3. Build a three-step CRR stock price tree using the following information: maturity: 3 months, i.e. each step is one month annual volatility of the stock: 0.35 annual, continuously compounded risk-free rate: 1% stock price today: 50 (a) What is the risk-neutral probability in the tree? Explain why the risk-neutral probability and not the real probability is used for option pricing. [ 5 marks ] (b) Calculate the price of an American put option with strike K = 50.

(c) You realise that during the last step in the tree the firm announces earnings. Assume that the stock is twice as volatile during this last step. What is the price of the American put option from (a) now? [ 10 marks ] (d) The market is quoting a price of $4.50 for the put. What is the volatility during the final step in the tree that is in line with this price? [ 5 marks ]