Investment Science
Chapter 13
Solutions to Suggested Problems
Dr. James A. Tzitzouris
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[email protected]
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13.1
The equation is best implemented on a computer.
The answer for the call stated in the
exercise is
C = $2.57
.
13.2
(a) For the expression
P(S) = a
1
S + a
2
S
γ
we have
Substituting in the BlackScholes equation and canceling terms we find that
Hence,
γ = 2r/σ^2
satisfies the equation.
Since
a
1
and
a
2
are arbitrary, this represents two
independent solutions to the secondorder differential equation; and hence is the general
solution.
(b)
P(∞) = 0
implies
a
1
= 0.
P(G) = K – G
implies
a
2
G
γ
= K – G
leading to
a
2
= (K – G)/G
γ
.
Hence,
P(S) = (K – G)(S/G)
γ
(c) It makes sense to maximize
P(S)
since the maximization is independent of
S
.
We
maximize
(KG)G
γ
.
Differentiation with respect to
G
gives the condition
Thus,
G = γK/(γ+1)
and
13.3
Using the spreadsheet implementation of the previous exercise, we adjust
σ
by trial and
error to obtain the given call premium.
The result is
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 Spring '10
 Won
 Electromagnet, secondorder differential equation, BlackScholes equation, Investment Science Chapter, Dr. James A.

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