Cornell University, Fall 2010 J. Wissel Sample Preliminary Exam Problems for ORIE 5600 Financial Engineering with Stochastic Calculus I Note: The number of questions and amount of material on this sample sheet does not correspond to the number of questions or amount of material in the preliminary exam. This sheet should only serve to give you an idea of what type of questions you can expect. Problem 1: Exercise 2.2 (i) – (iv) in Shreve, Stochastic Calculus for Finance II Problem 2: Put-call parity We consider three types of derivatives of a stock S . A European call option with maturity time N and strike K pays C N = ( S N-K ) + at time N . A European put option with maturity time N and strike K pays P N = ( K-S N ) + at time N . Finally, a forward contract with settlement time N and delivery price K is an agreement to buy the stock S at time N for the price K ; its payoﬀ at time N is F N = S N-K (the payoﬀ is negative if S N < K ). (a) Let
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