Estimation of the Realized High-Order Moments

In standard return modelling approaches, returns are often assumed to follow a normal distribution. This assumption implies a zero skewness as well as a zero excess kurtosis. Both of these implications do not correspond to empirical observation and eventually lead to problems e.g. in financial risk management. On the other side, the typical non-parametric estimation of these values require a huge amount of data to be reliable. For this reason, it is advisable to exploit the availability of high frequency data and construct estimators in the fashion of the well-known realized variance. A previous estimation approach is extended to non-martingale price processes. On the basis of Monte Carlo simulations, we show that our estimators are unbiased and consistent when the underlying price process can be modelled as a stochastic volatility jump diffusion process. Distribution properties of the estimators are discussed.

Joint work with: Manuel Schmid (TU Dresden) and Michael Rockinger (Uni Lausanne)