VARIANCE BOUNDS IN FINANCIAL INVERSE PROBLEMS: SIMULATION EVIDENCE FROM TIME-SCALE ESTIMATORS

ENRICO CAPOBIANCO

Abstract. The stochastic characterization of the problem which is studied here relies on a semimartingale approach for representing asset prices, and on the analysis of realised and integrated volatility measures. The former volatility is an empirical approximation of the other one, given by an average of high frequency returns observed within a certain time frame. Semimartingales are useful because allow for the quadratic variation principle to hold, thus leading to the convergence of the realised to the integrated volatility. The goal of this work is to show with simulations that the convergence properties hold also when time-scale coordinates are considered and wavelet-based estimators for the volatility process are adopted.