A q-binomial extension of the CRR asset pricing model

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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 (Formula presented.) is obtained.

Original languageEnglish
Pages (from-to)772-796
Number of pages25
JournalStochastic Models
Volume39
Issue number4
DOIs
Publication statusPublished - 2023

Keywords

  • CRR model
  • Continuous-time limit
  • Kemp random walk
  • default with logistic failure rate
  • option pricing
  • q-binomial coefficients
  • weak convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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