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Term structure models driven by Wiener process and Poisson measures: Existence and positivity (2009)
| Citations: | 7 - 3 self |
BibTeX
@MISC{Filipović09termstructure,
author = {Damir Filipović and Stefan Tappe and Josef Teichmann},
title = {Term structure models driven by Wiener process and Poisson measures: Existence and positivity},
year = {2009}
}
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Abstract
Abstract. In the spirit of [4], 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 [7, 8] 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. Key Words: term structure models driven by Wiener process and Poisson measures, Heath-Jarrow-Morton-Musiela equation, positivity preserving models, Brody-Hughston equation. 91B28, 60H15 1.
Keyphrases
poisson measure term structure model wiener process brody-hughston equation positivity preserving model characteristic coefficient time-dependent sde heath-jarrow-morton-musiela equation full existence forward curve dependent volatility uniqueness proof key word interest rate theory key role heath jarrow morton musiela equation moving frame
