You have been tasked with producing a report on the pricing of potential option investments being considered by your investment fund employer. The asset underlying the options is a stock (RSM) that has a current price of $50 and is expected to move up or down 8% over each upcoming 3-month period. The risk-free rate is 2% (APR with quarterly compounding).

(a) What is the price of an American put option with strike price of $55 and 1-year to expiry? What is the price of an European put option with a strike price of $55 and 1-year to expiry? Explain any differences between your answers.

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(b) Assume that you already own one share of RSM stock and that you would like to purchase one American put option from part a) to hedge your long position in the stock. In the same picture, draw (i) the gross and (ii) the net payoff (i.e., profit) diagrams at expiry for the hedged portfolio. What is the minimum value (net payoff) of the hedged position at expiry?

(c) How does the Delta of the American put option from part a) change if the price of RSM falls in each 3-month period? What would be your stock position at each 3-month interval if you wanted to maintain a delta neutral hedged position, i.e., if you wanted your portfolio to have a zero delta?

b and c please