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ass5_f09 - STAT/ACTSC 446/846 Assignment#5(due December 4...

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STAT/ACTSC 446/846 Assignment #5 (due December 4, 2009) 1-3. Problems from the textbook: Chapter 13: 13.5, 13.14, and 13.16 4. Using the risk-neutral pricing formula, find a closed-form expression for the price at time t = 0 of a call option with maturity T and strike K . Assume that the continuously compounded interest rate r is constant and that the price of a risky asset follows a geometric Brownian motion with volatility parameter σ . Show all steps in your derivation. 5. Denote the European call option price in the Black-Scholes model by C ( S ). Find an expression for the delta of the option ∂S C ( S ). Show all your calculations. 6. Suppose that under the real-world measure P , the short interest rate r follows the model dr t = σdW t . The initial spot rate r 0 is known to be 5%. Consider the following questions: (a) Obtain a PDE for a zero-coupon bond price with maturity T . Determine the solution to this PDE (for this, you may use results presented on page 787 in the textbook).
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