A put option on a stock with three months to maturity has the exercise price of $60. The stock is currently traded at $59 per share and a volatility of 30% per annum. The continuously compounded risk free rate is 3% per annum.

a. Using one month steps, what would be the price of the option if it is a European put option?

b. What is the price of the option if it is an American put option which could be exercised early? When is it likely to be exercised?