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Explosion in the quasi-Gaussian HJM model

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  • Dan Pirjol

    (J. P. Morgan)

  • Lingjiong Zhu

    (Florida State University)

Abstract

We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low-dimensional Markovian representation which simplifies their numerical implementation and simulation. We show rigorously that the short rate in these models explodes in finite time with positive probability, under certain assumptions for the model parameters, and that the explosion occurs in finite time with probability one under some stronger assumptions. We discuss the implications of these results for the pricing of the zero coupon bonds and Eurodollar futures under this model.

Suggested Citation

  • Dan Pirjol & Lingjiong Zhu, 2018. "Explosion in the quasi-Gaussian HJM model," Finance and Stochastics, Springer, vol. 22(3), pages 643-666, July.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:3:d:10.1007_s00780-018-0367-5
    DOI: 10.1007/s00780-018-0367-5
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    References listed on IDEAS

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    Cited by:

    1. Dan Pirjol & Lingjiong Zhu, 2019. "Small-noise limit of the quasi-Gaussian log-normal HJM model," Papers 1908.07098, arXiv.org.
    2. Szymon Peszat & Dariusz Zawisza, 2020. "The investor problem based on the HJM model," Papers 2010.13915, arXiv.org, revised Dec 2021.

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    More about this item

    Keywords

    HJM model; Stochastic modeling; Multidimensional diffusions; Explosion;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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