Fundamentals of Derivatives Markets

Week 4 Homework

Directions: Solve the problems below and submit them to the Drop box by midnight Sunday CT.

Problems

5.2

A $50.00 stock pays a $1.00 dividend every 3 months, with the first dividend coming 3 months from today. The continuous compound risk-free rate is 6%.

a) What is the price of a prepaid forward contract that expires 1 year from today, immediately after the fourth-quarter dividend?

= $50 − $0.985 − $0.970 − $0.956 − $0.942

= $50 − $3.853 = $46.147

b) What is the price of a forward contract that expires at the same time?

=$46.17 * e0.06*1=446.147*1.0618=$49.00

5.3

A $50.00 stock pays an 8% continuous dividend. The continuous compound risk-free rate is 6%.

a) What is the price of a prepaid forward contract that expires 1 year from today, immediately after the fourth-quarter dividend?

$46.15 = 0.0022 * 365 + 0.92 * 4 – 50.00

b) What is the price of a forward contract that expires at the same time?

$49.00993365 = 50.00 * 0.92311

5.5

Suppose you are a market-maker in S&R index forward contracts. The S&R index spot price is 1100, the risk-free rate is 5%, and the dividend yield on the index is 0.

a) What is the no-arbitrage forward price for delivery in 9 months?

1129.257

b) Suppose a customer wishes to enter a short index futures position. If you take the opposite position, demonstrate how you would hedge your resulting long position using the index and borrowing or lending.

1100* e (0.05−0.005)×0.75 = 1100*1.0343=1137.759

If we believe the dividend yield is 0.05, we consider the observed forward price of

1,129.257 to be too cheap. We will therefore buy the forward and create a synthetic short forward,

capturing a certain amount of $8.502. We engage in a reverse cash and carry arbitrage.

c) Suppose a customer wishes to enter a long index futures position. If you take the opposite position, demonstrate how you would hedge your resulting...