Advanced Monte Carlo methods for barrier and related exotic options
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.
|Date of creation:||Dec 2009|
|Date of revision:|
|Publication status:||Published in Bensoussan A., Zhang Q. et Ciarlet P. Mathematical Modeling and Numerical Methods in Finance, Elsevier, pp.497-528, 2009, Handbook of Numerical Analysis, <10.1016/S1570-8659(08)00012-4>|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00319947|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
References listed on IDEAS
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- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Phelim Boyle & Yisong Tian, 1998. "An explicit finite difference approach to the pricing of barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 17-43.
- Gobet, Emmanuel & Menozzi, Stéphane, 2004. "Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 201-223, August.
- L.C.G. Rogers & E.J. Stapleton, 1997. "Fast accurate binomial pricing," Finance and Stochastics, Springer, vol. 2(1), pages 3-17.
- Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
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