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Article Dans Une Revue Stochastic Models Année : 2023

A q-binomial extension of the CRR asset pricing model

Youssef El-Khatib
  • Fonction : Auteur
Jun Fan
  • Fonction : Auteur
Nicolas Privault
  • Fonction : Auteur

Résumé

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, and 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(1/N) is obtained when the tilt and stretch parameters are set equal to one.

Dates et versions

hal-03205108 , version 1 (22-04-2021)

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Jean-Christophe Breton, Youssef El-Khatib, Jun Fan, Nicolas Privault. A q-binomial extension of the CRR asset pricing model. Stochastic Models, 2023, ⟨10.1080/15326349.2023.2173231⟩. ⟨hal-03205108⟩
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