ch5sol - CHAPTER 5 OPTION PRICING THEORY AND MODELS Problem...

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CHAPTER 5 OPTION PRICING THEORY AND MODELS Problem 1 A. The values of the option parameters are as follows: S = $83 K = $85 t = 0.25 r = 3.80% Variance = 0.09 Value of call = $4.42 B. To replicate this call, you would have to: Buy 0.4919 Shares of Stock (this is N(d1) from the model) and Borrow K e -rt N(d2) = 85 exp -(0.038)(0.25) (0.4324) = $36.40 C. At an implied variance of 0.075, the call has a value of approximately $4.00 (the market price). Implied Standard Deviation = 0.075 = 0.2739 D. Stock Price $85 $90 E. Value of Three-month Put = C - S + Ke -rt = $4.42 - $83 + 85 exp -(0.038)(0.25) = $5.62 Problem 2 A. S = $28.75 K = $30 t = 0.25 r = 3.60% σ 2 = 0.04 PV of Expected Dividends = $0.28/(1.036) 2/12 = $0.28
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Dividend Discount Models 2 Value of Call = $0.64 B. The payment of a dividend reduces the expected stock price, and hence reduces the value of calls and increases the value of puts. Problem 3 A. First value the three-month call, as above: Value of Call = $0.64 Then, value a call to the first (and only) dividend payment, S = $28.75 K = $30 t = 2/12 r = 3.60% σ 2 = 0.04 y = 0 (since it assumes exercise before the dividend payment) Value of Call = $0.51 Since the value of the three-month call is higher, there is no anticipated exercise.
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