Roslin Robotics stock has a volatility of 26% and a current stock price of $49 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.)
As per Black Scholes Model | ||||||
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t) | ||||||
Where | ||||||
S = Current price = | 49 | |||||
t = time to expiry = | 1 | |||||
K = Strike price = | 49 | |||||
r = Risk free rate = | 5.0% | |||||
q = Dividend Yield = | 0% | |||||
σ = Std dev = | 26% | |||||
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) | ||||||
d1 = (ln(49/49)+(0.05-0+0.26^2/2)*1)/(0.26*1^(1/2)) | ||||||
d1 = 0.322308 | ||||||
d2 = d1-σ*t^(1/2) | ||||||
d2 =0.322308-0.26*1^(1/2) | ||||||
d2 = 0.062308 | ||||||
N(d1) = Cumulative standard normal dist. of d1 | ||||||
N(d1) =0.62639 | ||||||
N(d2) = Cumulative standard normal dist. of d2 | ||||||
N(d2) =0.524841 | ||||||
Value of call= 49*0.62639-0.524841*49*e^(-0.05*1) | ||||||
Value of call= 6.23 |
Roslin Robotics stock has a volatility of 26% and a current stock price of $49 per...
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