Question

You are considering a position as the director of finance in a company listed on the Lusaka Securities Exchange Plc. Since the firm is still new, the salary is not that great but your package will include call options on 5,000 shares of the company. The shares are currently selling for K5 per share. The call options granted to you if you accept the job have an exercise price of K5 and expire in three years. The call options cannot be exercised before maturity. The stock volatility is 28% and the three-year risk free rate is 3.6%. A call with a strike price of K30 costs K3. Required:Calculate the value of the call option.

Answer 1

Call Option is valued with the help of either binomial option model or Black-Scholes option model. We can use Black_scholes model to value the option. Following is the formula for Call option value under Black-Scholes model.

C = S(N(d) – Ke-rtN(dy)

Where

dı - Ini+(r + evt oſt

d2 = dı - 0 Vt

Now,

St= 5

K=5

r=3.6%

t=3

0. = 28%

d1=0.65716; d2= -0.46867

N(d1)= 0.7446: N(d2)= 0.31965

Hence, C= 2.2849