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BIMSA 数字经济实验室讨论班
BIMSA 数字经济实验室讨论班
Effective Filtering of Multiscale Stochastic Volatility from Realized Measures: homogenization, dimensional reduction, and optimal Sampling
Effective Filtering of Multiscale Stochastic Volatility from Realized Measures: homogenization, dimensional reduction, and optimal Sampling
演讲者
时间
2026年09月04日 15:00 至 16:00
地点
A3-2-303
线上
Zoom 242 742 6089
(BIMSA)
摘要
Multiscale stochastic volatility models capture financial market dynamics through coupled slow persistent trends and fast mean-reverting fluctuations, with volatility observed through discrete-block realized measures of sampling length $\Delta$ in high-frequency financial econometrics.
This multiscale structure creates a fundamental filtering dilemma: because block averaging smooths out rapid movements, estimating the fast state directly is impossible and renders full high-dimensional computational cost. Conversely, simply ignoring fast noise creates persistent systematic bias in the slow trend due to nonlinear averaging.
To resolve these obstacles, we develop a rigorous homogenization framework in the observed length. We construct an asymptotically nonlinear filter on the slow state, preserving a closed-form corrector to eliminate the bias from fast fluctuations. By establishing dual Sobolev energy bounds, we prove a error rate and derive the optimal block scale for estimating the stochastic volatility.
Extensive numerical simulations and empirical validations on high-frequency market data are also shown to verify the theoretical convergence rates, bias elimination, and order-of-magnitude computational gains of the proposed filter.
This multiscale structure creates a fundamental filtering dilemma: because block averaging smooths out rapid movements, estimating the fast state directly is impossible and renders full high-dimensional computational cost. Conversely, simply ignoring fast noise creates persistent systematic bias in the slow trend due to nonlinear averaging.
To resolve these obstacles, we develop a rigorous homogenization framework in the observed length. We construct an asymptotically nonlinear filter on the slow state, preserving a closed-form corrector to eliminate the bias from fast fluctuations. By establishing dual Sobolev energy bounds, we prove a error rate and derive the optimal block scale for estimating the stochastic volatility.
Extensive numerical simulations and empirical validations on high-frequency market data are also shown to verify the theoretical convergence rates, bias elimination, and order-of-magnitude computational gains of the proposed filter.