Explosion in the quasi-Gaussian HJM model

Dan Pirjol () and Lingjiong Zhu ()
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Dan Pirjol: J. P. Morgan
Lingjiong Zhu: Florida State University

Finance and Stochastics, 2018, vol. 22, issue 3, No 5, 643-666

Abstract: 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.

Keywords: HJM model; Stochastic modeling; Multidimensional diffusions; Explosion; 60J60; 60J70; 91G30; 93D30 (search for similar items in EconPapers)
JEL-codes: C32 C63 C65 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-018-0367-5

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