# Jump-telegraph models for the short rate: pricing and convexity adjustments of zero coupon bonds

## TL;DR

This paper introduces jump-telegraph models for short rate dynamics, deriving closed-form formulas for pricing zero-coupon bonds and analyzing convexity adjustments, with comparisons to numerical PDE solutions.

## Contribution

It provides new closed-form solutions for bond pricing under a Markov-modulated jump process, enhancing modeling accuracy for interest rates.

## Key findings

- Closed-form formulas for zero-coupon bond prices
- Comparison with numerical PDE solutions confirms accuracy
- Insights into convexity adjustments in jump-telegraph models

## Abstract

In this article, we consider a Markov-modulated model with jumps for short rate dynamics. We obtain closed formulas for the term structure and forward rates using the properties of the jump-telegraph process and the expectation hypothesis. The results are compared with the numerical solution of the corresponding partial differential equation.