Question

The Black-Scholes price of a three-month 50–strike put option is $0.75. The stock is trading at $49. Given an interest rate of 2%, and no dividends, what is the implied volatility of the stock extracted from this option?

(a) 0.55
(b) 0.66
(c) 0.77
(d) 0.88

Answer 1

Implied volatility will be find using Black sholes formula which is given as below:

P = Xe –r(T-t) [1-N(d2)] – S [1-N(d1)]

where P is $.75

X is strike price that is $50

S is stck price that is $49

r is risk free rate that is 2%

(T - t) is time that is 3 month

N(d2) and N(d1) will be find using

d2 = −log(X/S) − (r − 1 /2*σ^2) * (T-t)/σ √(T - t)

here σ is implied volatiltiy

putting all the value we will get the value of implied volatitlity will be .77.

Thus the correct answer is option c.