We compare our results on empirical analysis of financial data with simulations of two stochastic models of the dynamics of stock market prices. The two models are (i) the truncated Lévy flight recently introduced by us and (ii) the ARCH(1) and GARCH(1,1) processes. We find that the TLF well describes the scaling and its breakdown observed in empirical data, while it is not able to properly des...

The univariate Generalised Autoregressive Conditional Heterscedasticity (GARCH) model has successfully captured the symmetric conditional volatility in a wide range of time series financial returns. Although multivariate effects across assets can be captured through modelling the conditional correlations, the univariate GARCH model has two important restrictions in that it: (1) does not accommo...

This paper presents an effective way of combining two popular, yet distinct approaches used in the hedging literature – dynamic programming (DP) and time-series (GARCH) econometrics. Theoretically consistent yet realistic and tractable models are developed for traders interested in hedging a portfolio. Results from a bootstrapping experiment used to construct confidence bands around the competi...

By extending the GARCH option pricing model of Duan (1995) to more exible volatility estimation it is shown that the prices of out-of-the-money options strongly depend on volatility features such as asymmetry. Results are provided for the properties of the stationary pricing distribution in the case of a threshold GARCH model. For a stock index series with a pronounced leverage eeect, simulated...

We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the Metropolis-Hastings algorithm and the parameters of the proposal density are determined adaptively by using the data sampled by the Markov chain Monte Carlo simulation...

Wepropose a novel, simple, efficient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box-Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the non-linear GARCH framework. Our simulation studies indicate that t...

We present a general framework for a GARCH (1,1) type of process with innovations using a probability law of the mean-variance mixing type. We call the process the mean variance mixing GARCH (1,1) or MVM GARCH (1,1). One implication of this particular specification is a GARCH process with skewed innovations and constant mean dynamics. This is achieved without using a location parameter to compe...

a r t i c l e i n f o JEL classification: C53 G17 Keywords: GARCH Higher conditional moments Approximate predictive distributions Value-at-Risk S&P 500 Treasury bill rate Euro–US dollar exchange rate It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency...

We provide a consistent specification test for GARCH(1,1) models based on a test statistic of Cramér-von Mises type. Since the limit distribution of the test statistic under the null hypothesis depends on unknown quantities in a complicated manner, we propose a model-based (semiparametric) bootstrap method to approximate critical values of the test and verify its asymptotic validity. Finally, w...