A general Multidimensional Monte Carlo Approach for Dynamic Hedging under stochastic volatility
Abstract
In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for Galtchouk-Kunita-Watanabe decompositions, we propose a feasible and constructive methodology which allows us to compute pure hedging strategies w.r.t arbitrary square-integrable claims in incomplete markets. In particular, the methodology can be applied to quadratic hedging-type strategies for fully path-dependent options with stochastic volatility and discontinuous payoffs. We illustrate the method with numerical examples based on generalized Follmer-Schweizer decompositions, locally-risk minimizing and mean-variance hedging strategies for vanilla and path-dependent options written on local volatility and stochastic volatility models.
Cite
@article{arxiv.1308.1704,
title = {A general Multidimensional Monte Carlo Approach for Dynamic Hedging under stochastic volatility},
author = {Dorival Leão and Alberto Ohashi and Vinicius Siqueira},
journal= {arXiv preprint arXiv:1308.1704},
year = {2013}
}
Comments
Some typos are corrected in Section 6