Application of kernel-based stochastic gradient algorithms to option pricing

Barty Kengy, Girardeau Pierre, Strugarek Cyrille and Roy Jean-Sébastien
Additional contact information
Barty Kengy: EDF R&D, 1 avenue du Général de Gaulle, 92141 Clamart Cedex, France. Email: kengy.barty@edf.fr
Girardeau Pierre: EDF R&D, also with the École Nationale des Ponts et Chaussées (ENPC) and the École Nationale Supérieure de Techniques Avancées (ENSTA), France. Email: pierre.girardeau@cermics.enpc.fr
Strugarek Cyrille: EDF R&D when this research was done also, currently at Calyon, France. Email: cyrille.strugarek@calyon.com

Monte Carlo Methods and Applications, 2008, vol. 14, issue 2, 99-127

Abstract: We present an algorithm for American option pricing based on stochastic approximation techniques. Besides working on a finite subset of the exercise dates (e.g. considering the associated Bermudean option), option pricing algorithms generally involve another step of discretization, either on the state space or on the underlying functional space. Our work, which is an application of a more general perturbed gradient algorithm introduced recently by the authors, consists in approximating the value functions of the classical dynamic programming equation at each time step by a linear combination of kernels. The so-called kernel-based stochastic gradient algorithm avoids any a priori discretization, besides the discretization of time. Thus, it converges toward the optimum of the non-discretized Bermudan option pricing problem.We present a comprehensive methodology to implement efficiently this algorithm, including discussions on the numerical tools used, like the Fast Gauss Transform, or Brownian bridge.We also compare our results to some existing methods, and provide empirical statistical results.

Keywords: American option pricing; Monte-Carlo methods; kernel approximation; stochastic algorithms (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1515/MCMA.2008.006

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