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Heat Kernel Interest Rate Models With Time-Inhomogeneous Markov Processes

In: Financial Informatics An Information-Based Approach to Asset Pricing

Author

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  • JIRÔ AKAHORI
  • ANDREA MACRINA

Abstract

We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over time. The result is a so-called weighted heat kernel that by construction is a supermartingale with respect to the filtration generated by the time-inhomogeneous Markov processes. As an application, we show how this framework naturally fits the information-based asset pricing framework where time-inhomogeneous Markov processes are utilized to model partial information about random economic factors. We present examples of pricing kernel models which lead to analytical formulae for bond prices along with explicit expressions for the associated interest rate and market price of risk. Furthermore, we also address the pricing of fixed-income derivatives within this framework.

Suggested Citation

  • 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..
    • Handle: RePEc:wsi:wschap:9789811246494_0009
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    References listed on IDEAS

    as
    1. Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408.
    2. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Security Pricing with Information-Sensitive Discounting," Papers 1001.3570, arXiv.org, revised Jun 2010.
    3. Robert A. Jarrow, 2009. "Credit Risk Models," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 37-68, November.
    4. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Security Pricing with Information-Sensitive Discounting," World Scientific Book Chapters, in: Masaaki Kijima & Chiaki Hara & Keiichi Tanaka & Yukio Muromachi (ed.), Recent Advances In Financial Engineering 2009, chapter 6, pages 157-180, World Scientific Publishing Co. Pte. Ltd..
    5. Jiro Akahori & Yuji Hishida & Josef Teichmann & Takahiro Tsuchiya, 2009. "A Heat Kernel Approach to Interest Rate Models," Papers 0910.5033, arXiv.org.
    6. 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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    Citations

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    Cited by:

    1. Andrea Macrina & Priyanka A. Parbhoo, 2011. "Randomised Mixture Models for Pricing Kernels," Papers 1112.2059, arXiv.org.
    2. Andrea Macrina, 2012. "Heat Kernel Framework for Asset Pricing in Finite Time," Papers 1211.0856, arXiv.org, revised Sep 2013.
    3. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Security Pricing with Information-Sensitive Discounting," Papers 1001.3570, arXiv.org, revised Jun 2010.
    4. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Securities Pricing with Information-Sensitive Discounting," KIER Working Papers 695, Kyoto University, Institute of Economic Research.
    5. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    6. Andrea Macrina & David Skovmand, 2020. "Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks," Risks, MDPI, vol. 8(1), pages 1-18, March.
    7. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Risks, MDPI, vol. 6(1), pages 1-39, March.
    8. 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.

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    More about this item

    Keywords

    Financial Mathematics; Mathematical Finance; Financial Markets; Informatics; Asset Pricing; Asset Price Dynamics; Stochastic Modelling; Information Process; Information Flow; Signal Processing; Filtration; Brownian Motion; Brownian Bridge; Change of Measure; Stochastic Volatility; Credit Risk; Default; Equities; Bonds; Collateralized Debt Obligation; Discount Bond; Lévy Process; Lévy Random Bridge; Lévy Information; Gamma Bridge; Markov Bridge; Pricing Kernel; Option Pricing; Informed Traders; Insurance; Reinsurance; Insurance Claims; Bond Portfolio; Heat Kernel; Markov Process; Variance Gamma Process; Ornstein-Uhlenbeck Process; Commodities; Fake News;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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