Fractional Wishart Processes and $\varepsilon$-Fractional Wishart Processes with Applications

TL;DR

This paper introduces fractional and epsilon-fractional Wishart processes based on fractional Brownian motion, extending classic Wishart processes to model complex serial correlations and stochastic volatilities in financial markets.

Contribution

The paper develops new matrix stochastic processes incorporating fractional Brownian motion, extending Wishart processes to non-integer indices and applications in financial modeling.

Findings

Includes classic Wishart processes when Hurst index H=1/2

Models account for stochastic volatilities and correlations

Present serial correlation of the processes

Abstract

In this paper, we introduce two new matrix stochastic processes: fractional Wishart processes and $\varepsilon$-fractional Wishart processes with integer indices which are based on the fractional Brownian motions and then extend $\varepsilon$-fractional Wishart processes to the case with non-integer indices. Both of two kinds of processes include classic Wishart processes when the Hurst index $H$ equals $\frac{1}{2}$ and present serial correlation of stochastic processes. Applying $\varepsilon$-fractional Wishart processes to financial volatility theory, the financial models account for the stochastic volatilities of the assets and for the stochastic correlations not only between the underlying assets' returns but also between their volatilities and for stochastic serial correlation of the relevant assets.