Explosion in the quasi-Gaussian HJM model

Dan Pirjol, Lingjiong Zhu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)643-666
Number of pages24
JournalFinance and Stochastics
Volume22
Issue number3
DOIs
StatePublished - 1 Jul 2018

Keywords

  • Explosion
  • HJM model
  • Multidimensional diffusions
  • Stochastic modeling

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