The Log S-fBM model: Statistical analysis
本文通过统计分析方法研究了Log S-fBM模型，该模型解决了如何在粗糙波动率和多重分形波动率之间进行调和的问题。
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From rough to multifractal multidimensional volatility: A multidimensional Log S-fBM model
This work proposes a multidimensional log-stationary fractional Brownian motion (mLog S-fBM) model to jointly capture the roughness and multifractal characteristics of multi-asset volatility. The model constructs the volatility process by exponentiating a multidimensional stationary fractional Brownian motion, preserving the Gaussian kernel dependence structure while introducing a co-Hurst matrix and a co-intermittency matrix. This formulation extends the univariate Log S-fBM to the multivariate setting for the first time and accommodates degenerate cases that bridge distinct volatility paradigms. Calibration is performed via small-intermittency approximation and generalized method of moments (GMM). Empirical validation on both synthetic data and S&P 500 constituents confirms the model’s effectiveness: individual asset Hurst exponents cluster near zero—indicative of multifractality—while cross-asset co-Hurst exponents average around 0.12, with co-intermittency estimates consistent with univariate counterparts.
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The Log S-fBM model: Statistical analysis
本文通过统计分析方法研究了Log S-fBM模型，该模型解决了如何在粗糙波动率和多重分形波动率之间进行调和的问题。
0 citationsRead paper
From rough to multifractal multidimensional volatility: A multidimensional Log S-fBM model
This work proposes a multidimensional log-stationary fractional Brownian motion (mLog S-fBM) model to jointly capture the roughness and multifractal characteristics of multi-asset volatility. The model constructs the volatility process by exponentiating a multidimensional stationary fractional Brownian motion, preserving the Gaussian kernel dependence structure while introducing a co-Hurst matrix and a co-intermittency matrix. This formulation extends the univariate Log S-fBM to the multivariate setting for the first time and accommodates degenerate cases that bridge distinct volatility paradigms. Calibration is performed via small-intermittency approximation and generalized method of moments (GMM). Empirical validation on both synthetic data and S&P 500 constituents confirms the model’s effectiveness: individual asset Hurst exponents cluster near zero—indicative of multifractality—while cross-asset co-Hurst exponents average around 0.12, with co-intermittency estimates consistent with univariate counterparts.
0 citationsRead paper