Just c,d,e. a,b has been answered in chegg. Please dont use the same answer. thank you very much

[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,ST)LST where K=erTS0 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 ST at time T and show that X admits the following representation X=K+CT(K)LST 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 t(X) at time 0t0 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 ST at time T and show that X admits the following representation X=K+CT(K)LST 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 t(X) at time 0t