Assume that the current stock price (S0) is 42, and that it either increases at a rate of 10%(u=1:10) or it decreases at a rate of 5%(d=0:95) over a period of three months. Further assume a European call option written on the stock, with a strike price (K) equal to 40 and a time-to-maturity (T) equal to six months. The risk-free interest is 10% pa. (a) Draw a binomial tree showing the possible evolutions of the stock price over the next six months (i.e., until the maturity time of the option). (b) Compute the payoff of the European call option at maturity for each possible stock price, and indicate this payoff in the graph. (c) Compute the risk-neutral probability of an upward move and that of a downward move in the stock price. Do these differ across the binomial tree (i.e., are these different at time t=0 compared to, for example, time t=2) ? Why or why not? (d) Using the risk-neutral probabilities, compute the value of the European call option. (e) Would your answer to question (d) be different if the call option had not been European but instead American? Why or why not