Question

(PLEASE SHOW ALL WORK)

Roslin Robotics stock has a volatility of 25% and a current stock price of $48 per share. Roslin pays no dividends. The risk-free interest is 5%. Determine the Black-Scholes value of a one-year, at-the-money call option on Roslin stock. The Black-Scholes value of a one-year, at-the-money call option on Roslin stock is $ . (Round to the nearest cent.)

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		48
t = time to expiry =		1
K = Strike price =		48
r = Risk free rate =		5.0%
q = Dividend Yield =		0%
σ = Std dev =		25%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(48/48)+(0.05-0+0.25^2/2)*1)/(0.25*1^(1/2))
d1 = 0.325
d2 = d1-σ*t^(1/2)
d2 =0.325-0.25*1^(1/2)
d2 = 0.075
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.627409
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.529893
Value of call= 48*0.627409-0.529893*48*e^(-0.05*1)
Value of call= 5.92