Suppose we have a 2-year European put with the strike price of $52. The current price of the underlying stock is $50. The volatility of returns on the underlying stock is 20% and the annual risk free rate is 5%.

1. Use two-period binomial model to price this option

2. Use three-period binomial model to price this option

3. Now, suppose that this is an American put option. Use two-period binomial model to price this option.