1. (5 points) An investor enters an FRA at no cost to borrow $100,000 in 6 months for a period of 3 months. The 3- month, 6-month, and 9-month interest rates are given by 5.2%, 5.0%, and 4.8% respectively when the FRA is entered. Suppose 3 months later, the 3-month, 6-month, and 9-month interest rates become $4.4%, 4.6% and 4.8% respectively. Assume continuous compounding. What is the value of the FRA to the investor at this time?

2. (5 points) A European call on a stock with strike $30 and maturity 6 months costs $2. The current stock price is $29. The stock will pay a dividend of $0.5 in 2 months and 5 months. The risk free interest rate is constant at 10% per year with continuous compounding. What is the price of a European put with strike $30 that expires in 6 months? Construct an arbitrage strategy if the put price were $2.45.

3. (5 points) The price of an American call with strike and maturity on an asset with continuous yield is bounded by the following for any ? [0, ]: ? ( 0 ? ? ? )+. Construct an arbitrage strategy if this is violated for some ? [0, ].

4. (5 points) A diagonal spread is created by selling a European call on a non-dividend-paying stock with strike 105 and maturity 6 months, and buying a European call on the same asset with strike 95 and maturity 12 months. Construct a diagram showing the payoff of the diagonal spread in 6 months. What is the market view of a trader who holds such a spread?

IE 420 HW3 Name____________________________ Score____________ 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. (5 points) An investor enters an FRA at no cost to borrow $100,000 in 6 months for a period of 3 months. The 3month, 6-month, and 9-month interest rates are given by 5.2%, 5.0%, and 4.8% respectively when the FRA is entered. Suppose 3 months later, the 3-month, 6-month, and 9-month interest rates become $4.4%, 4.6% and 4.8% respectively. Assume continuous compounding. What is the value of the FRA to the investor at this time? 2. (5 points) A European call on a stock with strike $30 and maturity 6 months costs $2. The current stock price is $29. The stock will pay a dividend of $0.5 in 2 months and 5 months. The risk free interest rate is constant at 10% per year with continuous compounding. What is the price of a European put with strike $30 that expires in 6 months? Construct an arbitrage strategy if the put price were $2.45. 3. (5 points) The price of an American call with strike and maturity on an asset with continuous yield is bounded by the following for any [0, ]: (0 )+ . Construct an arbitrage strategy if this is violated for some [0, ]. 4. (5 points) A diagonal spread is created by selling a European call on a non-dividend-paying stock with strike 105 and maturity 6 months, and buying a European call on the same asset with strike 95 and maturity 12 months. Construct a diagram showing the payoff of the diagonal spread in 6 months. What is the market view of a trader who holds such a spread