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A q-binomial extension of the CRR asset pricing model

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  • Jean-Christophe Breton
  • Youssef El-Khatib
  • Jun Fan
  • Nicolas Privault

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.

Suggested Citation

  • Jean-Christophe Breton & Youssef El-Khatib & Jun Fan & Nicolas Privault, 2021. "A q-binomial extension of the CRR asset pricing model," Papers 2104.10163, arXiv.org, revised Feb 2023.
    • Handle: RePEc:arx:papers:2104.10163
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    References listed on IDEAS

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