1710 a.
The inputs to the Black and Scholes option pricing model are P = 5, X = 2, r
RF
= 6%,
σ
= 50%, and t = 2 years.
Given these inputs, the value of a call option is calculated
as:
t
t
]
2
/
r
[
)
X
/
P
ln(
d
2
RF
1
σ
σ
+
+
=
=
8191
.
1
2
5
.
0
2
]
2
/
5
.
0
06
.
0
[
)
2
/
5
ln(
2
=
+
+
.
t
d
d
1
2
σ
−
=
=
1120
.
1
2
5
.
0
819
.
1
=
−
.
Using Excel’s Normsdist function N(d
1
) = 0.9656, and N(d
2
) = 0.8669.
This gives a
value of the call option equal to:
=
.
)]
[N(d
Xe
)]
P[N(d
V
2
t
r
1
RF
−
=
3.29
[0.8669]
2e
5[0.9656]
)
2
(
06
.
0

=
−
b.
The debt must therefore be worth 53.29 = $1.71 million.
Its yield is
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 Spring '08
 Staff
 Options, Mathematical finance, Black–Scholes, Stochastic volatility, Scholes option pricing

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