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Modeling and pricing with a random walk in random environment

Isabel Castro

Departamento de Matemáticas, CINVESTAV-IPN. A. Postal 14-740, Ciudad de México 07360, México

E-mail Address: micastro@math.cinvestav.mx

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and

Carlos G. Pacheco

Departamento de Matemáticas, CINVESTAV-IPN. A. Postal 14-740, Ciudad de México 07360, México

E-mail Address: cpacheco@math.cinvestav.mx

Corresponding author.

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https://doi.org/10.1142/S242478632050053XCited by:2 (Source: Crossref)

Abstract

We propose a parsimonious model for financial pricing that incorporates the existence of a random environment; such construction can be though as an extension of the Cox–Ross–Rubinstein (CRR) model. Our model is motivated from the Sinai random walk, but we mention the difficulty of applying such model if we try to use it with the CRR procedure. As it was done with Sinai’s walk, we provide a method to connect the most visited sites of the model with the minimum points of a function of the environment. We present some simulations and a numerical experiment to bring a new perspective.

This research was partially supported by CONACYT.

Keywords:

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