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Small-noise limit of the quasi-Gaussian log-normal HJM model

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  • Dan Pirjol
  • Lingjiong Zhu

Abstract

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 greatly simplifies their numerical implementation. We present a qualitative study of the solutions of the quasi-Gaussian log-normal HJM model. Using a small-noise deterministic limit we show that the short rate may explode to infinity in finite time. This implies the explosion of the Eurodollar futures prices in this model. We derive explicit explosion criteria under mild assumptions on the shape of the yield curve.

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  • Dan Pirjol & Lingjiong Zhu, 2019. "Small-noise limit of the quasi-Gaussian log-normal HJM model," Papers 1908.07098, arXiv.org.
    • Handle: RePEc:arx:papers:1908.07098
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    1. 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.
    2. 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..
    3. Dan Pirjol & Lingjiong Zhu, 2018. "Explosion in the quasi-Gaussian HJM model," Finance and Stochastics, Springer, vol. 22(3), pages 643-666, July.
    4. Nusret Cakici & Jintao Zhu, 2001. "Pricing Eurodollar Futures Options with the Heath—Jarrow—Morton Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 21(7), pages 655-680, July.
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