Stock Exchange Investors have paid more attention to the banking group in recent years so that in many cases, the direction of the banking index has changed the general direction of the market. Therefore, exploring the banking index fluctuation is important from the point of view of investors as...

Electricity markets are considered to be the most volatile amongst commodity markets. The non-storability of electricity and the need for instantaneous balancing of demand and supply can often cause extreme short-lived fluctuations in electricity prices. These fluctuations are termed price...

Electricity markets are considered to be the most volatile amongst commodity markets. The non-storability of electricity and the need for instantaneous balancing of demand and supply can often cause extreme short-lived fluctuations in electricity prices. These fluctuations are termed price...

Several empirical studies in finance have examined whether or not the risk associated with any stock market responds differently in two different states of the stock market, especially in bull and bear markets. This paper studies this problem in the modelling framework, where (i) the conditional...

A critique that has been directed towards the log-GARCH model is that its log-volatility specification does not exist in the presence of zero returns. A common ``remedy" is to replace the zeros with a small (in the absolute sense) non-zero value. However, this renders Quasi Maximum Likelihood...

We introduce the notion of continuous invertibility on a compact set for volatility models driven by a Stochastic Recurrence Equation (SRE). We prove the strong consistency of the Quasi Maximum Likelihood Estimator (QMLE) when the optimization procedure is done on a continuously invertible...

Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in ordinary ARCH models, in particular when...

A critique that has been directed towards the log-GARCH model is that its logvolatility specification does not exist in the presence of zero returns. A common "remedy" is to replace the zeros with a small (in the absolute sense) non-zero value. However, this renders Quasi Maximum Likelihood...

We introduce the notion of continuously invertible volatility models that relies on some Lyapunov condition and some regularity condition. We show that it is almost equivalent to the volatilities forecasting efficiency of the parametric inference approach based on the Stochastic Recurrence...