Question

Working with the Black-Scholes model and a call option for a particular stock, you calculate the following values:
d₁ = 0.73

d₂=0.58

N(d1)= 0.85

N(d₂) = 0.57

C₀ = 3.46

Given the information that you have, what is the best estimate as to what the new call price would be if shares of the underlying stock increased by $0.24?

For this question, you do not need to calculate any of the Black-Scholes equations to solve for d₁, d₂, or C₀

Answer 1

Following is formula to calculate the value of call option under the Black-Scholes Model

C0 = P*N (d1) - N (d2) *X*e ^ (-r*t) ………………………. (1)

Where

C0 = call price = $3.46

P = current stock price of underlying stock

N = cumulative standard normal probability distribution

N(d1)= 0.85

N(d2) = 0.57

t = days until expiration

Standard deviation, SD = σ

X = option strike price

r = risk free interest rate =

e = exponential function = 2.7183

Formula to calculate d1 and d2 are -

d1 = {ln (P/X) +(r+ σ^2 /2)* t}/σ *√t = 0.73

d2 = d1 – σ *√t = 0.58

If shares of the underlying stock increased by $0.24 and other things remained the same; we can see in equation (1) that the call price will increase by change in price of underlying stock * d1 (N)

Therefore, the best estimate as to what the new call price = Old call price + change in price of underlying stock * d1 (N)

= $3.46 + $0.24 * 0.85

= $3.664