1. A q-binomial extension of the CRR asset pricing model.
- Author
-
Breton, Jean-Christophe, El-Khatib, Youssef, Fan, Jun, and Privault, Nicolas
- Subjects
PRICES ,RANDOM walks ,BLACK-Scholes model ,DEFAULT (Finance) ,PROBABILITY theory - 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. [ABSTRACT FROM AUTHOR]- Published
- 2023
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