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A Heat Kernel Approach to Interest Rate Models

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  • 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.

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File URL: http://arxiv.org/pdf/0910.5033
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Paper provided by arXiv.org in its series Papers with number 0910.5033.

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Date of creation: Oct 2009
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Handle: RePEc:arx:papers:0910.5033

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Web page: http://arxiv.org/

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  1. M. R. Grasselli & T. R. Hurd, 2003. "Wiener Chaos and the Cox-Ingersoll-Ross model," Papers math/0307197, arXiv.org.
  2. Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408.
  3. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 77-105, January.
  4. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(2), pages 157-176.
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Cited by:
  1. Jiro Akahori & Andrea Macrina, 2010. "Heat Kernel Interest Rate Models with Time-Inhomogeneous Markov Processes," Papers 1012.1878, 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 & Priyanka A. Parbhoo, 2011. "Randomised Mixture Models for Pricing Kernels," Papers 1112.2059, arXiv.org.

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