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Unformatted text preview: 1. Describe the profit from the following portfolio: a long forward contract on an underlying asset, and a long European put option on the asset with the same maturity as the forward contract. The strike price of the option is equal to the forward price of the underlying asset as the time the portfolio is set up. Answer: The terminal value of the long forward contract is: S T- F where S T is the price of the asset at maturity and F is the forward price of the asset at the time the portfolio is set up. (The delivery price in the forward contract is F .) The terminal value of the put option is: max( F- S T , 0) The terminal value of the portfolio is therefore S T- F + max( F- S T , 0) = max(0 ,S T- F ) This is the same as the terminal value of a European call option with the same maturity as the forward contract and an exercise price equal to F . The profit equals the terminal value less the amount paid for the option. 2. A 10-year 8% coupon bond currently sells for $90. A 10-year 4% coupon bond currently sells for $80. What is the 10-year zero rate? Answer: A long position in two of the 4% coupon bonds combined with a short position in one of the 8% coupon bonds leads to the following cash flows. Y ear 0 : 90- 2 80 =- 70 Y ear 10 : 200- 100 = 100 since the coupons cancel out. The 10-year spot rate is therefore 1 10 ln 100 70 = 0 . 0357 or 3.57% per annum. 3. Suppose that you enter into a six-month forward contract on a non-dividend-paying stock when the stock price is $30 and the risk-free interest rate (with continuous compounding) is 12% per annum. What is the forward price? Explain your reason clearly.is 12% per annum....
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This note was uploaded on 11/02/2011 for the course ACTSC 446 taught by Professor Adam during the Winter '09 term at Waterloo.
- Winter '09