRM, CIPM

CFA |

This series highlights lessons from our 50-minute screencast called Option Pricing Models: Binomial and the Black-Scholes. This screencast earns 1.0 credit hours under the Professional Development (PD) program at CFA Institute.

Plain vanilla stock option

A stock option is the right, but not the obligation, to purchase a stock at a given strike (a.k.a., exercise) price. A plain-vanilla option is issued at fair market value (FMV). That means the strike price (X) is equal to the stock price (S). At this instant the option has no intrinsic value; e.g., if the stock price (S) is $100 and the strike price is also $100, you would have to pay $100 in cash to exercise only to receive back $100 in stock value. That's why we say there is "no intrinsic value" and we also say "the option is at-the-money."

If the stock price is greater than the exercise price (if S > X), the option has some intrinsic value and is "in the money." If the stock price is less than the exercise price (if S < X), the option has no intrinsic value and is "out of the money." So, intrinsic value equals the stock price minus the strike price: intrinsic value = S-X. Note that an option (unlike a futures contract), is not symmetrical: there is no negative intrinsic value. The worst position is zero.

So an option issued at FMV would be worthless except for time value. We hold the option on the hope that the stock price will increase above the strike price (see hypothetical price path below):

We can therefore say that option value = intrinsic value + time value.

 

Six factors

In the diagram above, further, we see there are six factors that impact the stock option's present value. Five of the six are probably intuitive:

  • The higher the stock price (all other things being equal), the more valuable the option
  • The lower the strike price (all other things being equal), the more valuation the option
  • The more time we have to exercise (i.e., a longer contract life), the more valuable the option
  • Higher volatility creates a more valuable option. Why? Because higher volatility increases the odds that our option will eventually find itself in-the-money. Note that higher volatility is only good because options are asymmetrical: if high volatility works against us, we don't care too much about far down the stock goes. Once the option is underwater ("out-of-the-money"), we can't do worse than zero.
  • The riskless rate is not easy to figure by intuition. It will make more sense when we look at the Black-Scholes.
  • A higher dividend yield creates a less valuable option. The dividend is paid on the underlying stock, not to the option holders. So, if you hold an option, you forgo the dividend. Less of the total return will go to price appreciation and the opportunity cost of holding the option (as opposed to owning the stock) is greater.

These six factor apply to both the Black-Scholes and the binomial model.

Comments

  1. Be the first to leave a comment!

Leave a Comment