Discussions are underway between Daimler and General Motors (GM) regarding the sale by Daimler of 10 million shares of Chrysler to GM. The transaction will take place in 6 months. The current price of Chrysler is $100 per share. The Chrysler stock does not pay dividends and its annual volatility is 25%. The risk-free interest rate (with continuous compounding) is 4% per annum. Both parties seem willing to fix the delivery price that will be paid when the transaction will take place. Therefore, GM is going to buy a call option (from Daimler) for the Chrysler shares in 6 months with a strike price equal to the current spot price.

(a) (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 Chrysler's shares will go up in 6 months?

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

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