We would like to thank the Editor, Dilip Madan, and the two anonymous referees for constructive criticism and comments. We also thank P. Collin-Dufresne, J. Detemple, G. Dhaene, D. Duffie, J.D. Fermanian, S. Galluccio, C. Gouriéroux, A. Kaul, M. Musiela, and R. Stulz for many stimulating discussions. We have received fruitful comments from participants at the FAME doctoral workshop, AFFI meeting 2003, ESEM 2003, EFA 2003, and finance seminars at Imperial College, BNP Paribas, Zürich, Lugano, and CREST (Paris). The authors received support by the Swiss National Science Foundation through the National Center of Competence Research (NCCR): Financial Valuation and Risk Management. The first author also received a Doctoral Research Grant from International Centre FAME for completing the project. Part of this research was done when the second author was visiting THEMA and IRES.
LINEAR-QUADRATIC JUMP-DIFFUSION MODELING
Article first published online: 14 SEP 2007
Volume 17, Issue 4, pages 575–598, October 2007
How to Cite
Cheng, P. and Scaillet, O. (2007), LINEAR-QUADRATIC JUMP-DIFFUSION MODELING. Mathematical Finance, 17: 575–598. doi: 10.1111/j.1467-9965.2007.00316.x
- Issue published online: 14 SEP 2007
- Article first published online: 14 SEP 2007
- Manuscript received March 2005; final revision received January 2007.
- linear-quadratic models;
- affine models;
- standard transform;
- option pricing
We aim at accommodating the existing affine jump-diffusion and quadratic models under the same roof, namely the linear-quadratic jump-diffusion (LQJD) class. We give a complete characterization of the dynamics of this class by stating explicitly the structural constraints, as well as the admissibility conditions. This allows us to carry out a specification analysis for the three-factor LQJD models. We compute the standard transform of the state vector relevant to asset pricing up to a system of ordinary differential equations. We show that the LQJD class can be embedded into the affine class using an augmented state vector. This establishes a one-to-one equivalence relationship between both classes in terms of transform analysis.