Optimal Delaunay and Voronoi quantization schemes for pricing American style options

Gilles Pagès (1) , Benedikt Wilbertz (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We review in this article pure quantization methods for the pricing of multiple exercise options. These quantization methods have the common advantage, that they allow a straightforward implementation of the Backward Dynamic Programming Principle for optimal stopping and stochastic control problems. Moreover we present here for the first time a unified discussion of this topic for Voronoi and Delaunay quantization and illustrate the performances of both methods by several numerical examples.

Mots clés: Optimal vector quantization; Voronoi diagram; Delaunay triangulation; American option; Quantization tree

Domaines: Probabilités [math.PR]

Gilles Pagès, Benedikt Wilbertz. Optimal Delaunay and Voronoi quantization schemes for pricing American style options. Numerical Methods in Finance, 12, Springer, pp.171-213, 2012, Springer Proceedings in Mathematics, ⟨10.1007/978-3-642-25746-9_6⟩. ⟨hal-00572709⟩