Monotonicity of the collateralized debt obligations term structure model

Abstract

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.

Keywords::

• CDO model
• bond market
• HJM condition
• HJMM equation
• monotonicity

AMS Subject Classification::

• 91B28
• 91B70
• 91B24

Keywords::

• G10
• G11

Acknowledgements

The author would like to thank A. Rusinek, T. Schmidt, S. Tappe and J. Zabczyk for inspiring discussions and helpful suggestions.

Additional information

Funding

The paper was supported by The Polish MNiSW [grant number NN201419039].