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FNCE 30007 DERIVATIVE SECURITIES

Tutorial Questions

Forward and Futures pricing

Question 1

A one-year long forward contract on a non-dividend paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding.

a) What are the forward price and the initial value of the forward contract?

b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%. What are the forward price and the value of the forward contract?

Question 2

Assume that the risk-free interest rate is 9% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August, and November, dividends are paid at a rate of 5% per annum. In other months, dividends are paid at a rate of 2% per annum. Suppose that the value of the index on July 15 is 1,300. What is the futures price for a contract delivered on December 15 of the same year?

Question 3

Suppose that the risk-free rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create?

Question 4

The two-month interest rates in Switzerland and the United States are 2% and 5% per annum, respectively, with continuous compounding. The spot price of the Swiss franc is $0.80. The futures price for a contract deliverable in two months is $0.81. What arbitrage opportunities does this create?

Question 5

Suppose that F₁ and F₂ are two futures contracts on the same commodity with times to maturity, t₁ and t₂, where t₂ > t₁. Prove that

where r is the interest rate (assumed constant) and there are no storage costs. For the purposes of this problem, assume that a futures contract is the same as a forward contract.

Question 6

When a known future cash outflow in a foreign currency is hedged by a company using a forward contract, there is no foreign exchange risk. When it is hedged using futures contracts, the marking-to-market process does leave the company exposed to some risk. Explain the nature of this risk. In particular, consider whether the company is better off using a futures contract or a forward contract when:

a) The value of the foreign currency falls rapidly during the life of the contract.

b) The value of the foreign currency rises rapidly during the life of the contract.

c) The value of the foreign currency first rises and the falls back to its initial value.

d) The value of the foreign currency first falls and then rises back to its initial value.

Assume that the forward price equals the futures price.