A stock has a current price of $50. You determine that the standard deviation () of the stocks returns has historically been 20% annually.

a) Use a three-step binomial model to find the value of an American Call option on the stock which expires in three months time and has a strike price of $45. The risk-free rate is 4% per annum.

b) Suppose you found an option with exactly these parameters trading in the market for a premium of $8. What would the implied volatility of the option be?