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# Dan Gorman FINA 6211 Problem Set 5 1. Consider the situation in which stock price movements during the life of a European option are governed by a...

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Dan Gorman FINA 6211 Problem Set 5 1. Consider the situation in which stock price movements during the life of a European option are governed by a two-step binomial tree. Explain why it is not possible to set up a position in the stock and the option that remains riskless for the whole of the life of the option. 2. A stock price is currently \$50. It is known that at the end of six months it will be either \$60 or \$42. The risk-free rate of interest with continuous compounding is 12% per annum. Calculate the value of a six-month European call option on the stock with an exercise price of \$48. Verify that no-arbitrage arguments and risk-neutral valuation arguments give the same answers. 3. Consider a European call option on a non-dividend-paying stock where the stock price is \$40, the strike price is \$40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months. (a) Calculate u , d , a and p for a two-step tree. [Use 4 decimal places in your calculations.] (b) Value the option using a two-step tree. [Give your final answer to 2 decimal places.]

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