Chapter13 - Investment Science Chapter 13 Solutions to...

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Investment Science Chapter 13 Solutions to Suggested Problems Dr. James A. Tzitzouris < jimt2@ams.jhu.edu > 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 we have Substituting in the Black-Scholes 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 second-order differential equation; and hence is the general solution. (b) P(∞) = 0 implies a 1 = 0. P(G) = K – G implies a 2 G = K – G leading to a 2 = (K – G)/G . Hence, P(S) = (K – G)(S/G) (c) It makes sense to maximize P(S) since the maximization is independent of S . We maximize (K-G)G . 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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Chapter13 - Investment Science Chapter 13 Solutions to...

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