Question

Suppose that you just joined the Kuala Lumpur office of the Standard Chartered Bank. On your...

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.

Homework Answers

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

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