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Unformatted text preview: Math 623, F 2011: Homework 5. For full credit, your solutions must be clearly presented and all code included. (1) This problem deals with the pricing of a strangle option using a binomial tree. The underlying stock price S t follows geometric Brownian motion with volatility σ = 0 . 28 (in units year- 1 / 2 ) and the interest rate is r = 5 . 24% per year, continuously compounded. The stock pays a continuous dividend yield of D = 1% per year. It is currently trading at S = 36. The option pays Φ( S ) if exercised when the stock price is S . Here Φ( S ) = 30- S if 0 ≤ S ≤ 30 if 30 < S ≤ 40 S- 40 if S > 40 . Today is t = 0. The option expires in T = 1 / 2 years. (a) Using the Black-Scholes formulas, find the exact value of the European strangle option today. (b) Construct a binomial tree with time step Δ t = T/ 2 10 . Compute the parame- ters p u , p d , u , d and the corresponding value of the option under the following conditions: (i) The (noncentral) moments of...
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- Fall '08
- Binomial, Interest rate swap, Zero-coupon bond, Geometric Brownian motion