Linear-Quadratic Jump-Diffusion Modelling with Application to Stochastic Volatility

60 Pages Posted: 16 May 2003

See all articles by Peng Cheng

Peng Cheng

FAME; Université de Genève

O. Scaillet

Swiss Finance Institute - University of Geneva

Date Written: November 2002

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 underlying this class of models as well as identification constraints, and compute standard and extended transforms relevant to asset pricing. We also show that the LQJD class can be embedded into the affine class through use of an augmented state vector. We further establish that an equivalence relationship holds between both classes in terms of transform analysis. An option pricing application to multifactor stochastic volatility models reveals that adding nonlinearity into the model significantly reduces pricing errors, and further addition of a jump component in the stock price largely improves goodness-of-fit for in-the-money calls but less for out-of-the-money ones.

Keywords: Linear-quadratic models, affine models, jump-diffusions, generalized Fourier transform, option pricing, stochastic volatility

JEL Classification: G12

Suggested Citation

Cheng, Peng and Scaillet, Olivier, Linear-Quadratic Jump-Diffusion Modelling with Application to Stochastic Volatility (November 2002). Available at SSRN: https://ssrn.com/abstract=381820 or http://dx.doi.org/10.2139/ssrn.381820

Peng Cheng (Contact Author)

FAME

40, Boulevard du Pont-d'Arve
40, Bd du Pont-d'Arve
1211 Geneva 4, CH-6900
Switzerland

Université de Genève

40, Boulevard du Pont-d'Arve
Genève, CH - 1205
Switzerland

Olivier Scaillet

Swiss Finance Institute - University of Geneva ( email )

Geneva
Switzerland

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