Pricing and Hedging Contingent Claims via Malliavin Calculus

Emilio Barucci and Maria Elvira Mancino - University of Florence

In this paper we present a method for pricing and hedging European contingent claims. We provide a Wiener Chaos decomposition of the no-arbitrage price of a contingent claim and of the associated hedging strategy and then we derive their Hermite polynomials expansion, assuming that the final payoff is a square integrable random variable. A complete analysis is developed when the stochastic process for the asset price is characterized by deterministic coefficients, some results are obtained when they are stochastic. In some cases the coefficients of the expansions are explicitly computed. The methodology is applied to dynamic hedging under transaction costs and to recover the risk neutral probability implied in option prices.

Scheduled for Session 2.2 Modeling Economic Dynamics And Adjustment Costs