Asset Pricing with Matrix Jump Diffusions

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 modeling

JEL Classification: D51, E43, G13, G12