Black-Scholes model: European claim.

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, ST) LST where K ert So and L > 0 is an arbitrary constant. We take for granted the Black-Scholes pricing formulae for the call and put options. = (c) Find the limit lim 140 70(X). (d) Find the limit lim o too To(X). (e) Explain why the price of 70(X) is positive when L = 1 by analysing the payoff X when L=1. 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, ST) LST where K ert So and L > 0 is an arbitrary constant. We take for granted the Black-Scholes pricing formulae for the call and put options. = (c) Find the limit lim 140 70(X). (d) Find the limit lim o too To(X). (e) Explain why the price of 70(X) is positive when L = 1 by analysing the payoff X when L=1