Given below is the Option Pricing Model (OPM) derived Black and Scholes in 1973 for predicting the market price of call options.

Required:

a) State and briefly explain the relationship between a call option‟s price and the following determinants:

1) the underlying stock‟s price.

2) the exercise price

3) the time to maturity

4) the risk-free rate.

b) The following data relate to call options on two shares, A and B

Required:

Using the Black-Scholes Option Pricing Model (OPM).

1) Calculate the price of call option A.

2) Of the two call options, which would you expect to have the higher price? Why? (Do not compute).

c) On 1 March 2001, a Kenyan importer purchased goods from the United States of America worth U.S.$120,000 to be paid for two months later on 30 April 2001.

Kenyan shillings futures were available in the money market and could be bought in blocks of Ksh.100,000 and each future contract cost Ksh.1,000.

Spot exchange rate on 1 March 2001 was Ksh.76.50 = US$ 1. The two-month forward exchange rate on 30 April 2001 was Ksh.79.50 = US$1 and the exchange rate at which futures were closed out was Ksh.77.50 = US$1.

Required:

The net loss(gain) of using the futures contract.

ANSWER

a) Factors affecting value of a

call: **Stock price:**

The call value increases with the stock price. If price is higher than exercise price one would be willing to pay more for the call.

**Exercise Price**

The lower the exercise price the more valuable the call will be.

**Time to maturity:**

The longer the time to maturity, the greater the chance that the stock price will climb higher above the exercise price hence the higher the value of call.

**The risk-free rate:**

If the risk-free rate increases (and nothing else changes), then the call must be worth more because the discounted present value of the exercise price declines.

b) Value of a call A using black scholes (use normal distribution tables) OPM

ii) Call B will be more valuable because it has longer time to expiration. It has a greater chance if it will finish in the money.

1. Cost of purchase/importation 1st March 120,000 x 76.5 = Ksh.9,180,000.