TY - JOUR
T1 - Explosion in the quasi-Gaussian HJM model
AU - Pirjol, Dan
AU - Zhu, Lingjiong
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - 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.
AB - 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.
KW - Explosion
KW - HJM model
KW - Multidimensional diffusions
KW - Stochastic modeling
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U2 - 10.1007/s00780-018-0367-5
DO - 10.1007/s00780-018-0367-5
M3 - Article
AN - SCOPUS:85047969789
SN - 0949-2984
VL - 22
SP - 643
EP - 666
JO - Finance and Stochastics
JF - Finance and Stochastics
IS - 3
ER -