# Short Rate as a Sum of Two CKLS-Type Processes

## Abstract

We study the short rate model of interest rates, in which the short rate is defined as a sum of two stochastic factors. Each of these factors is modelled by a stochastic differential equation with a linear drift and the volatility proportional to a power of the factor. We show a calibration methods which - under the assumption of constant volatilities - allows us to estimate the term structure of interest rate as well as the unobserved short rate, although we are not able to recover all the parameters. We apply it to real data and show that it can provide a better fit compared to a one-factor model. A simple simulated example suggests that the method can be also applied to estimate the short rate even if the volatilities have a general form. Therefore we propose an analytical approximation formula for bond prices in such a model and derive the order of its accuracy.

## Keywords

Interest Rate Term Structure Bond Price Short Rate Interest Rate Model## Notes

### Acknowledgements

The work was supported by VEGA 1/0251/16 grant and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN *STRIKE – Novel Methods in Computational Finance*).

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