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Advanced Monte Carlo Methods for Barrier and Related Exotic Options

MATHEMATICAL MODELLING AND NUMERICAL METHODS IN FINANCE, A. Bensoussan, Qiang Zhang, Philippe Ciarlet, eds., Forthcoming

36 Pages Posted: 10 Sep 2008  

Emmanuel Gobet

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Date Written: January 2, 2008

Abstract

In this work, we present advanced Monte Carlo techniques applied to the pricing of barrier options and other related exotic contracts. It covers in particular the Brownian bridge approaches, the barrier shifting techniques (BAST) and their extensions as well. We leverage the link between discrete and continuous monitoring to design efficient schemes, which can be applied to the Black-Scholes model but also to stochastic volatility or Merton's jump models. This is supported by theoretical results and numerical experiments.

Suggested Citation

Gobet, Emmanuel, Advanced Monte Carlo Methods for Barrier and Related Exotic Options (January 2, 2008). MATHEMATICAL MODELLING AND NUMERICAL METHODS IN FINANCE, A. Bensoussan, Qiang Zhang, Philippe Ciarlet, eds., Forthcoming. Available at SSRN: https://ssrn.com/abstract=1265669

Emmanuel Gobet (Contact Author)

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees ( email )

Palaiseau Cedex, 91128
France

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