1. The 6-month, 1-yr, 1.5-yr, and 2-yr interest rates are 1.75%, 2.00%, 2.25% and 2.50% with continuous compounding. a. Calculate the present value of $100 in 1.5 years (=18 months). b. Calculate the equivalent 6-month, 1-yr, 1.5-yr, and 2-yr interest rates with “quarterly” compounding. c. Calculate the 6-month forward rate between 1.5 years and 2 years. Answer the forward rate with continuous compounding.
2. On 7/1/2014, A short 18-month forward contract on a non-dividend-paying stock was entered into. The fixed delivery price of the contract was agreed at $50. On 7/1/2015 (after 12 months since the contract was written), this contract has 6 months to maturity. The risk-free rate with continuous compounding is 1.5% per annum, the current stock price is $45. Calculate the value of this short forward contract. Hint: value of short forward contract = value of long forward contract * -1
3. Suppose a bank needs to borrow (not lend) $20 million for 3 months starting in March 2016. Unfortunately, this position is risky because nobody knows what the interest rates will be next year. The bank wants to lock in this March 2016 3-m interest rate today. a. Devise a plan to lock in the borrowing rate today. Be specific about the name of the futures contract futures expiration month how many contracts whether to take a long or short position of the contract. b. Suppose you are a speculator (not the bank above) and you are certain the interest rate will increase next year. What action should you take today to capitalize your prediction?
4. Suppose a bank has unmatched asset and liability. Specifically, the bank has fixed rate loans as assets (receiving fixed rate mortgage interests) but has floating rate deposits as liability (paying floating rate interests). This is a risk to the bank because it can suffer a loss, if the floating rate increases over time. What can the bank do with interest rate swaps to eliminate this risk? Be specific.