# Two-factor term structure model with uncertain volatility risk

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## Abstract

This paper aims to study two-factor uncertain term structure model where the volatility of the uncertain interest rate is driven by another uncertain differential equation. In order to solve this model, the nested uncertain differential equation method is employed. This paper is also devoted to the study of the numerical solutions for the proposed nested uncertain differential equation using the \(\alpha \)-path methods. We also use the built two-factor term structure model to value the bond price with the help of proposed numerical method. Finally, we give a numerical example where the price of a zero-coupon bond is calculated based on the \(\alpha \)-path methods.

## Keywords

Two-factor term structure Uncertain short interest rate Volatility risk Bond pricing Uncertain differential equation## Notes

### Acknowledgements

The author gratefully acknowledges the financial support provided by National Natural Science Foundation of China (Grant Nos. 61673225, 61304182 and 61374082), Distinguished Young Scholar Project of Renmin University of China and China Scholarship Council under Grant 201606365008.

### Compliance with ethical standards

### Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

### Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

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