Question

Roslin Robotics stock has a volatility of 26% and a current stock price of $56 per share. Roslin pays no dividends. The​ risk-free interest is 6%. Determine the​ Black-Scholes value of a​ one-year, at-the-money call option on Roslin stock.

Answer 1

In this case, S0 = 56; X = 56; r = 0.06; sd = 0.26 and T = 1

d1 = [{ln(S0/X)} + {t(r - q + sd²/2)}] / [sd(t)^1/2]

= [{ln(56/56)} + {(1)(0.06 + 0.26²/2)}] / [0.26(1)^1/2]

= 0.0938 / 0.26 = 0.3608

d2 = d1 - [s(t)1/2]

= 0.3608 - [0.26(1)^1/2]

= 0.3608 - 0.26 = 0.1008

C = [S0 * e-qt * N(d1)] - [X * e-rt * N(d2)]

= [$56 * e^-0*(1) * N(0.3608)] - [$56 * e^-0.06*(1) * N(0.1008)]

= [$56 * 1 * 0.6409] - [$56 * 0.9418 * 0.5401]

= $35.89 - $28.49 = $7.40