Question

Consider stock S, which is traded at the price of $45, and has a return volatility of 43% pa. The riskfree rate of interest is 3% pa. What is the price of 3-month call option with exercise price of $48?

Write the answer in number, round it to 2 decimal places.

Answer 1

We can use The Black-Scholes Model call option formula

C = SN (d1) - N (d2) Ke ^ (-rt)

Where,

C = call value =?

S = current stock price =$45

N = cumulative standard normal probability distribution

t = days until expiration = 3 months = 0.25 years

Standard deviation σ = 43% = 0.43

K = option exercise price = $ 48

r = risk free interest rate = 3% = 0.03

Formula to calculate d1 and d2 are -

d1 = {ln (S/K) +(r+ σ^2 /2)* t}/σ *√t

= {ln (45/48) + (0.03 + (0.43^2)/2) * 0.25} / 0.43 * √0.25

= -0.15780

d2 = d1 – σ *√t = -0.15780 – 0.43 *√0.25 = -0.37280

Now putting the value in the above formula

C = 45 * N (-0.15780) – N (-0.37280)* 48 * e^ (-0.03*0.25)

= 45* 0.43731– 0.35465*48 * 0.9925 = 2.78

Price of call option is $ 2.78