Question

Suppose that you just joined the Kuala Lumpur office of the Standard Chartered Bank. On your first day on the job, you have been asked to value a European option on a stock. The stock is currently trading at 60.00 ringgits per share. The 4-month nominal risk-free ringgit interest rate is 6.5%. Your colleague, who was previously working in the stock, has estimated the weekly return volatility (i.e., the volatility based on weekly return) to be 3.1%.

(a)       Find the value of a 4-month European call option on the stock with strike or exercise price equal to 55 ringgits.

(b)       Find the value of a 8-month European call option on the stock with strike or exercise price equal to 55 ringgits.

Answer 1

Annualized volatility (since there are 52 weeks in an year) = Weekly volatility*(52^0.5)

Annualized volatility = 0.031*(52^0.5) = 22.35%

Part a)

T = 4/12 years

d1 = (ln(60/55) + (0.065+0.2235*0.2235/2)*(4/12))/(0.2235*(4/12)^0.5)

d1 = 0.906

d2 = 0.906- (0.2235*(4/12)^0.5) = 0.777

N(d1) = 0.817

N(d2) = 0.781

c = 60*0.817- (55*e^(-0.065*4/12))*0.781

c = 6.98

Hence, the call price = 6.98 ringgits

Part b)

T = 8/12 years

d1 = (ln(60/55) + (0.065+0.2235*0.2235/2)*(8/12))/(0.2235*(8/12)^0.5)

d1 = 0.8055

d2 = 0.8055- (0.2235*(8/12)^0.5) = 0.6230

N(d1) = 0.790

N(d2) = 0.7333

c = 60*0.790- (55*e^(-0.065*8/12))*0.7333

c = 8.778

Hence, the call price = 8.778 ringgits