Microsoft PowerPoint - PoF.ppt

Black-Scholes model: Main ideasƒ 231

The

BS analysis is analogous to the anal

ysis used to value options in the

binomial asset pricing model.

ƒ

Consider a

portfolio consisting of a position

in the option and a position

in the underlying stock

.

The

derivative is defined in terms of the underlying

Ä

the derivative

price should be highly correl

ated with the underlying price.

In any short period of time, the price of

a call option is perfectly positively

correlated with the price of the underlying

stock and the price of a put option is

perfectly negatively correlated wi

th the price of the underlying stock.

Ä

We should be able to

balance derivative against underlying in our

portfolio, so as to cancel the randomness

. In other words, we should be

able to choose the weights of

the portfolio such that we get

a riskless

portfolio.
Derivative securities: Options - Black-Scholes model