Multi-Resolution Properties of Semi-Parametric Volatility Models

Abstract

Wavelet approximation and decomposition techniques are applied to non-stationary high frequency financial time series by means of global and local optimization algorithms implemented through function dictionaries. One of the objectives is to verify what possible role wavelets might have in the domain of finance, where signal processing methods may be built so to detect the latent structures characterizing volatility processes. Here the observed data have features which result difficult to handle and whose extraction by standard volatility models may not be possible. We measure the performance of computational algorithms, test their approximation power and control their effectiveness with respect to the multi-resolution pursuit.