Application of kernel-based stochastic gradient algorithms to option pricing

Kengy Barty, Pierre Girardeau, Cyrille Strugarek and 
Jean-Sébastien Roy
july, 2008
Type de publication :
Article (revues avec comité de lecture)
Journal :
Monte Carlo Methods and Applications, vol. 14, pp. 99-127
Mots clés :
Valorisation d'options américaines, méthodes de Monte-Carlo, approximation par noyaux, algorithmes stochastiques.
Résumé :
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.
BibTeX :
    author={Kengy Barty and Pierre Girardeau and Cyrille Strugarek and 
           Jean-Sébastien Roy },
    title={Application of kernel-based stochastic gradient algorithms to 
           option pricing },
    journal={Monte Carlo Methods and Applications },
    year={2008 },
    volume={14 },