Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view, 21 December 2017
Bruno Bouchard, Ki Wai Chau, Arij Manai, Ahmed Sid-Ali:
We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear reaction/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is
not efficient, while a simple randomization procedure provides very good results.
https://wakeupcall.project.cwi.nl/research-topics/papers/ki-wai-chau/1712-07383.pdf/view
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Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view, 21 December 2017
Bruno Bouchard, Ki Wai Chau, Arij Manai, Ahmed Sid-Ali:
We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear reaction/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is
not efficient, while a simple randomization procedure provides very good results.