1.You're an investor in futures contracts. The spot price of a futures contract on an asset is $50 and matures in 3 years. Assume that the risk-free rate is 7% per annum with continuous compounding.

a) determine the fair price of the contract

b) determine the fair price of the contract assuming the asset pays out cash dividends of $5 at the end of year2 and year3c) determine the fair price of the contract assuming the asset pays a yield of 2% during the life of the contract

2.Consider a $100 par value coupon-bearing bond with a 3% coupon rate and 5-year maturity. The prevailing risk-free rate during the life of the bond is 6% per annum with continuous compounding.

a) calculate the price of the bond described above

b) calculate the duration of the bond

c) calculate the convexity of the bond

d) use the approximation given by duration and convexity, to calculate the percentage change in bond price given a 40 basis points increase in yield.

3. You enter into a short crude oil futures contract at $51.9 per barrel. One contract is for 1,000 barrels of oil. The initial margin for each contract is $3,325, and the maintenance margin is $2,800. You will get a margin call when the price per barrel of oil is above X per barrel or below X per barrel.

a) What is X?

b) Will you get a margin call when the price of the oil is above or below X?