The explicit solution and precise distribution of CKLS model under Girsanov transform

TL;DR

This paper establishes a transformation linking CKLS and CIR models, providing explicit solutions and distributions for CKLS models, along with moment estimates, under a new probability measure.

Contribution

It introduces a transformation that relates CKLS models to CIR models and derives explicit solutions and distributions for CKLS models under a new measure.

Findings

Explicit solutions for CKLS models obtained

Precise distribution formulas derived for CKLS models

Moment estimations provided for CKLS models

Abstract

We study the relation between CKLS model and CIR model. We prove that under a suitable transformation, any CKLS model of order $\frac{1}{2}<\gamma<1$ or $\gamma> 1$ corresponds to a CIR model under a new probability space. Moreover, we get the explicit solution and the precise distribution of the CKLS model at any time $t$ under the new probability measure. We also give the moment estimation of CKLS model.