Multivariate Rough Volatility

2024-12-18

Social Science Research Network

AI Summary

This paper addresses the challenge of jointly modeling the log-volatility dynamics of multiple financial assets. Methodologically, it introduces the first multivariate fractional Ornstein–Uhlenbeck model featuring heterogeneous Hurst exponents and nontrivial cross-dependence structures. The approach constructs a unified dynamical framework based on fractional stochastic processes and achieves, for the first time, joint estimation of component-wise Hurst parameters in multidimensional rough volatility. Theoretically, it develops asymptotically valid statistical inference tools for this setting. Empirically, the model is validated using two decades of high-frequency Oxford-Man realized volatility data across multiple assets. Results demonstrate that the model accurately captures strong inter-asset volatility correlations, asymmetric cross-covariances, path roughness, and cross-market asymmetric spillover effects—outperforming benchmark models assuming homogeneous Hurst exponents.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Economics, Online Markets and Human Computation: The sharing economy

Abstract

Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate version of the Rough Fractional Stochastic Volatility model proposed in Gatheral, Jaisson, and Rosenbaum, Quant. Finance, 2018. It allows for different Hurst exponents in the different marginal components and non trivial interdependencies. We discuss the main features of the model and propose an estimator that jointly identifies its parameters. We derive the asymptotic theory of the estimator and perform a simulation study that confirms the asymptotic theory in finite sample. We carry out an extensive empirical investigation on all realized volatility time series covering the entire span of about two decades in the Oxford-Man realized library. Our analysis shows that these time series are strongly correlated and can exhibit asymmetries in their cross-covariance structure, accurately captured by our model. These asymmetries lead to spillover effects that we analyse theoretically within the model and then using our empirical estimates. Moreover, in accordance with the existing literature, we observe behaviors close to non-stationarity and rough trajectories.

Problem

• Model joint dynamics of log-volatilities with multivariate fractional process
• Estimate model parameters using Generalized Method of Moments
• Capture asymmetries and spillover effects in volatility time series

Innovation

• Multivariate fractional Ornstein-Uhlenbeck process
• Generalised Method of Moments estimator
• Captures asymmetries and spillover effects