Heat Kernel Interest Rate Models With Time-Inhomogeneous Markov Processes
AbstractWe 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 InfoArticle 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 ()
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Web page: http://www.worldscinet.com/ijtaf/ijtaf.shtml
Other versions of this item:
- Jiro Akahori & Andrea Macrina, 2010. "Heat Kernel Interest Rate Models with Time-Inhomogeneous Markov Processes," Science & Finance (CFM) working paper archive 1012.1878, Science & Finance, Capital Fund Management.
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- 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.
- 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.
- Andrea Macrina & Priyanka A. Parbhoo, 2010. "Securities Pricing with Information-Sensitive Discounting," KIER Working Papers 695, Kyoto University, Institute of Economic Research.
- 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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