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Unformatted text preview: STOR 890 Midterm Exam Solutions Spring 2011 (1) What are the differences between taking a long position in a forward contract with the forward price $20 and buying a call option with a strike price $20? Answer: (i) No cost for entering a forward contract; but need to pay a price for buying a call option. (ii) At the maturity T , the payoff for the forward contract is S ( T )- 20, but the payoff for the call option is [ S ( T )- 20] + . (2) Assume an annual interest rate 5% and quarterly compounding. Which of the following two plans is a better investment? Why? Plan A: investing $10,000 today, receiving $5,000, $4,500, $4,500 after 3,6,9 months re- spectively; Plan B: investing $11,480 today, receiving $5,500, $5,000, $5,000 after 3,6,9 months re- spectively. Answer: Let r = 0 . 05 / 4 be the quarterly compounding rate and b = 1 1+ r . Motivated by the time value of money, consider the present values of cash ows driven by Plan A and Plan B respectively, with the difference PV A- PV B = 1480- 500 ( b + b 2 + b 3 ) 16 . 7 > . Therefore, Plan A is a better investment. (3) Consider a single period market in which a bank account has an interest rate r = 0 . 05. (3a) If a stock S follows a binomial tree with up factor u = 1 . 05 and down factor d = 0 . 96, can we determine the time-0 value V (0) of a contingent claim g ( S (1))? Explain why. Answer: If an EMM Q existed, it would be given by Q ( S (1) /S (0) = u ) = q = 1 + r- d u- d = 1 in this case due to 1 + r = u . Such a degenerate measure Q cannot be equivalent to the physical measure P . Hence there exists an arbitrage opportunity. Here is an example: Short....
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