IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v395y2021ics0096300320308079.html
   My bibliography  Save this article

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

Author

Listed:
  • López, Oscar
  • Oleaga, Gerardo
  • Sánchez, Alejandra

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.

Suggested Citation

  • López, Oscar & Oleaga, Gerardo & Sánchez, Alejandra, 2021. "Markov-modulated jump-diffusion models for the short rate: Pricing of zero coupon bonds and convexity adjustment," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308079
    DOI: 10.1016/j.amc.2020.125854
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320308079
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125854?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    2. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    3. Nikita Ratanov, 2007. "A jump telegraph model for option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 575-583.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Nikita Ratanov, 2016. "Option Pricing Under Jump-Diffusion Processes with Regime Switching," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 829-845, September.
    6. Wu, Shu & Zeng, Yong, 2006. "The term structure of interest rates under regime shifts and jumps," Economics Letters, Elsevier, vol. 93(2), pages 215-221, November.
    7. Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
    8. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    9. 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.
    10. Tak Kuen Siu, 2010. "A Markov Regime-Switching Marked Point Process for Short-Rate Analysis with Credit Risk," International Journal of Stochastic Analysis, Hindawi, vol. 2010, pages 1-18, December.
    11. A. Pelsser, 2003. "Mathematical foundation of convexity correction," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 59-65.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hinnerich, Mia, 2008. "Inflation-indexed swaps and swaptions," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2293-2306, November.
    2. Robert Jarrow & Haitao Li & Feng Zhao, 2007. "Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?," Journal of Finance, American Finance Association, vol. 62(1), pages 345-382, February.
    3. Beliaeva, Natalia & Nawalkha, Sanjay, 2012. "Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 151-163.
    4. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    5. Lin, Shih-Kuei & Wang, Shin-Yun & Chen, Carl R. & Xu, Lian-Wen, 2017. "Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 359-373.
    6. Dungey, Mardi & McKenzie, Michael & Smith, L. Vanessa, 2009. "Empirical evidence on jumps in the term structure of the US Treasury Market," Journal of Empirical Finance, Elsevier, vol. 16(3), pages 430-445, June.
    7. Leippold, Markus & Strømberg, Jacob, 2014. "Time-changed Lévy LIBOR market model: Pricing and joint estimation of the cap surface and swaption cube," Journal of Financial Economics, Elsevier, vol. 111(1), pages 224-250.
    8. Michael S. Johannes & Nicholas G. Polson & Jonathan R. Stroud, 2009. "Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2559-2599, July.
    9. Chris Kenyon & Andrew Green, 2015. "Dirac Processes and Default Risk," Papers 1504.04581, arXiv.org.
    10. Carl Chiarella & Thuy-Duong Tô, 2006. "The Multifactor Nature of the Volatility of Futures Markets," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 163-183, May.
    11. Mr. Vadim Khramov, 2013. "Estimating Parameters of Short-Term Real Interest Rate Models," IMF Working Papers 2013/212, International Monetary Fund.
    12. Torben G. Andersen & Luca Benzoni, 2010. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 65(2), pages 603-653, April.
    13. Michael Bauer & Mikhail Chernov, 2024. "Interest Rate Skewness and Biased Beliefs," Journal of Finance, American Finance Association, vol. 79(1), pages 173-217, February.
    14. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2010. "Real-world jump-diffusion term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 23-37.
    15. Lena Cleanthous & Pany Karamanou, 2011. "The ECB Monetary Policy and the Current Financial Crisis," Working Papers 2011-1, Central Bank of Cyprus.
    16. Fan, Longzhen & Johansson, Anders C., 2010. "China's official rates and bond yields," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 996-1007, May.
    17. Jozef Barunik & Pavel Fiser, 2019. "Co-jumping of Treasury Yield Curve Rates," Papers 1905.01541, arXiv.org.
    18. Takami, Marcelo Yoshio & Tabak, Benjamin Miranda, 2008. "Interest rate option pricing and volatility forecasting: An application to Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 755-763.
    19. J. Benson Durham, 2005. "Jump-diffusion processes and affine term structure models: additional closed-form approximate solutions, distributional assumptions for jumps, and parameter estimates," Finance and Economics Discussion Series 2005-53, Board of Governors of the Federal Reserve System (U.S.).
    20. Carl Chiarella & Thuy-Duong To, 2005. "The Multifactor Nature of the Volatility of the Eurodollar Futures Market," Research Paper Series 150, Quantitative Finance Research Centre, University of Technology, Sydney.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308079. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.