Neale A. El-Dash, Luiz K. Hotta, Non-parametric Volatility Estimation in Continuous Time

The idea of volatility is fundamental to precise definition of risk and, hence, its estimation (or prediction) is a very important task in finance applications. We present some ideas on nonparamateric estimation of volatility function in diffusion models. A nonlinear wavelet estimate of the volatiltiy function is proposed and its performance is compared to three kernel estimators in both simulated and real data. Simulation is developed for eight volatility shapes and some interesting, but not unexpected, results are presented. Some issues such as online estimation and prediction, robustness to oversmoothing and performance under sudden changes in pattern of volatility are also discussed.