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Unformatted text preview: Hagfraeði og staerðfraeði fjármálamarkaða 04.07.50 Midterm 2007, Oktober 31st, 16:00 1. Consider the single-period CRR model in which the price of the stock today is S (0) = 100 . In the next period it can go up to 120 , or go down to 80 , with probabilities 80% and 20% respectivly. The risk free rate is R = 5% and let K = 90 a) How many shares of the stock should you buy to replicate the payoff of a put option, C = ( K- S (1)) + b) What is the arbitrage free price of the put? 2. Assume that the stock does not pay dividends. a) Prove using a no-arbitrage argument that the value of a European call plus the present value of K in the bankacount is equal to the value of the European put: c ( t ) + Ke- r ( T- t ) = p ( t ) + S ( t ) b) Let the strike price be equal to the stock price at time t = 0 , K = S (0) , and assume that the European put and call have the same value, p (0) = c (0) . If the American Put is worth 10 , P (0) = 10 , what is the value of the American Call, C (0) =? Why?Why?...
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- Fall '09