Fractional Wishart processes and ε-fractional Wishart processes with applications

摘要

In this paper, we introduce two new matrix stochastic processes: fractional Wishart processes and epsilon-fractional Wishart processes with integer indices which are based on the fractional Brownian motions and then extend epsilon-fractional Wishart processes to the case with non-integer indices. Both processes include classic Wishart processes (if the Hurst index H equals 1/2) and present serial correlation of stochastic processes. Applying epsilon-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. (C) 2018 Elsevier Ltd. All rights reserved.