We introduce a methodology for dynamic modelling and forecasting of realized covariance matrices based on generalization of the heterogeneous autoregressive model (HAR) for realized volatility. Multivariate extensions of popular HAR framework leave substantial information unmodeled in residuals....

Many electricity markets exhibit an oligopolistic structure with market participants whose individual trading activities may shift prices essentially. In this context, the question of how to optimally liquidate an existing electricity futures portfolio over a fixed time horizon under the...

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...

Three concepts: stochastic discount factors, multi-beta pricing and mean-variance efficiency, are at the core of modern empirical asset pricing. This chapter reviews these paradigms and the relations among them, concentrating on conditional asset-pricing models where lagged variables serve as...

Under the CAPM assumptions, the market capitalization weighted portfolio is mean-variance efficient. In real world applications it has been shown by various authors that low risk portfolios outperform the market capitalization weighted portfolio. We revisit this anomaly using high-frequency data...

The risky assets prices of the bi-variate model are reviewed under the hegemonize concentration filtered physical probability space. In the stochastic variance of the Cox-Ingersoll-Ross process. The Mean-variance hedging expanse on the Föllmer-Schweizer decomposition is stringent to the...

We propose a number of volatility measures that are based on ensemble averaging instead of time averaging. These measures allow fast measurement of current volatility without relying on series of past data (realized volatility) of future expectations (implied volatility). The introduced...