Affine processes on positive semidefinite matrices

TL;DR

This paper develops the mathematical foundation for affine processes on positive semidefinite matrices, which are increasingly used in finance for modeling multi-asset options, stochastic volatility, and correlated risk factors.

Contribution

It provides the first rigorous mathematical framework for stochastically continuous affine processes on the cone of positive semidefinite matrices.

Findings

Established existence and uniqueness of affine processes on positive semidefinite matrices.

Applied the theory to financial models involving stochastic volatility and correlation.

Enhanced understanding of matrix-valued stochastic processes in finance.

Abstract

This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.