Pricing of Outperformance Option
We consider a European-style option written on the S&P500 Index (denoted S1) and the MSCI index (denoted S2) which payoff at maturity T is given by: C(S1(T), S2(T)) = max(aS1(T) − bS2(T), 0) Payoff analysis: 1. By choosing a suitable numeraire, show that the option payoff is merely the payoff of a call option on a new underlying with a given strike. Give the expression for the new underlying in function of S1 and S2 as well as the strike value. 1 2. Similarly, by choosing a suitable numeraire, show that the option payoff is merely the payoff of a put option on a new underlying with a given strike. Give also the expression for the new underlying in function of S1 and S2 as well as the strike value.
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