Monotonicity of the collateralized debt obligations term structure model

The problem of existence of arbitrage-free and monotone collateralized debt obligations term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath-Jarrow-Morton-Musiela equation for the -forward rates with the use of the Milian-type result are formulated....

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Bibliographic Details
Published in:Stochastics (Abingdon, Eng. : 2005) Eng. : 2005), 2014-09, Vol.86 (5), p.835-864
Main Author: Barski, Michał
Format: Article
Language:English
Subjects:
bond market
CDO model
HJM condition
HJMM equation
Mathematical analysis
Mathematical models
monotonicity
Probability theory
Randomness
Regularity
Sobolev space
Volatility
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Summary:The problem of existence of arbitrage-free and monotone collateralized debt obligations term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath-Jarrow-Morton-Musiela equation for the -forward rates with the use of the Milian-type result are formulated. Two state spaces are taken into account - of square integrable functions and a Sobolev space. For the first the regularity results concerning pointwise monotonicity are proven. Arbitrage-free and monotone models are characterized in terms of the volatility of the model and characteristics of the driving Lévy process.
ISSN:1744-2508
1744-2516
DOI:10.1080/17442508.2013.879145