Microsoft PowerPoint - PoF.ppt

ƒ 241

Call

ƒ

When

S becomes very small

, a call option is

almost certain to be not

exercised

.

Ä

Expect the

call price to be 0

.

ƒ

This is in fact the call price given by

the BS formula since when S becomes very

small, both d1 and d2 become very small

and since N(x) is the probability that a

variable with a standard normal distribution

, i.e. N(0,1), will be less than x, N(d1)

and N(d2) are both close to zero.

ƒ

Put

ƒ

When

S becomes very small

, a European put option is

almost certain to be

exercised

. It then becomes very similar to a

forward sale

contract with delivery

price E.

Ä

Expect the

European put price to be

ƒ

This is in fact the European put price given by the BS formula since when S becomes very small, both d1 and d2 become very sm

all and since N(x) is the probability that a

variable with a standard normal distribution

, i.e. N(0,1), will be less than x, N(-d1)

and N(-d2) are both close to one.

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Derivative securities: Options - Black-Scholes modelProperties of the Black-Scholes prices