FIN 5535 Homework 3

Q1  Continuously compounding  
 6-mionth 2.00%  
 12-month 2.25%  
 18-month 2.50%  
 24-month 2.75%  
    
a. Calculate the present value of $100 in 2 years.   
b. Calculate are the equivalent 6­month, 12­month, 18­month, 24­month interest rates with
c. Calculate the forward rate for the six­month period beginning in 18 months. In other words,

Q2. A short forward contract on a non­dividend­paying stock was entered into some time ago.
Currently, it has 6 months to maturity. The risk­free rate with continuous compounding is 3% per
annum, the current stock price is $30 and the delivery price of the contract is $28. Calculate the
value of this short forward contract.

Q3. Suppose a bank needs to borrow (not lend) $50 million for 3 months starting in March 2017.
Unfortunately, nobody knows what the 3­m borrowing rate will be in the future so the bank
wants to hedge this interest rate risk.

which futures contract
how many contracts
futures expiration month
whether to take a long or short position of the contract

b. What’s the 3­m interest rate that the bank can lock in today? Use www.cmegroup.com to
answer the actual interest rate in percentage per annum. Include the screenshot of the source.
c. Suppose you are a speculator (not the bank above) and you think the interest rate will be
higher than what you answered in b. What action should you take now in the futures market?

Q4. Suppose a bank has unmatched asset and liability. Specifically, the bank has fixed rate loans
as assets (receiving fixed rate interests) but has floating rate deposits as liability (paying variable
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 swaps to eliminate this risk?