a) An investor buys European call on a share for sh 5. The share price is sh 90 and the strike price is sh 85. Under which circumstances does the investor make profit? When will the option be exercised? Draw a diagram to show the variation in the investors profit and the share price at the maturity of the option.
b) Consider an option on a non dividend paying stock whose share price is sh 120. The exercise price is sh 130, risk free rate is 10% per annum, volatility is 20% per annum and the time to maturity is one year.
Construct a two stage binomial tree and determine; i. European call price ii. European put price iii. Calculate the value of the call and put option using the Black and Scholes option pricing model.
QUESTION TWO
a) Consider a stock with a current price of sh 5. There is a two thirds probability that the stock will increase in value by 20% and a one third probability that the stock will decrease by 20% at the end of one year period. Further assume that the exercise price is sh 4 and the risk free rate is 5% per annum.
Required;
i. Show the movement in stock prices clearly indicating the expected value of the stock and the call option value at the end of the period.
ii. Calculate the delta of the call option and explain how an investor can use this information to create a perfectly hedged position.
iii. Calculate the call option value at the beginning of the period.
b) Suppose that put options on a stock with strike prices sh 30 and sh 35 costs sh 4 and sh 7 respectively.
How can options be used to create; i) A bull spread ii) A bear spread