A q-binomial extension of the CRR asset pricing model

Jean-Christophe Breton, Youssef El-Khatib, Jun Fan and Nicolas Privault

Papers from arXiv.org

Abstract: We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on $q$-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities varying according to a trend parameter on a non-self-similar binomial tree. In particular, it includes tilt and stretch parameters that control increment sizes. Option pricing formulas are written using $q$-binomial coefficients, and we study the convergence of this model to a Black-Scholes type formula in continuous time. A convergence rate of order $O(N^{-1/2})$ is obtained.

Date: 2021-04, Revised 2023-02
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