Markov-modulated jump-diffusion models for the short rate: Pricing of zero coupon bonds and convexity adjustment

Abstract

In this article, we consider a Markov-modulated model with jumps for the short rate. Using the main properties of a telegraphic process with jumps we compute the expected short rate. We obtain closed formulas for the zero coupon bond price assuming the Unbiased Expectation Hypothesis for the forward rates. Next, we obtain the coupled system of partial differential equations for the bond price using only no-arbitrage arguments. Numerical solutions are provided for some selected examples. The results obtained from both methods are compared and allow to estimate the magnitude of the convexity-adjustment.