An FBSDE Approach to American Option Pricing with an Interacting Particle Method
In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise premium can be cast into the form of a decoupled non-linear FBSDE. We numerically solve the FBSDE by applying an interacting particle method recently proposed by Fujii and Takahashi (2012d), which allows one to perform a Monte Carlo simulation in a fully forward-looking manner. We perform the fourth-order analysis for the Black-Scholes (BS) model and the third-order analysis for the Heston model. The comparison to those obtained from existing tree algorithms shows the effectiveness of the particle method.
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- Marek Rutkowski, 1994. "The Early Exercise Premium Representation Of Foreign Market American Options," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 313-325.
- Masaaki Fujii & Akihiko Takahashi, 2012. "ANALYTICAL APPROXIMATION FOR NON-LINEAR FBSDEs WITH PERTURBATION SCHEME," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1250034-1-1.
- S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
- Duffie, Darrell & Huang, Ming, 1996. " Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-49, July.
- Masaaki Fujii & Akihiko Takahashi, 2011. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," Papers 1106.0123, arXiv.org, revised Jan 2012.
- Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," Papers 1202.0608, arXiv.org, revised Sep 2012.
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