Question

Let S = {S(t), t > 0) denote the price of a continuous dividend-paying stock. The prepaid forward price for delivery of one share of this stock in one year equals $98.02.

Assume that the Black-Scholes model is used for the evolution of the stock price. Consider a European call and European put option both with exercise date in one year. They have
the same strike price and the same Black-Scholes price equal to $9.37. What is the implied volatility of the underlying stock?

Answer 1

Answer:

Implied Volatility =

Expected range of Strike price of Stock = Prepaid Forward Price of Stock x Implied Volatility of Underlying stock x $\sqrt{No of Days / 365 days }$

$ 9.37 = $ 98.02 x  Implied Volatility of Underlying stock x  $\sqrt{365 Days / 365 days }$

$ 9.37 = $ 98.02 x Implied Volatility of Underlying stock x 1

Implied Volatility of Underlying stock = $ 9.37 / $ 98.02 = 0.0956 i.e 9.56%