Work

A q -binomial extension of the CRR asset pricing model

Year: 2023

Type: article

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.

Source: Stochastic Models

DOI: 10.1080/15326349.2023.2173231

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

Institutions: Université de Rennes, United Arab Emirates University, University of Nottingham Ningbo China, University of Nottingham, Nanyang Technological University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Ministry of Education - Singapore, Agence Nationale de la Recherche

Awards: Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation, G7371357886