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:
CSNdeSNd
e
X
rT
0012
=−
−
()()
where,
d
S
S
rT
T
X
1
0
2
2
=
++
ln
σ
σ
and
ddT
21
=−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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