Suppose someone longs a $75 stock when the risk-free rate is 10 percent. The stock is held for 2 years and can go up by 33.33% of its value every year. 

a. If the investor purchased a call option with a $60 strike price, solve for the call option price using the binomial pricing model. Be sure to sketch the binomial lattice. 

b. If the investor purchased a put option also with a $60 strike price, solve for the put option price using the binomial pricing model. Be sure to sketch the binomial lattice. 

c. Compute the call gamma and the put gamma, using the numbers you have obtained from period two options. 

d. If the stock price changes, what is the probability that the moneyness of the option will change? Explain your answer. 

e. Use the put-call parity relationship to test the binomial pricing model.