This paper provides a comprehensive framework for comparing predictors of univariate time series in the mean square norm. Initially, the forecast errors are assumed to be unbiased, independent, and normally distributed. Each of these is progressively relaxed. A new heteroscedasticity and...

Option prices seem to behave in ways inconsistent with the Black-Scholes model. Implied volatility varies with the strike price in a parabolic shape that is often called the volatility 'smile.' My objective in this paper is to identify implied probability distributions that might explain this...

We investigate the marginal predictive content of small versus large jump variation, when forecasting one-week-ahead cross-sectional equity returns, building on Bollerslev et al. (2020). We find that sorting on signed small jump variation leads to greater value-weighted return differentials...