Multivariate Rough Volatility

ArXiv ID: 2412.14353 “View on arXiv”

Authors: Unknown

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 a Generalised Method of Moments 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 empirical cross-covariance function, accurately captured by our model. These asymmetries lead to spillover effects, which we derive analytically within our model and compute based on empirical estimates of model parameters. Moreover, in accordance with the existing literature, we observe behaviors close to non-stationarity and rough trajectories.

Keywords: Realized Volatility, Fractional Ornstein-Uhlenbeck, Rough Volatility, Generalised Method of Moments (GMM), Multivariate Stochastic Volatility

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic calculus and fractional calculus, including multivariate fractional Brownian motion and derived asymptotic theory for estimators, indicating high mathematical complexity. It includes an extensive empirical investigation on 20 years of realized volatility data from the Oxford-Man library, with parameter estimation via GMM and spillover analysis, demonstrating high empirical rigor.

  flowchart TD
    A["Research Goal: Model joint dynamics of log-volatilities<br>to capture empirical cross-covariance asymmetries"] --> B["Data: Oxford-Man Realized Library<br>~20 years of realized volatility time series"]
    B --> C["Methodology: Multivariate Fractional OU Process<br>Hurst exponents & non-trivial interdependencies"]
    C --> D["Estimation: Generalised Method of Moments (GMM)<br>Joint parameter identification & asymptotic theory"]
    D --> E["Computational Analysis: Simulation study &<br>Empirical investigation of spillover effects"]
    E --> F["Key Findings: Asymmetries captured<br>Rough trajectories & near-stationarity observed<br>Spillover effects derived analytically"]