The Mathematics of Financial Modelingand Investment Management

2-Financial Markets Page 68 Wednesday, February 4, 2004 1:15 PM

68 The Mathematics of Financial Modeling and Investment Management

to the expiration date; they depend on whether the total proceeds at the

expiration date would be greater by holding the option or exercising

and reinvesting any cash proceeds received until the expiration date.

Factors that Influence the Option Price

There are six factors that influence the option price:

1. Current price of the underlying asset.


2. Strike price.


3. Time to expiration of the option.


4. Expected return volatility of the underlying asset over the life of the
   option.


5. Short-term risk-free interest rate over the life of the option.


6. Anticipated cash payments on the underlying asset over the life of the
   option.

The impact of each of these factors may depend on whether the option

is a call or a put, and whether the option is an American option or a

European option. A summary of the effect of each factor on put and call

option prices is presented in Exhibit 2.2.

Option Pricing Models

Earlier we illustrated that the theoretical price of a futures contract can

be determined on the basis of arbitrage arguments. Theoretical bound-

ary conditions for the price of an option also can be derived through

arbitrage arguments. For example, using arbitrage arguments it can be

shown that the minimum price for an American call option is its intrin-

sic value; that is:

EXHIBIT 2.2 Summary of Factors that Affect the Price of an Option

Effect of an Increase of Factor on

Factor Call Price Put Price

Current price of underlying asset Increase Decrease

Strike price Decrease Increase

Time to expiration of option Increase Increase

Expected price volatility Increase Increase

Short-term interest rate Increase Decrease

Anticipated cash payments Decrease Increase