Question

There is an American put option on a stock that expires in two months. The stock price is $82, and the standard deviation of the stock returns is 67 percent. The option has a strike price of $90, and the risk-free interest rate is an annual percentage rate of 6 percent. What is the price of the option?

Answer 1

S0 = underlying price	$82
E = strike price	$90
? = volatility (% p.a.)	0.67
?^2 = variance (% p.a.)	0.45
r = continuously compounded risk-free interest rate (% p.a.)	0.06
d = continuously compounded dividend yield (% p.a.)	0
t = time to expiration (years in %) =	0.1667
C = S × e–dt × N(d1) – E × e–Rt × N(d2)
d1 = [ln(S/E) + (R – d + ?2 / 2) × t] / (? × sqrt(t))
d2 = d1 – ? × sqrt(t)
d1 = [ln($82/$90+ (.06 - 0 + .45/2) × .1667] / (.67× sqrt (.1667 )	-0.1670
d2 =- .0278 - .67x sqrt(.1667)	-0.44
Normal Distribution N( d1) using NormDIST	0.4337
Normal Distribution N(d2)	0.33
e-dt	1
e-rt	0.990049834
C = $82 x 1 x .4889 - $90 x .9900 x .38	$6.177
(b)Value of put p(0) = e?rT KN(?d2) ? S(0)N(?d1).
P = $90e – .06(.1667) +6.177 – 82	$13.28