Question

Stock price	=	$85
Exercise price	=	$80
Risk-free rate	=	3.80% per year, compounded continuously
Maturity	=	5 months
Standard deviation	=	55% per year

Find the put price of the option. Round your Z scores to 2 decimal spaces and provide an answer accurate to the nearest cent without the $ sign.

Answer 1

In this case, S0 = 85; X = 80; r = 0.038; sd = 0.55 and T = 5/12

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

= [{ln(85/80)} + {(5/12)(0.038 + 0.55²/2)}] / [0.55(5/12)^1/2]

= 0.1395 / 0.3550 = 0.3929

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

= 0.3929 - [0.55(5/12)^1/2]

= 0.3929 - 0.3550 = 0.0378

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

= [$80 * e^{-0.038*(5/12)} * N(-0.0378)] - [$85 * e^-0*(5/12) * N(-0.3929)]

= [$80 * 0.9843 * 0.4849] - [$85 * 1 * 0.3472]

= $38.18 - $29.51 = $8.67