A General Multidimensional Monte Carlo Approach for Dynamic Hedging under Stochastic Volatility

We propose a feasible and constructive methodology which allows us to compute pure hedging strategies with respect to arbitrary\udsquare-integrable claims in incomplete markets. In contrast to previous works based on PDE and BSDE methods, themainmerit\udof our approach is the flexibility of quadratic hedging in full generality without a priori smoothness assumptions on the payoff.\udIn particular, the methodology can be applied to multidimensional quadratic hedging-type strategies for fully path-dependent\udoptions with stochastic volatility and discontinuous payoffs. In order to demonstrate that our methodology is indeed applicable,\udwe provide a Monte Carlo study on generalized F¨ollmer-Schweizer decompositions, locally risk minimizing, and mean variance\udhedging strategies for vanilla and path-dependent options written on local volatility and stochastic volatility models.LNCC (Laboratório Nacional de Computação Científica, Brasil)CNPq (Grant no. 308.742