Non-Parametric Estimation of Time-Changed Levy Models
Jose E. Figueroa-Lopez
Department of Statistics
Volatility clustering and leverage are two of the most prominent features of the real dynamics of asset prices. In order to incorporate these features as well as the typical fat-tails of the log return distributions, several types of exponential Levy models with random clocks have been proposed in the literature. After a brief preview of this class of models, we study the problem of estimating the parameters controlling the jump behavior of the process as well as the underlying random clock, which introduces volatility clustering into the model. We obtain consistent estimation of the relevant parameters when both the sampling time-horizon and frequency get larger. The performance of the estimators is subsequently illustrated numerically and empirically.