# Cox-Ingersoll-Ross Model¶

## Overview¶

In mathematical finance, the Cox-Ingersoll-Ross model describes the evolution of interest rates. It is a type of “one factor model” (short rate model) as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives. It was introduced in 1985 by John C. Cox, Jonathan E. Ingersoll and Stephen A. Ross as an extension of the Vasicek model (from Wiki).

As widely-used of the Extended Cox-Ingersoll-Ross (ECIR) model, the Cox-Ingersoll-Ross (CIR) model is a now outdated.

## Implementation¶

This section mainly introduces the implementation process of short-rate and discount, which is applied in Tree Swaption Engine. They are core part for option pricing. As part of Tree Engine, the class $$CIRModel$$ implements the single-factor CIR model to calculate short-rate and discount by using continuous compounding. The implementation process is introduced as follows:

1. Since the short-rate at the current time point is independent from the short-rate at the previous time point, there is no need to calculate the short-rate in this module.
2. For implementing the generic Tree framework, this model only performs the calculation of some trinomial tree related parameters.
1. The discount is calculated at time point $$t$$ with the duration $$dt$$ based on the short-rate.