HEAT KERNEL INTEREST RATE MODELS WITH TIME-INHOMOGENEOUS MARKOV PROCESSES

Jiro Akahori and Andrea Macrina
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Andrea Macrina: Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom and Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-Ku, Kyoto 606-8501, Japan

Chapter 1 in Finance at Fields, 2012, pp 1-15 from World Scientific Publishing Co. Pte. Ltd.

Abstract: 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.

Keywords: Mathematical Finance; Financial Mathematics; Risk Management; Asset Pricing; Computational Finance; Derivatives; Option Pricing; Portfolio Optimization (search for similar items in EconPapers)
Date: 2012
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Related works:
Chapter: HEAT KERNEL INTEREST RATE MODELS WITH TIME-INHOMOGENEOUS MARKOV PROCESSES (2022)
Journal Article: HEAT KERNEL INTEREST RATE MODELS WITH TIME-INHOMOGENEOUS MARKOV PROCESSES (2012)
Working Paper: Heat Kernel Interest Rate Models with Time-Inhomogeneous Markov Processes (2010)
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