2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130542We propose an adaptive algorithm for tracking of historical volatility. The algorithm is built under the assumption that the historical volatility function belongs to the Stone-Ibragimov-Khasminskii class of $k$ times differentiable functions with bounded highest derivative and its subclass of functions satisfying a differential inequalities. We construct an estimator of the Kalman filter type and show optimality of the estimator's convergence rate to zero as sample size $n\to\infty$. This estimator is in the framework of GARCH design, but a tuning procedure of its parameters is faster than with traditional GARCH techniques.20 pages, 4 figuresProbabilityOptimization and ControlStatistics Theory60G35, 60G51, 62G05, 62M20, 91B70text