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Heat Kernel Interest Rate Models with Time-Inhomogeneous Markov Processes

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  • Jiro 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.

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File URL: http://arxiv.org/pdf/1012.1878
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Paper provided by arXiv.org in its series Papers with number 1012.1878.

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Date of creation: Dec 2010
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Handle: RePEc:arx:papers:1012.1878

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

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