Please provide step by step solution with all formulas shown and explanation answer.

1.Consideran American put option written on a non-dividend paying stock. The strike price is 50. The put will expire in two years. The stock pricefollows a two-period binomial as in the graph. At each date,the natural probability that thestock price increases is one half. The stock is currently selling at 50. Atwo-year annual coupon bond with annual coupon rate of 10% is selling at par.

(a)Whatis the price of the American put option?

(b)Whatis the price of an American call option written on the same stock with the samestrike price and expiration date?

(c)Proveor disprove: the put-call parity holds for American puts and American calls.