MANG3020Futures and Options

Class 2

2014/2015

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?

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Question 2

Suppose that the risk-free interest 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 3

The current value of the Dow Jones Industrial Average is

11,200. The dividend yield is 3.00% per annum,

assuming continuous compounding and a 365-day year.

The interest rate is 10% with annual compounding.

a) Calculate the continuously compounded interest rate.

What is the 60-day Dow Jones Industrial Average futures

price?

b) Suppose that an investor held a long position of a 60-

day Dow Jones Industrial Average forward contract.

Afterwards, the Dow slides down and a week later ends

at 10,500. What is the 53-day forward price?

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c) What is the value of the forward contract to the long

position a week later (with 53 days left)? Assume that the

forward contract’s payoffs are determined by multiplying

the above results by $10.

Question 4

An investor sells a European call option and buys a

European put option with the same strike price and

maturity. Describe the investor's position.

Question 5

An investor buys a European put option on a share for

$3. The strike price is $40. Under what circumstances

will the option be exercised? Under what circumstances

will the investor make a profit? Draw a diagram showing

the variation of the investor’s profit with the stock price

at the maturity of the option.

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Question 6

Assume that a European call option to buy a share for

$100 costs $5 and is held until maturity. Under what

circumstances will the option be exercised? Under what

circumstances will the holder of the option make a

profit? Draw a diagram showing how the profit from a

long position in the option depends on the stock price at

maturity of the option.

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