Assignment

Requirements
1. Credits are only given to solutions with detailed derivations/calculations. 2. Print out (double-sided if possible) on a piece of A4 paper and work on that.

Keep 4 digits after the decimal point in your solutions.

1. (10 points) In this assignment, you do some simple bond math. Consider the following four bonds (face value $100):

1. 1)  Compute 6-, 12-, 18-, 24-month zero rates. Plot the zero curve.
2. 2)  Compute the yields of the bonds.
3. 3)  Compute the durations of the bonds. Which bond is the most sensitive to a yield change?
4. 4)  Compute the convexities of the bonds. Suppose there is an upward shift of 60 basis points on the yield curve. Using the durations and convexities, approximate new bonds prices.

2. (5 points) 3-month LIBOR rates for Euro and USD are 4.75% and 5.70%, respectively, with continuous compounding. The current exchange rate between Euro and USD is 1.41 USD/EUR. The 3-month forward price for Euro quoted by a bank is 1.40 USD/EUR. What arbitrage opportunity does this create?

3. (5 points) A stock is expected to pay dividends of $1 per share in 2 months and 5 months. The stock price is $50. An investor has just taken a short position in a 6-month forward contract on the stock at no cost. 2-, 5- and 6- month LIBOR rates are 2.0%, 3.0%, 3.2%, respectively, with continuous compounding. Three months later, the price of the stock turns out to be $48. 2- and 3-month LIBOR rates are 2.0%, 2.5%, respectively. What is the value of the short forward position to the investor?