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Unformatted text preview: Practice Midterm (with answers) Financial Instruments Robert NovyMarx Winter 2007 Instructions. Please answer all questions in the space provided. Show all relevant computations. Brief, clear, and accurate responses will get maximum points. Good luck! 1. (25 points) SHORT QUESTIONS (a) (5 points) True or False . Suppose the lognormal model is wrong ( i.e., the future spot price is not lognormally distributed), because stocks have stochastic (random) volatility. Then the putcall par ity no longer holds for European options (you can assume non dividend paying stocks, if you like). Answer: Putcall parity holds for nondividend paying stock, re gardless of the distributional assumptions on the underlying. (b) (5 points) If the interest rate is 0%, should you ever considering exercising an American call early? How about an American put? Answer: It may be beneficial to exercise the American Call early, if the dividend payments are large enough. With zero interest rates, it is never beneficial to exercise the American Put early: the interest payments on the strike price are the only advantage from exercising the put early. 1 (c) (5 points) Suppose you want to price a 6 month European op tion on IBM stock. You determine that you want to use a 2step Binomial tree, where each step represents 3 months. You obtain the following information: The (continuously compounded, annu alized) interest rate is 3.98%. The return on IBM stock is on average 8% annually and the variance of the return is 16% annu ally. What are your values for the Binomial tree parameters u,d and r ? Answer: Using the equal probability method, with Δ t = 1 / 4 and σ = √ . 16 = . 40, we have d = 2 e μ Δ t e 2 σ √ Δ t + 1 = 2 e . 08 / 4 e 2 · . 40 / 2 + 1 = 0 . 819 u = de 2 σ √ Δ t = 0 . 819 e . 4 = 1 . 222 . Alternatively, you can follow Cox, Ross, and Rubinstein and let u = e σ √ Δ t and d = 1 /u , but you’ll get the same answers (we set it up that way; this happens when μ = σ 2 / 2). (d) (10 points) Pricing a digital option . Consider the n = 1 step binomial tree model. Pick u = 2 , d = 1 / 2 and r = 1 . 1. The current stock price is S = 100 . ( i ) What are the risk neutral probabilities of going up and down? Answer : q = 1+ r d u d = 1 . 1 . 5 2 . 5 = 0 . 4 , 1 q = 0 . 6 ( ii ) What is the price of a digital option that pays $110 when the final stock price is greater than $120 and $0 otherwise? Answer : The price of the digital option is . 4 × 110 1 . 1 = 40 . 2 2. (25 points) Foreign currency forwards . You are running the trading desk at a large, highgrade investment bank. You have the following rates available to you Spot Dollar/Euro Exchange Rate 0.80 e /$ 3month Forward Dollar/Euro Rate 0.7936 e /$ 1month US (dollar) Riskfree Interest Rate 3% 3month US (dollar) Riskfree Interest Rate...
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 Winter '07
 NovyMarx
 Interest Rates, Option style, Rational pricing

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