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final2010sol - Introduction to derivatives Fall 2011 BUSI...

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Introduction to derivatives, Fall 2011 BUSI 588, Final exam solutions Introduction to derivatives BUSI 588, Final Exam Solutions, Fall 2010 Problem 1 - Oratio Dominica (25 points) 1. The Black-Scholes ABC. (a) According to the Black-Scholes model, the price of a put option on an asset with current value S = 50, annual volatility σ = 0 . 2, one-year maturity, and a strike of K = 50 would be $2.81. (b) In order to replicate the put, Black-Scholes would suggest shorting - 0.37 units of the underlying asset and lending $21.08. (c) If the underlying asset would go down, Black-Scholes would suggest that we short more of the underlying asset, lending the proceeds. 2. Discuss whether you agree with the following two statements (keep the discussions separate, and use less than 50 words for each). (a) Disagree: “A call is equivalent to a put, coupled with a long position in the underlying asset and borrowing.” (b) Agree. “A put is equivalent to shorting the underlying asset and lending, using the money from the cash account to buy more of the underlying asset as the stock price goes up.” Problem 2 - Wyoming (30 points) 1. Using the put-call parity we have that C = P + S - K (1 + r f ) T = 1 . 265 + 20 - 20 1 . 08 = 2 . 746 Note that I use the 1-year rate obtained from the 1-year bond (8%, the 6-month bond has a yield of 6%). 2. By inspection, the calls with a strike of $22.5 are mispriced with respect to the puts with that same strike, so there is a strong violation of the put-call parity. In particular, the puts are relatively expensive. The table below details a trade that generates arbitrage profits. Today In one-year S * < 22 . 5 S * 22 . 5 Buy call - 1 . 65 0 S * - 22 . 5 Short asset +20 - S * - S * Lend PV of 22.5 - 20 . 83 +22 . 5 +22 . 5 Sell put +2 . 55 - (22 . 5 - S * ) 0 Net 0 . 07 0 0 c Diego Garc´ ıa, Kenan-Flagler Business School Page 1 of 4
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