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Heat Kernel Interest Rate Models With Time-Inhomogeneous Markov Processes

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  • JIRÔ AKAHORI

    ()
    (Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu 52-8577, Shiga, Japan)

  • ANDREA MACRINA

    ()
    (Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK; Institute of Economic Research, Kyoto University Yoshida-Honmachi, Sakyo-Ku, Kyoto 606-8501, Japan)

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.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 15 (2012)
Issue (Month): 01 ()
Pages: 1250007-1-1250007-15

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Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:01:p:1250007-1-1250007-15

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Related research

Keywords: Time-inhomogeneous Markov processes; Lévy processes; heat kernels; pricing kernels; information-based pricing; interest rate models; fixed-income assets;

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References

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  1. Robert A. Jarrow, 2009. "Credit Risk Models," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 37-68, November.
  2. Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408.
  3. Jiro Akahori & Yuji Hishida & Josef Teichmann & Takahiro Tsuchiya, 2009. "A Heat Kernel Approach to Interest Rate Models," Science & Finance (CFM) working paper archive 0910.5033, Science & Finance, Capital Fund Management.
  4. 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.
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Cited by:
  1. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Security Pricing with Information-Sensitive Discounting," Science & Finance (CFM) working paper archive 1001.3570, Science & Finance, Capital Fund Management, revised Jun 2010.
  2. Andrea Macrina, 2012. "Heat Kernel Framework for Asset Pricing in Finite Time," Science & Finance (CFM) working paper archive 1211.0856, Science & Finance, Capital Fund Management, revised Sep 2013.
  3. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Securities Pricing with Information-Sensitive Discounting," KIER Working Papers 695, Kyoto University, Institute of Economic Research.
  4. Andrea Macrina & Priyanka A. Parbhoo, 2011. "Randomised Mixture Models for Pricing Kernels," Science & Finance (CFM) working paper archive 1112.2059, Science & Finance, Capital Fund Management.

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