Question

What is the price of a European put option on a stock when the stock price is $69, the strike price is $70, the interest rate is 5%, the stocks volatility is 35%, and the exercise time is six months?

Answer 1

Using Black-Scholes model, we have

Inputs: Current stock price (S) Strike price (K) Time until expiration(in years) volatility (s) risk-free rate (0) 69.00 70.00 0.500 35.0% 5.00%

Formulas:

d1 = {ln(S/K) + (r +s^2/2)t}/(s(t^0.5))

d2 = d1 - (s(t^0.5))

N(-d1) - Normal distribution of -d1

N(-d2) - Normal distribution of -d2

P = K*(e^(-rt))*N(-d2) - S*N(-d1)

Result:

d1	0.1666
d2	(0.0809)
N(-d1)	0.4338
N(-d2)	0.5322
Put premium (P)	6.4014

Put price is $6.4014