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Classes of Interest Rate Models Under the HJM Framework

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Abstract

Although the HJM term structure model is widely accepted as the most general and perhaps the most consistent, framework under which to study interest rate derivatives, the earlier models of Vasicek, Cox-Ingersoll-Ross, Hull-White, and Black-Karasinki remain popuar among both academics and practitioners. It is often stated that these models are special cases of the HJM framework, but the precise links have not been fully established in the literature. By beginning with certain forward rate volatility processes, it is possible to obtain classes of interest model under the HJM framework that closely resemble the traditional models listed above. Further, greater insight into the dyanmics of the interest rate process emerges as a result of natural links being established between the model parameters and maret observed variables.

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  • Carl Chiarella & Oh-Kang Kwon, 1999. "Classes of Interest Rate Models Under the HJM Framework," Research Paper Series 13, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:13
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    1. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26, March.
    2. M. Rutkowski, 1996. "Valuation and hedging of contingent claims in the HJM model with deterministic volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(3), pages 237-267.
    3. Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(3), pages 423-440, September.
    4. 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..
    5. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
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    Cited by:

    1. Andrew Matacz & Jean-Philippe Bouchaud, 1999. "Explaining the forward interest rate term structure," Science & Finance (CFM) working paper archive 500046, Science & Finance, Capital Fund Management.
    2. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
    3. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    4. Rihab Bedoui & Islem Kedidi, 2018. "Modeling Longevity Risk using Consistent Dynamics Affine Mortality Models," Working Papers hal-01678050, HAL.
    5. Claudio Henrique Barbedo & Octávio Bessada Lion & Jose Valentim Machado Vicente, 2010. "Pricing Asian Interest Rate Options with a Three-Factor HJM Model," Brazilian Review of Finance, Brazilian Society of Finance, vol. 8(1), pages 9-23.
    6. Blackburn, Craig & Sherris, Michael, 2013. "Consistent dynamic affine mortality models for longevity risk applications," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 64-73.
    7. Andrew Matacz & Jean-Philippe Bouchaud, 1999. "An empirical investigation of the forward interest rate term structure," Science & Finance (CFM) working paper archive 500047, Science & Finance, Capital Fund Management.
    8. Carl Chiarella & Sara Pasquali & Wolfgang Runggaldier, 2001. "On Filtering in Markovian Term Structure Models (An Approximation Approach)," Research Paper Series 65, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Antje Berndt & Peter Ritchken & Zhiqiang Sun, 2010. "On Correlation and Default Clustering in Credit Markets," The Review of Financial Studies, Society for Financial Studies, vol. 23(7), pages 2680-2729, July.
    10. Antje Berndt & Peter Ritchken & Zhiqiang Sun, "undated". "On Correlation Effects and Default Clustering in Credit Models," GSIA Working Papers 2008-E36, Carnegie Mellon University, Tepper School of Business.
    11. Andrew Matacz & Jean-Philippe Bouchaud, 2000. "An Empirical Investigation Of The Forward Interest Rate Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 703-729.
    12. Chiarella, Carl & Clewlow, Les & Musti, Silvana, 2005. "A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 325-336, March.
    13. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena.
    14. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series 283, Quantitative Finance Research Centre, University of Technology, Sydney.
    15. Chang, Chia-Chien, 2014. "Valuation Of Mortgage Insurance Contracts With Counterparty Default Risk: Reduced-Form Approach," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 303-334, May.
    16. Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August.
    17. Andrew Matacz & Jean-Philippe Bouchaud, 2000. "Explaining The Forward Interest Rate Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 381-389.
    18. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.

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