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Professor Juhani Linnainmaa USC Marshall FBE 441/555 Problem Set #5 Instructions: You can complete this problem sets in groups of up to four students. Please show enough work so that it is possible to infer how you arrived at the solution. If applicable, you should write down the equation that allows you to solve the problem. You will lose points if you state the answer without justification. Questions 1. Suppose that the USD-EUR exchange rate is such that one U.S. dollar buys 0.9 Euros. Suppose that the one-year spot rate is 1% in the U.S. and 1% in Europe, and that the two-year spot rates are 2% and 4%. The rates compounded annually. (a) What are the forward USD-EUR exchange rates for contracts that mature in one or two years? (b) Is EUR expected to strengthen or weaken against U.S. dollar, and when? 2. Suppose a stock is trading at $120 per share. There are both European put and call options written on this stock. Both options expire in four months and both have a strike price of $110. If the price of the call option is $15, what is the price of the put option? The risk-free rate is 4% per year, compounded monthly. 3. Suppose that the put option in the previous problem is trading at $3 per contract. As you can verify, this means that there is an arbitrage opportunity. Describe carefully the trades that you would need to make to take advantage of this opportunitythat is, what to buy, sell, or write and how much to borrow or lend. 1 4. A stock currently trades at $100, and its price can increase or decrease by 10% over the following year. The risk-free rate is 3% per year. (a) We have call and put options written on this stock with strike prices of $105. What are the prices of these options? (b) How many shares would you need to buy to replicate the call option; that is, what is of the call option? (c) Suppose now that the stock price today is $101 instead of $100. What is the new price of the call option? (d) Suppose now that the stock price is again $100, but that instead of increasing or decreasing by 10% over the following year, the stock price will increase or decrease by 30%. What are the new prices of the call and put options? 2