Q7

1)The Black-Scholes option pricing model suggests that European call option value equals the stock price minus the present value of the strike price, adjusted for the probability that the stock price will exceed the strike price when the option expires.

Required: Assess the above statement by discussing the relationship between value of the call option and current stock price. (You may wish to draw a diagram to show the relationship between the value of the call and current stock price.)

(7 marks)

2) The Black-Scholes Model for the European call option is as follows:

= 0(1) (2)

0 2 0 2 ln()+(+ 2) ln()+( 2)

1 = ; 2 = = 1

a) What element of the model can be used an indication of the option delta when the model is applied to hedge the risk exposure of an equity portfolio?

(2 marks)

b) Explain why in reality N(1) is usually used as a proxy for option delta in managing equity financial risks. (6 marks)

3) The Black-Scholes Model assumes that there are no dividends on the stock during the life of the option.

a) Is this a valid assumption? Explain why.(3 marks) b) What adjustment is needed to the Black-Scholes Model if the above-mentioned assumption needs to be relaxed? Explain why the adjustment is needed, considering the impact of dividends on the interest of share-holders and option-holders. (7 marks)