7. The 6-month, 12-month. 18-month, and 24-month zero rates are 3%, 3.5.%, 3.9%, and
4.1% with semi-annual compounding.
a) What are the rates with continuous compounding?
b) What is the forward rate for the six-month period beginning in 18 months with
continuous compounding?
8. On Jan 1st
, A stock is expected to pay a dividend of $4 per share in three months and in six
months. The stock price is $90, and the risk-free rate of interest is 8% per annum with
continuous compounding for all maturities. An investor has just taken a long position in a
nine-month forward contract on the stock, which matures in September.
a) What is the forward price and what is the initial value of the forward contract?
b) On April 1st, the price of the stock is $82 and the risk-free rate of interest is still 8% per
annum. What is the forward price of a contract maturing on September 1st?
c) On April 1st, what is the value of the long position in the forward contract entered into
on Jan 1st?
9. Consider a long forward contract to purchase a non-dividend paying stock in six months.
The current spot price is 62, and the interest rate is 4% per annum. You observe a price of
61 on a forward contract that matures in six months.
a) Explain in words why you might think this is an arbitrage strategy and how you can
capitalize on it.
b) Produce a statement of cash flows that shows the in- and outflows of cash today and in
six months if you were to execute the arbitrage strategy. What is the risk-free gain?
