5. Determine the price of a two-year AMERICAN put option with a strike price of $65 on a stock that is currently priced at $49.50 which has a volatility of 48%pa if the risk free rate was 2.7%. After the first year, the stock pays a dividend of $2 and after the second year, the stock is expected to pay a dividend of $2.15. 

a) What is the delta of this option? 

b) What is the probability of a move up for this stock? 

c) What is the probability of a move down for this stock? 

d) What is the fair value for the call option with the same strike price? 

e) What is the delta of the call option? 

f) What is the proportional move up for this stock 

g) What is the proportional move down for this stock