Fi,2), w3, w4),0,S2], and F2 be the collection of all subsets of S2. Consider a riskless asset with price process S (S,t - 0,1,2) where S0 1 for all t, and a risky asset with price process S Si,t 0,1,2) such that Then X max(0, S 6, S1 - 6, S2-6) is the value at time T of a so-called look-back option, where this value de- pends on the maximum of the prices of the underlying asset S1 over the time interval from 0 to T. 3.7. Exercises 53 (a) Draw a tree to indicate the possible "paths" followed by the risky asset price process S1 (b) Find an equivalent martingale measure for the model. (c) Find a replicating strategy for the option whose value at time T is given by X (d) What is the arbitrage free price for the option at time zero? Fi,2), w3, w4),0,S2], and F2 be the collection of all subsets of S2. Consider a riskless asset with price process S (S,t - 0,1,2) where S0 1 for all t, and a risky asset with price process S Si,t 0,1,2) such that Then X max(0, S 6, S1 - 6, S2-6) is the value at time T of a so-called look-back option, where this value de- pends on the maximum of the prices of the underlying asset S1 over the time interval from 0 to T. 3.7. Exercises 53 (a) Draw a tree to indicate the possible "paths" followed by the risky asset price process S1 (b) Find an equivalent martingale measure for the model. (c) Find a replicating strategy for the option whose value at time T is given by X (d) What is the arbitrage free price for the option at time zero