A stock price is currently $40. Over each of the next two 3-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum with continuous compounding. 3.1. Draw two binomial trees: one showing the stock price variations for an option on this stock expiring in 6-month, and the second tree showing the value of the risk-free asset at each node of the three over the 6-month period. [3+3] 3.2. What is the value of a 6-month European put option with a strike price of $42 ? [6] 3.3. What is the value of a 6 -month European Call option with a strike price of 342 ? [5]