Pricing Derivative Instruments Using the Black-Scholes Model

Pricing Derivative Instruments Using the Black-Scholes Model 

To price an option, its fair value at contract initiation must be calculated. This value is a function of the options expected terminal payoff, discounted to the day the contract was struck. Expression (8.12) describes the expected value of a call option at maturity T. 

Cj = the price of the call option at maturity T E= s the expectations operator 

Sr = the price of the underlying asset at maturity T X = the strike price of the option 

According to (8.12), only two outcomes are possible at maturity either the option is in the money and the holder earns Sr - X, or it is out of the money and expires worthless. Modifying (8.12) to incorporate probability 

Ct = the price of the call option at maturity T E= s the expectations operator S-r = the price of the underlying asset at maturity T X = the strike price of the option 

Equation (8.13) derives the expected value of a call option on maturity. Equation (8.14) derives the fair price of the option at contract initiation by discounting the value given by (8.13) back to this date. 

---