Asset Pricing with Matrix Jump Diffusions

57 Pages Posted: 3 Apr 2010

See all articles by Markus Leippold

Markus Leippold

University of Zurich - Department of Banking and Finance; University of Zurich - Faculty of Economics, Business Administration and Information Technology

Fabio Trojani

Swiss Finance Institute; University of Geneva

Multiple version iconThere are 2 versions of this paper

Date Written: March 16, 2010

Abstract

We introduce a new class of flexible and tractable matrix affine jump-diffusions (AJD) to model multivariate sources of financial risk. We first provide a complete transform analysis of this model class, which opens a range of new potential applications to, e.g., multivariate option pricing with stochastic volatilities and correlations, fixed-income models with stochastically correlated default intensities, or multivariate dynamic portfolio choice with volatility and correlation jumps. We then study in more detail some of the new structural features of our modeling approach in two applications to option pricing and dynamic portfolio choice. First, we find that a three-factor matrix AJD model can generate variations of the implied volatility skew term structures that are largely unrelated to the level and composition of the spot volatility. This feature can allow the model to improve on benchmark AJD settings in reproducing the overall shape of the smile of equity index options. Second, we find that volatility and correlation jumps can imply an economically relevant intertemporal hedging demand in optimal dynamic portfolios, when jump intensities exhibit co-movement with the returns' covariance matrix.

Keywords: Affine jump-diffusions, matrix subordinator, stochastic volatility, stochastic correlations, option pricing, portfolio choice, yield curve models

JEL Classification: D51, E43, G13, G12

Suggested Citation

Leippold, Markus and Trojani, Fabio, Asset Pricing with Matrix Jump Diffusions (March 16, 2010). Available at SSRN: https://ssrn.com/abstract=1572576 or http://dx.doi.org/10.2139/ssrn.1572576

Markus Leippold

University of Zurich - Department of Banking and Finance ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

University of Zurich - Faculty of Economics, Business Administration and Information Technology ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

Fabio Trojani (Contact Author)

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva ( email )

Geneva, Geneva
Switzerland

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