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Heath–Jarrow–Morton Interest Rate Dynamics And Approximately Consistent Forward Rate Curves

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  • Claudia La Chioma
  • Benedetto Piccoli

Abstract

We study a finite‐dimensional approach to the Heath–Jarrow–Morton model for interest rate and introduce a notion of approximate consistency for a family of functions in a deterministic and stochastic framework. This amounts to asking the decrease of the minimum distance in least squares sense. We start from a general linearly parameterized set of functions and extend the theory to a nonlinear Nelson–Siegel family. Necessary and sufficient condition to have approximately consistency are given as well as a criterion of stability for the approximation.

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  • Claudia La Chioma & Benedetto Piccoli, 2007. "Heath–Jarrow–Morton Interest Rate Dynamics And Approximately Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 427-447, July.
    • Handle: RePEc:bla:mathfi:v:17:y:2007:i:3:p:427-447
    DOI: 10.1111/j.1467-9965.2007.00310.x
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    Cited by:

    1. 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.
    2. Roncoroni, Andrea & Galluccio, Stefano & Guiotto, Paolo, 2010. "Shape factors and cross-sectional risk," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2320-2340, November.
    3. 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.
    4. J. C. Arismendi-Zambrano & Vladimir Belitsky & Vinicius Amorim Sobreiro & Herbert Kimura, 2020. "The Implications of Tail Dependency Measures for Counterparty Credit Risk Pricing," Economics Department Working Paper Series n306-20.pdf, Department of Economics, National University of Ireland - Maynooth.
    5. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2016. "The stochastic string model as a unifying theory of the term structure of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 217-237.
    6. Arismendi-Zambrano, Juan & Belitsky, Vladimir & Sobreiro, Vinicius Amorim & Kimura, Herbert, 2022. "The implications of dependence, tail dependence, and bounds’ measures for counterparty credit risk pricing," Journal of Financial Stability, Elsevier, vol. 58(C).

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