Stock returns are often modeled as having infinite second or fourth moments with consequences for test statistics which have not yet been fully explored. Conclusions on the existence of moments are usually drawn from a generalized Pareto or simple Pareto tail index estimate. In a recent study...

Availability of high-frequency data, in line with IT developments, enables the use of Availability of high-frequency data, in line with IT developments, enables the use of more information to estimate not only the variance (volatility), but also higher realized moments and the entire realized...

We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. Exploiting the special structure of the jump tails and the pricing thereof we identify and estimate a new Investor Fears index. The index suggests both large and...

We show that the compensation for rare events accounts for a large fraction of the equity and variance risk premia in the S&P 500 market index. The probability of rare events vary significantly over time, increasing in periods of high market volatility, but the risk premium for tail events...

We argue against the view that it is mostly the peaks of the empirical densities of stock returns (and of other risky returns as well) that set such data aside from ‘normal’ variables. We show that peaks depend on sample size and on the way returns are standardized, and that for given data...

We investigate price duration variance estimators that have long been neglected in the literature. We show i) how price duration estimators can be used for the estimation and forecasting of the integrated variance of an underlying semi-martingale price process and ii) how they are affected by a)...