Since their introduction by Engle (1982) and Bollerslev (1986), respectively, autoregressive conditional heteroscedastic (ARCH) and generalized autoregressive conditional heteroscedastic (GARCH) models have found extraordinarily wide use. The survey article by Bollerslev, Chou, and Kroner (1982) cited more than 300 papers applying ARCH, GARCH, and other closely related models. As they showed, A...

GARCH model has gained popularity during the last two decades, because of their ability to capture non-linear dynamics in the real life data which we often observe especially in financial markets. This paper discuss four common information criteria (AIC, AICc, BIC and HQ) and their ability of correct selection in the presence of GARCH effect, based on their probability of correct selection as a...

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering limiting models for our resulting approximating GARCH-Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffus...

It is well-known that causal forecasting methods that include appropriately chosen Exogenous Variables (EVs) very often present improved forecasting performances over univariate methods. However, in practice, EVs are usually difficult to obtain and in many cases are not available at all. In this paper, a new causal forecasting approach, called Wavelet Auto-Regressive Integrated Moving Average w...

We propose a multiplicative component model for intraday volatility. The model consists of a seasonality factor, as well as a semiparametric and parametric component. The former captures the well-documented intraday seasonality of volatility, while the latter two account for the impact of the state of the limit order book, utilizing an additive structure, and fluctuations around this state by m...