Term Structure Models Driven by Wiener Process and Poisson Measures: Existence and Positivity
Abstract
In the spirit of Bj\"ork-DiMasi-Kabanov-Runggaldier, we investigate term structure models driven by Wiener process and Poisson measures with forward curve dependent volatilities. This includes a full existence and uniqueness proof for the corresponding Heath--Jarrow--Morton type term structure equation. Furthermore, we characterize positivity preserving models by means of the characteristic coefficients, which was open for jump-diffusions. Additionally we treat existence, uniqueness and positivity of the Brody-Hughston equation of interest rate theory with jumps, an equation which we believe to be very useful for applications. A key role in our investigation is played by the method of the moving frame, which allows to transform the Heath--Jarrow--Morton--Musiela equation to a time-dependent SDE.
Cite
@article{arxiv.0905.1413,
title = {Term Structure Models Driven by Wiener Process and Poisson Measures: Existence and Positivity},
author = {Damir Filipovic and Stefan Tappe and Josef Teichmann},
journal= {arXiv preprint arXiv:0905.1413},
year = {2009}
}