A q-binomial extension of the CRR asset pricing model

被引：2

作者：

Breton, Jean-Christophe ^{[1
,5
]}

El-Khatib, Youssef ^{[2
]}

Fan, Jun ^{[3
]}

Privault, Nicolas ^{[4
]}

机构：

[1] Univ Rennes, Rennes, France

[2] United Arab Emirates Univ, Al Ain, U Arab Emirates

[3] Univ Nottingham Ningbo, Ningbo, Peoples R China

[4] Nanyang Technol Univ, Singapore, Singapore

[5] Univ Rennes, CNRS, UMR 6625, IRMAR, F-35000 Rennes, France

来源：

STOCHASTIC MODELS | 2023年 / 39卷 / 04期

关键词：

Continuous-time limit; CRR model; default with logistic failure rate; Kemp random walk; option pricing; weak convergence; q-binomial coefficients; ORDER CONVERGENCE; EUROPEAN OPTIONS; PRICES;

D O I：

10.1080/15326349.2023.2173231

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：772 / 796

页数：25

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