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Finance and Stochastics

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04-06-2018

Explosion in the quasi-Gaussian HJM model

Authors: Dan Pirjol, Lingjiong Zhu

Published in: Finance and Stochastics | Issue 3/2018

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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.

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Note that in Eq. (43) in [29], there is a typo: the factor on the right-hand side of this equation should be \(\frac{P(0,T)}{P(0,T+\delta)}\).

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Title: Explosion in the quasi-Gaussian HJM model
Authors: Dan Pirjol
Lingjiong Zhu
Publication date: 04-06-2018
Publisher: Springer Berlin Heidelberg
Published in: Finance and Stochastics / Issue 3/2018
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-018-0367-5

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