We develop efficient computational methods for the Bayesian estimation of rough stochastic volatility (RSV) models. To address the computational challenges associated with large covariance matrices in rough volatility models, we investigate several covariance factorization strategies for likelihood evaluation. Monte Carlo experiments reveal a clear trade-off between numerical accuracy and computational efficiency. While Cholesky-based methods deliver higher accuracy, the FFT embedding approach provides substantial computational speedups with minimal precision loss, and GPU acceleration significantly reduces runtime for recursion-based algorithms. We apply our framework to the S&P 500 returns, the log realized variance of S&P 500 and VIX series. The empirical results confirm the rough nature of equity volatility, though the VIX index exhibits substantially smoother dynamics. Our findings demonstrate that modern numerical linear algebra techniques and GPU-accelerated algorithms make the Bayesian estimation of high-dimensional rough stochastic volatility models computationally feasible.
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