You are a market maker at CBOE. A big institutional trader just purchased from you put options on 10 million shares of Tesla's stock. The option has a strike price of $725 and a maturity of 1 month. The current stock price of Tesla is $720 per share. The Tesla stock does not pay dividends and its annual volatility is 80%. The risk-free interest rate (with continuous compounding) is 2% per annum.

(7 pts.) If you were to use the risk neutral method to price the option, what should be u, d, and the risk neutral probability that the price of Tesla's shares will go up in 1 moth?

(8 pts.) If you want to hedge the short position of the put option using stocks and bonds, how many shares of Tesla should you trade? Should you long or short the stock?

(10 pts.) How much in total should you charge the institutional trader this option? Evaluate the option using a one-step Binomial tree. You can use either the risk-neutral or the no arbitrage argument.