Let S be the current price of a stock. Suppose that the stock price a year...
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Let S be the current price of a stock. Suppose that the stock price a year from now, denoted by S may take three possible values, represented by the three-dimensional vector (S(1-u), S, S(1+u)). Suppose that the current price of the bond that pays one dollar for sure a year from now is 1. Let qi be the price of basic security, b(i), i = 1, 2, 3. a) (6 points) Show that the risk-neutral probability 7¡ equals q¡ for i = 1, 2, 3. b) (6 points) Under the risk-neutral probability, calculate the expected value of S, Ê[S]. c) (6 points) Can you solve for the values of qi, i = 1, 2, 3? Why and why not? Explain carefully. d) (7 points) Now assume that it is known that the variance of the stock return S/S is o² under the risk-neutral probabilities and that o² < u². Prove that q₁q3= 0²/2u² and 92 = 1 - 0²/u². Let S be the current price of a stock. Suppose that the stock price a year from now, denoted by S may take three possible values, represented by the three-dimensional vector (S(1-u), S, S(1+u)). Suppose that the current price of the bond that pays one dollar for sure a year from now is 1. Let qi be the price of basic security, b(i), i = 1, 2, 3. a) (6 points) Show that the risk-neutral probability 7¡ equals q¡ for i = 1, 2, 3. b) (6 points) Under the risk-neutral probability, calculate the expected value of S, Ê[S]. c) (6 points) Can you solve for the values of qi, i = 1, 2, 3? Why and why not? Explain carefully. d) (7 points) Now assume that it is known that the variance of the stock return S/S is o² under the risk-neutral probabilities and that o² < u². Prove that q₁q3= 0²/2u² and 92 = 1 - 0²/u².
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a 6 points The basic securities are b1 S1u b2 S b3 S1u The riskneutral probabilities i equal the pri... View the full answer
Related Book For
Corporate Finance A Focused Approach
ISBN: 978-1439078082
4th Edition
Authors: Michael C. Ehrhardt, Eugene F. Brigham
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