Pricing and hedging of best of asset options, a Malliavin calculus approach

Abstract

In this paper, we developed a formulation for pricing and Hedging of Rainbow Option and in particular the Best of Asset Option with pay-off max(S1,S2, …Sn,K).Rainbow option is a class of options that involves multiple assets and the behaviour of the underlying determine the specific type of the Rainbow option in question. In this study, we consider a Best of Asset type of Rainbow option with Pay-off given as max (S1,S2, …Sn,K). Here, we make use of the Malliavin Calculus and the Clack Ocone formula to formulate the Price and the Hedging strategy in closed form.The price of the Best of Asset option will be determined from the Clark-Haussmann Ocone CHO formula as the discounted expectation of the pay-off f (w) while the hedging portfolio will be obtained from the integrant in the Martingale representation theorem set up of the Payoff.The integrant involves the Malliavin derivative of the pay-off and its market price of risk and in the case that the latter is time -dependent, it reduces to the discounted expectation of the malliavin derivative of f (w) conditioned with respect to the filtration.