2. [10 marks] Black-Scholes model: European claim. We place ourselves within the setup of the Black-Scholes market model M = (B, S) with a unique martingale measure 1?. Consider a European contingent claim X with maturity T and the following payoff X = max(K,ST) LST where K = e'TSu and L > 0 is an arbitrary constant. We take for granted the Black-Scholes pricing formulae for the call and put options. (3.) Sketch the prole of the payoff X as a function of the stock price ST at time T and show that X admits the following representation X = K + 01(K) L33 where CT(K) denotes the payoff at time T of the European call option with strike K. (b) Find an explicit expression for the arbitrage price m(X ) at time 0 S t