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Modeling and pricing with a random walk in random environment

Author

Listed:
  • Isabel Castro

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

  • Carlos G. Pacheco

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

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.

Suggested Citation

  • Isabel Castro & Carlos G. Pacheco, 2020. "Modeling and pricing with a random walk in random environment," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 1-20, December.
    • Handle: RePEc:wsi:ijfexx:v:07:y:2020:i:04:n:s242478632050053x
    DOI: 10.1142/S242478632050053X
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    Cited by:

    1. Héctor Jasso-Fuentes & Carlos G. Pacheco & Gladys D. Salgado-Suárez, 2023. "A discrete-time optimal execution problem with market prices subject to random environments," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 562-583, October.

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