2. [8 marks] Static hedging with options. Consider a parametrised family of European contingent claims with the payoff X(L) at time T given by the following expression X(L) = min (2|K Srl + K - Sr, L) where a real number K > 0 is fixed and L is an arbitrary real number such that L>0. (c) Consider a complete arbitrage-free market model M= (BS) defined on some finite state space N. Show that the arbitrage price of X(L) at time t = 0) is a monotone function of the variable L > 0 and find the limits lim (+3K T0(X(L)), lim 1700 70(X(L)) and lim 70 70(X(L)) using the representations from part (b). 2. [8 marks] Static hedging with options. Consider a parametrised family of European contingent claims with the payoff X(L) at time T given by the following expression X(L) = min (2|K Srl + K - Sr, L) where a real number K > 0 is fixed and L is an arbitrary real number such that L>0. (c) Consider a complete arbitrage-free market model M= (BS) defined on some finite state space N. Show that the arbitrage price of X(L) at time t = 0) is a monotone function of the variable L > 0 and find the limits lim (+3K T0(X(L)), lim 1700 70(X(L)) and lim 70 70(X(L)) using the representations from part (b)