Ever since Harry Markowitz published his seminal paper on portfolio selection, investors have incorporated estimates of future volatilities and correlations into their asset allocation process. While portfolio construction methods continue to evolve, many investors continue to forecast...

In this article we introduce a linear quadratic volatility model with co-jumps and show how to cal- ibrate this model to a rich dataset. We apply GMM and more specifically match the moments of realized power and multi-power variations, which are obtained from high-frequency stock market data....

We propose a mixed frequency stochastic volatility (MFSV) model for the dynamics of intraday asset return volatility. In order to account for long-memory we separate stochastic daily and intraday volatility patterns by introducing a long-run component that changes at daily frequency and a...

Both unconditional mixed-normal distributions and GARCH models with fat-tailed conditional distributions have been employed for modeling financial return data. We consider a mixed-normal distribution coupled with a GARCH-type structure which allows for conditional variance in each of the...

We derive a nonparametric test for constant (continuous) beta over a fixed interval of time. Continuous beta is defined as the ratio of the continuous covariation between an asset and observable risk factor (e.g., the market return) and the continuous variation of the latter. Our test is based...

We overview different methods of modeling volatility of stock prices and exchange rates, focusing on their ability to reproduce the empirical properties in the corresponding time series. The properties of price fluctuations vary across the time scales of observation. The adequacy of different...

We consider a tractable affine stochastic volatility model that generalizes the seminal Heston (1993) model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider options written on the realized variance, and we examine the impact of the distribution of...

For underlying asset motions calibrating skewness and kurtosis beyond the volatility it becomes possible to consider these entities as responding to their observations in past data. Models with stochastic skewness and kurtosis are constructed by allowing the second, third and fourth power...

A Hidden Markov Model (HMM) is used to model the VIX (the Cboe Volatility Index). A 4- state Gaussian mixture is fitted to the VIX price history from 1990 to 2022. Using a growing window of training data, the price of the S&P500 is predicted and two trading algorithms are presented, based on the...

An enhanced option pricing framework that makes use of both continuous and discontinuous time paths based on a geometric Brownian motion and Poisson-driven jump processes respectively is performed in order to better fit with real-observed stock price paths while maintaining the analytical...