Question

A non-dividend paying stock price is $100, the strike price is $100, the risk-free rate is 6%, the volatility is 15% and the time to maturity is 3 months which of the following is the price of an American Call option on the stock. For full credit I expect each step of the calculations tied to the correct formulas.

Answer 1

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

     = [{ln(100/100)} + {0.25(0.06 + 0.15²/2)}] / [0.15(0.25)^1/2]

     = 0.0178 / 0.075 = 0.2375

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

     = 0.2375 - [0.15(0.25)^1/2]

= 0.5235 - 0.075 = 0.1625

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

= [100 x e^-0*0.25 x N(0.2375)] - [100 x e^-0.06*0.25 x N(0.1625)]

= [100 x 0.5939] - [100 x e^-0.06*0.25 x 0.5645]

= 59.39 - 55.61 = 3.77, or $3.77