Fnce4304

FNCE 4304 – Financial Risk Management

Spring 2016

Solutions to Assignment of Chapter 5

Problem 5.9.

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?

a) The forward price, F0 , is given by equation (5.1) as:

F0  40e011  4421

or $44.21. The initial value of the forward contract is zero.

b) The delivery price K in the contract is $44.21. The value of the contract, f, after six

months is given by equation (5.5) as:

f  45  4421e0105

 295

i.e., it is $2.95. The forward price is:

45e0105  4731

or $47.31.

Problem 5.11.

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 31

is 1,300. What is the futures price for a contract deliverable on December 31 of the same

year?

The futures contract lasts for five months. The dividend yield is 2% for three of the months

and 5% for two of the months. The average dividend yield is therefore

1

(3  2  2  5)  32%

5

The futures price is therefore

1,300 e ( 0.090.032)0.4167  1,331 .80

or $1,331.80.

Problem 5.14.

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

$0.8000. The futures price for a contract deliverable in two months is $0.8100. What

arbitrage opportunities does this...