Microsoft PowerPoint - PoF.ppt

ƒ 235

Black-Scholes formula where N(x) is cumulative standard no

rmal distribution at x. In other

words, it is the probability that

a variable with a standard normal

distribution, i.e. N(0,1), will be less than x.Note: The equations for the call price and the put price are of course related via the put-call parity, i.e. via

p

t

= c

-St

t

+ PV

(E)t

.

(

)

(

)

() ()T

d

d

T

T

r

S E

d

d

N

S

d

N

Ee

p

d

N

Ee

d

N

S

c

t

t

rT

t

rT

t

t

σ

σ

σ

−

=

⎞ ⎟⎟ ⎠

⎛ ⎜⎜ ⎝

+

+

⎞ ⎟ ⎠

⎛ ⎜ ⎝

=

−

−

−

=

−

=

−

−

1

2

2

ln

1

1

2

2

1

2

Derivative securities: Options - Black-Scholes modelBlack-Scholes model: Pricing formula