volatility of carbon emissions, it is not surprising that crude oil and coal have recently become a very important research topic … causality and volatility spillovers in spot and futures prices of carbon emissions, crude oil, and coal. A likelihood ratio test … is developed to test the multivariate conditional volatility Diagonal BEKK model, which has valid regularity conditions …

conditional variance is modelled by a stochastic volatility process. We develop a Monte Carlo maximum likelihood method to obtain … variance, in the order of integration, in the short memory characteristics and in the volatility of volatility. …

The three most popular univariate conditional volatility models are the generalized autoregressive conditional … models are important in estimating and forecasting volatility, as well as capturing asymmetry, which is the different effects … on conditional volatility of positive and negative effects of equal magnitude, and leverage, which is the negative …

While the stochastic volatility (SV) generalization has been shown to improvethe explanatory power compared to the … then investigate the respectiveeffect of stochastic interest rate, systematic volatility and idiosyncraticvolatility on … thesystematc volatility of the consumption process, our estimation results suggestthat the short-term interest rate fails to be a …

common belief, the auction prices for gas storage are mostly affected by the volatility of current market prices rather than … with the volatility of the spot market. This is an intuitive result because storage capacity can serve as an effective …

simulation algorithm exists for this process, at present this is not the case for the Heston stochastic volatility model, where …

The characteristic functions of many affine jump-diffusion models, such as Heston’s stochastic volatility model and all …