Question

A stock index is trading at 1,544. Consider a call option, with r = 1.00% , q = 2.00% , volatility at 30.00%, the strike price is 1,700 and time to expiry is 1 year. What is the probability that the option will pay off? (Just calculate the number, you don’t have to derive the expression.)

This is all the info I got.

Answer 1

S = dividend adjusted stock price

So = Current stock price = 1544

K = Strike price = 1700

r = risk-free rate = 1%

q= dividend yield =2%

Volatility = 30%

T=1

S= 1544* e^(-0.02*1) = $1513.426

Substituting the values,

d1 = (ln(1513.426/1700) + (0.01+(0.3*0.3/2))*1)/(0.3*1) = -0.204174

d2= -0.204174 - (0.3*1) = -0.50417

N(d2) = 0.307071

N(d2) is the probability of the option expiring in the money (ie. option will pay-off)

Hence, the probability is 0.307071