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Derivatives and Risk Management, 1st Edition
book

Derivatives and Risk Management, 1st Edition

by Sundaram Janakiramanan
May 2024
Intermediate to advanced content levelIntermediate to advanced
542 pages
27h 26m
English
Pearson India
Content preview from Derivatives and Risk Management, 1st Edition
The Black–Scholes Options Pricing Model 393
16.4 The Black–Scholes Model for Pricing Call Options
Under the assumptions shown in Section 16.2, the Black–Scholes formula is written as:
C S N d e S N d
e
X
rT
0 0 1 2
=
( ) ( )
where,
d
S
S
r T
T
X
1
0
2
2
=
+ +
ln
σ
σ
and
d d T
2 1
= σ
N(d
1
) and N(d
2
) represent the cumulative probability function for a standardized normal variable.
A comparison of the Black–Scholes formula with the binomial options pricing formula derived in
Section 15.1 shows the following:
Black–Scholes formula: C
0
= S
0
N(d
1
)–e
rT
S
x
N(d
2
)
Binomial options pricing formula: C
0
= n
C
S
0
n
C1
S
X
(1 + r)
T
A comparison of these two formulas shows ...
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Publisher Resources

ISBN: 9781299447547Publisher Website