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

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  • Oscar Lopez
  • Gerardo E. Oleaga
  • Alejandra Sanchez

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.

Suggested Citation

  • Oscar Lopez & Gerardo E. Oleaga & Alejandra Sanchez, 2019. "Jump-telegraph models for the short rate: pricing and convexity adjustments of zero coupon bonds," Papers 1901.02995, arXiv.org.
    • Handle: RePEc:arx:papers:1901.02995
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    References listed on IDEAS

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    1. López, Oscar & Ratanov, Nikita, 2012. "Kac’s rescaling for jump-telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1768-1776.
    2. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    3. Shu Wu & Yong Zeng, 2007. "An Exact Solution of the Term Structure of Interest Rate Under Regime-Switching Risk," International Series in Operations Research & Management Science, in: Rogemar S. Mamon & Robert J. Elliott (ed.), Hidden Markov Models in Finance, chapter 1, pages 1-14, Springer.
    4. Michael Johannes, 2004. "The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models," Journal of Finance, American Finance Association, vol. 59(1), pages 227-260, February.
    5. A. Pelsser, 2003. "Mathematical foundation of convexity correction," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 59-65.
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