Microsoft PowerPoint - PoF.ppt

Properties of the Black-Scholes pricesƒ 240

Call

ƒ

When

S becomes very large

, a call option is

almost certain to be exercised

. It

then becomes very similar to a

forward purchase

contract with delivery price E.

Ä

Expect the

call price to be

ƒ

This is in fact the call price given by

the BS formula since when S becomes very

large, both d1 and d2 become very large

and since N(x) is th

e 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.

ƒ

Put

ƒ

When

S becomes very large

, a European put option is

almost certain to be not

exercised

.

Ä

Expect the

European put price to be 0

.

ƒ

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

.

rT

t

t

Ee

S

c

−

−

=

Derivative securities: Options - Black-Scholes model