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A Heat Kernel Approach to Interest Rate Models

Author

Listed:
  • Jiro Akahori
  • Yuji Hishida
  • Josef Teichmann
  • Takahiro Tsuchiya

Abstract

We construct default-free interest rate models in the spirit of the well-known Markov funcional models: our focus is analytic tractability of the models and generality of the approach. We work in the setting of state price densities and construct models by means of the so called propagation property. The propagation property can be found implicitly in all of the popular state price density approaches, in particular heat kernels share the propagation property (wherefrom we deduced the name of the approach). As a related matter, an interesting property of heat kernels is presented, too.

Suggested Citation

  • Jiro Akahori & Yuji Hishida & Josef Teichmann & Takahiro Tsuchiya, 2009. "A Heat Kernel Approach to Interest Rate Models," Papers 0910.5033, arXiv.org.
    • Handle: RePEc:arx:papers:0910.5033
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    References listed on IDEAS

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    1. Jirô Akahori & Takahiro Tsuchiya, 2006. "What is the Natural Scale for a Lévy Process in Modelling Term Structure of Interest Rates?," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 299-313, December.
    2. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson‐Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94, October.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408.
    5. Lane Hughston & Avraam Rafailidis, 2005. "A chaotic approach to interest rate modelling," Finance and Stochastics, Springer, vol. 9(1), pages 43-65, January.
    6. M. R. Grasselli & T. R. Hurd, 2003. "Wiener Chaos and the Cox-Ingersoll-Ross model," Papers math/0307197, arXiv.org.
    7. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176, April.
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    Cited by:

    1. Jirô Akahori & Andrea Macrina, 2022. "Heat Kernel Interest Rate Models With Time-Inhomogeneous Markov Processes," World Scientific Book Chapters, in: Dorje Brody & Lane Hughston & Andrea Macrina (ed.), Financial Informatics An Information-Based Approach to Asset Pricing, chapter 9, pages 179-193, World Scientific Publishing Co. Pte. Ltd..
    2. Andrea Macrina & Priyanka A. Parbhoo, 2011. "Randomised Mixture Models for Pricing Kernels," Papers 1112.2059, arXiv.org.
    3. Andrea Macrina & Priyanka Parbhoo, 2014. "Randomised Mixture Models for Pricing Kernels," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 281-315, November.
    4. Andrea Macrina, 2012. "Heat Kernel Framework for Asset Pricing in Finite Time," Papers 1211.0856, arXiv.org, revised Sep 2013.
    5. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Security Pricing with Information-Sensitive Discounting," Papers 1001.3570, arXiv.org, revised Jun 2010.
    6. Stephane Crepey & Andrea Macrina & Tuyet Mai Nguyen & David Skovmand, 2015. "Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments," Papers 1502.07397, arXiv.org.
    7. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    8. Andrea Macrina & David Skovmand, 2020. "Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks," Risks, MDPI, vol. 8(1), pages 1-18, March.
    9. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Securities Pricing with Information-Sensitive Discounting," KIER Working Papers 695, Kyoto University, Institute of Economic Research.

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