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hw9 - X shares of a put with a strike price of 85 and a...

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ORIE 4630 — D. Ruppert Homework #9 — due Friday, Oct 29, 2010 Note: Students are required to work independently on homework. 1. Par 1000 zero-coupon bonds of maturities of 0.5, 1, 1.5, and 2 years are selling at 980.39, 957.41, 923.18, and 888.489, respectively. (a) Find the 0.5, 1, 1.5, and 2 year semi-annual spot rates. (b) A par 1000 coupon bond has a maturity of 2 years. The semi-annual coupon payments is $21. What is the price of this bond? 2. A par 1000 bond matures in 4 years and pays semi-annual coupons of $26. The price of the bond is $1020. What is the semi-annual yield to maturity of this bond? 3. An investor has 1000 shares of a stock selling at 95. The investor plans to buy
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Unformatted text preview: X shares of a put with a strike price of 85 and a maturity of 1 year. The implied volatility of the put is 0.2/year and the risk-free rate is 0.01/year. (a) What is the Black-Scholes price of this put? (b) What is the Delta of this put? (c) The change in price of this portfolio from times t 1 to t 2 will be approximately 1000( S t 2-S t 1 ) + X Δ( S t 2-S t 1 ) = (1000 + X Δ)( S t 2-S t 1 ) where Δ is the Delta of the put. Find X so that (1000+ X Δ) = 0. What fraction of the portfolio is in the put? (Comment: Buying the put on X shares is called Delta-hedging.) 1...
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