We consider the problem of estimating the volatility of a financial asset from a time series record. We believe the underlying volatility process is smooth, possibly stationary, and with potential abrupt changes due to market news. By drawing parallels between time series and regression models, in particular between stochastic volatility models and Markov random fields smoothers, we propose a semiparametric estimator of volatility. For the selection of the smoothing parameter, we derive a universal rule borrowed from wavelet smoothing. Our Bayesian posterior mode estimate is the solution to an `1-penalized likelihood optimization that we solve with an interior point algorithm that is efficient since its complexity is bounded by O(T3=2), where T is the length of the time series. We apply our volatility estimator to real financial data, diagnose the model and perform back-testing to investigate to forecasting power of the method by comparison to (I)GARCH.