Illustrate the concept of risk-neutral pricing by valuing the following exotic derivative. The derivative is "European", i.e. it only pays out at the end of the contract (1 year from now). The payoff of the derivative equals max(Smax - K; 0); where Smax denotes the maximum observed price between now (t) and the end of the contract (T = t + 1) and K is the strike price. The derivative hence locks in the maximum price gain above K: Consider the following situation: the current price of the asset St = 110; K = 100: Price the derivative (i.e. compute the current price of the derivative, using the binomial tree approach), on the basis of a partition of time in three levels _t = 1=3 and assuming that the upstate u(t = 1/3) = 1.2 and d(t = 1/3) = 1/1.2:Finally the gross interest rate over the interval t = 1/3 is given by Rf(t = 1/3) = 1.05. Explain your answer in detail an illustrate graphically.