Question

Great Edventure stock is at $800. The return has an annualized volatility (sigma) of 70%. IT pays no dividend and we are given a zero interest rate. Compute the Black-Merton-Scholes value on a 6-month European call option onGreat adevtnrue with a strike price at $1000.

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 =$800

N = cumulative standard normal probability distribution

t = days until expiration = 6 months = 0.5 years

Standard deviation σ = 70% = 0.70

K = option exercise price = $1000

r = risk free interest rate = 0%

Formula to calculate d1 and d2 are -

d1 = {ln (S/K) +(r+ σ^2 /2)* t}/σ *√t

= {ln (800/1000) + (0 + (0.70^2)/2) * 0.5} / 0.70 * √0.5

= -0.2033

d2 = d1 – σ *√t = -0.2033 – 0.70 *√0.5 = -0.6983

Now putting the value in the above formula

C = 800 * N (-0.2033) – N (-0.6983)* 1000 * e^ (-0*0.5)

= 800* 0.4194 – 0.2425 *1000 * 1 = $93.06

Price of call option is $93.06