Question

What is the value of a call option if the underlying stock price is $67, the strike price is $69, the underlying stock volatility is 31 percent, and the risk-free rate is 4 percent? Assume the option has 110 days to expiration. (Use 365 days in a year. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Value of a call option?

*Please note that this is the complete question and no other info is available. Also, 5.08 is not correct

Answer 1

In this case, S0 = 67; K = 69; r = 0.04; = 0.31 and T = 110/365

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

     = [{ln(67/69)} + {(110/365)(0.04 + 0.31²/2)}] / [0.31(110/365)^1/2]

     = -0.0029 / 0.1702 = -0.0169

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

     = -0.0169 - [0.31(110/365)^1/2]

= -0.0169 - 0.1702 = -0.1871

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

= [67 x e^-0*(110/365) x N(-0.0169)] - [69 x e^{-0.04*(110/365)} x N(-0.1871)]

= [67 x 0.4933] - [69 x 0.9980 x 0.4258]

= 33.05 - 29.03 = 4.02, or $4.02