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Derivatives

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Submitted By Hektor1453
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Due Sunday Feb 8th
1. Assume that the risk-free interest rate is 9% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August, and November, dividends are paid at a rate of 5% per annum. In other months, dividends are paid at a rate of 2% per annum. Suppose that the value of the index on July 31 is 1,300. What is the futures price for a contract deliverable on December 31 of the same year? (Hint: calculate an average yield)
2. Suppose that and are two forward contracts on the same commodity with times to maturity, and , where . Prove that where is the interest rate (assumed constant) and there are no storage costs.

3. The current USD/euro exchange rate is 1.4000 dollar per euro. The no-arbitrage 6-month forward exchange rate is 1.3950. The 6- month USD interest rate is 1% per annum continuously compounded. Estimate the 6-month euro interest rate.
4. A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock.
a) What are the forward price and the initial value of the forward contract?
b) Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the forward contract?

5. A bank offers a corporate client a choice between borrowing cash at 11% per annum and borrowing gold at 2% per annum. (If gold is borrowed, interest must be repaid in gold. Thus, 100 ounces borrowed today would require 102 ounces to be repaid in one year.) The risk-free interest rate is 9.25% per annum, and storage costs are 0.5% per annum.

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