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 P. Consider a European contingent claim X with maturity T and the following payoff X = max (K, Sr) - LST where K = e'T S, and L > 0 is an arbitrary constant. We take for granted the Black-Scholes pricing formulae for the call and put options. (a) Sketch the profile of the payoff X as a function of the stock price Sr at time T and show that X admits the following representation X = K + Cr(K) - LST where Cr(K) denotes the payoff at time T of the European call option with strike K. (b) Find an explicit expression for the arbitrage price :(X) at time 0 0 is an arbitrary constant. We take for granted the Black-Scholes pricing formulae for the call and put options. (a) Sketch the profile of the payoff X as a function of the stock price Sr at time T and show that X admits the following representation X = K + Cr(K) - LST where Cr(K) denotes the payoff at time T of the European call option with strike K. (b) Find an explicit expression for the arbitrage price :(X) at time 0