You own Macquarie Group Shares (MQG) currently valued at $170 per share, and believe the recent weakness in the banking system may present some downside risks. As a result, you decide to purchase a 2-month 'at-the-money' Put Option on MQG shares to protect your risk. The volatility of MQG shares is 25%, and the Shares pay a dividend of $5 at the end of month 1. The risk free rate is 4.5% for all maturities. All variables are required to be calculated using continuous compounding (recall use of e^rt). Show all workings and calculate:

The stock price Lattice over 2-months: E.g., Stock prices at t=1 (Su and Sd) and stock prices at t=2 (Suu, Sud, Sdu, and Sdd) (hint: make this a recombining tree)

The value of a 2-month European put option given by a two-step binomial tree (show all workings at t=2, t=1 and t=0)

Suppose a trader buys 1,000 European put options (10 put contracts). What position in the stock is necessary to hedge the traders position at the time of the trade

What is the value of your portfolio at V(0) and V(u)? What was the rate of return on this portfolio