Question

Roslin Robotics stock has a volatility of

24 %24%

and a current stock price of

$ 51$51

per share. Roslin pays no dividends. The​ risk-free interest is

6 %6%.

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

​$nothing.

​(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 =		51
t = time to expiry =		1
K = Strike price =		51
r = Risk free rate =		6.0%
q = Dividend Yield =		0%
σ = Std dev =		24%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(51/51)+(0.06-0+0.24^2/2)*1)/(0.24*1^(1/2))
d1 = 0.37
d2 = d1-σ*t^(1/2)
d2 =0.37-0.24*1^(1/2)
d2 = 0.13
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.644309
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.551717
Value of call= 51*0.644309-0.551717*51*e^(-0.06*1)
Value of call= 6.36