Please answer this question clearly, thank you.
2. [8 marks] Static hedging with options. Consider a parametrised family of European contingent claims with the payoff Y at time T given by the following expression Y = min (K,L - Sr+2 L-Srl) where a real number L > 0 is fixed and K is an arbitrary real number such that K>0. (a) Sketch the profile of the payoff Y as a function of the stock price Sr and find a decomposition of Y in terms of terminal payoffs of standard call and put op- tions with expiration date T. Notice that the decomposition of Y may depend on the value of the variable K. (b) Assume that call and put options are traded at time 0 at some finite prices. For each value of K > 0, find a representation of the arbitrage price To(Y) of the claim Y at time t = 0 in terms of prices of call and put options at time 0 using the decompositions from part (a). (c) Consider a complete arbitrage-free market model M=(B, S) defined on some finite state space 2. Show that the arbitrage price of Y at time t = 0) is a monotone function of the variable K > 0 and find the limits lim k 334 To(Y), lim Kyo To(Y) and lim K 10 To(Y) using the representations from part (b). (d) For any K > 0, examine the sign of an arbitrage price of the claim Y in any (not necessarily complete) arbitrage-free market model M = (B, S) with a finite state space 2. Justify your answer. 2. [8 marks] Static hedging with options. Consider a parametrised family of European contingent claims with the payoff Y at time T given by the following expression Y = min (K,L - Sr+2 L-Srl) where a real number L > 0 is fixed and K is an arbitrary real number such that K>0. (a) Sketch the profile of the payoff Y as a function of the stock price Sr and find a decomposition of Y in terms of terminal payoffs of standard call and put op- tions with expiration date T. Notice that the decomposition of Y may depend on the value of the variable K. (b) Assume that call and put options are traded at time 0 at some finite prices. For each value of K > 0, find a representation of the arbitrage price To(Y) of the claim Y at time t = 0 in terms of prices of call and put options at time 0 using the decompositions from part (a). (c) Consider a complete arbitrage-free market model M=(B, S) defined on some finite state space 2. Show that the arbitrage price of Y at time t = 0) is a monotone function of the variable K > 0 and find the limits lim k 334 To(Y), lim Kyo To(Y) and lim K 10 To(Y) using the representations from part (b). (d) For any K > 0, examine the sign of an arbitrage price of the claim Y in any (not necessarily complete) arbitrage-free market model M = (B, S) with a finite state space 2. Justify your
