LINEAR‐QUADRATIC JUMP‐DIFFUSION MODELING

Peng Cheng and Olivier Scaillet

Mathematical Finance, 2007, vol. 17, issue 4, 575-598

Abstract: 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.

Date: 2007
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