Heat Kernel Framework for Asset Pricing in Finite Time
A heat kernel approach is proposed for the development of a general, flexible, and mathematically tractable asset pricing framework in finite time. The pricing kernel, giving rise to the price system in an incomplete market, is modelled by weighted heat kernels which are driven by multivariate Markov processes and which provide enough degrees of freedom in order to calibrate to relevant data, e.g. to the term structure of bond prices. It is shown how, for a class of models, the prices of bonds, caplets, and swaptions can be computed in closed form. The dynamical equations for the price processes are derived, and explicit formulae are obtained for the short rate of interest, the risk premium, and for the stochastic volatility of prices. Several of the closed-form asset price models presented in this paper are driven by combinations of Markovian jump processes with different probability laws. Such models provide a rich basis for consistent applications in several sectors of a financial market including equity, fixed-income, commodities, and insurance. The flexible, multidimensional and multivariate structure, on which the asset price models are constructed, lends itself well to the transparent modelling of dependence across asset classes. As an illustration, the impact on prices by spiralling debt, a typical feature of a financial crisis, is modelled explicitly, and contagion effects are readily observed in the dynamics of asset returns.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Farshid Jamshidian, 1996. "Bond, futures and option evaluation in the quadratic interest rate model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(2), pages 93-115.
- Jirô Akahori & Andrea Macrina, 2012.
"Heat Kernel Interest Rate Models With Time-Inhomogeneous Markov Processes,"
International Journal of Theoretical and Applied Finance (IJTAF),
World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-15.
- Jirô Akahori & Andrea Macrina, 2012. "Heat Kernel Interest Rate Models With Time-Inhomogeneous Markov Processes," World Scientific Book Chapters, in: Finance at Fields, chapter 1, pages 1-15 World Scientific Publishing Co. Pte. Ltd..
- Jiro Akahori & Andrea Macrina, 2010. "Heat Kernel Interest Rate Models with Time-Inhomogeneous Markov Processes," Papers 1012.1878, arXiv.org.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992.
"Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation,"
Econometric Society, vol. 60(1), pages 77-105, January.
- David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
- Edward Hoyle & Lane P. Hughston & Andrea Macrina, 2010. "Stable-1/2 Bridges and Insurance," Papers 1005.0496, arXiv.org, revised Apr 2014.
- Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
- Dorje C. Brody & Lane P. Hughston & Andrea Macrina, 2008. "Information-Based Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 107-142.
- Jiro Akahori & Yuji Hishida & Josef Teichmann & Takahiro Tsuchiya, 2009. "A Heat Kernel Approach to Interest Rate Models," Papers 0910.5033, arXiv.org.
- Back, Kerry, 2010. "Asset Pricing and Portfolio Choice Theory," OUP Catalogue, Oxford University Press, number 9780195380613, December.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1211.0856. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.