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
Date Written: January 2, 2008
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.
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