In practice, Financial Time Series have serious volatility cluster, that is large volatility tend to be concentrated in a certain period of time, and small volatility tend to be concentrated in another period of time. While GARCH models can well describe the dynamic changes of the volatility of financial time series, and capture the cluster and heteroscedasticity phenomena. At the beginning of ...

This paper examines the behaviour of European option price (Duan (1995)) and the Black-Scholes model bias when stock returns follow a GARCH (1,1) process. The GARCH option price is not preferenceneutral and depends on the unit risk premium (λ) as well as the two GARCH (1,1) process parameters (α1 , β1). In general, the GARCH option price does not seem overly sensitive to these parameters. Deep-...

We analyze the time-dependence of exchange rate correlations using a new multivariate GARCH model. This model consists of two parts. First, we transform the exchange rate changes into their principal components and specify univariate GARCH models for all components. Second, we use the inverse of the principal components construction to transform the conditional component moments back into those...

We test the importance of multivariate information for modelling and forecasting inflation’s conditional mean and variance. In the literature, the existence of inflation’s conditional heteroskedasticity has been debated for years, as it seemed to appear only in some datasets and for some lag lengths. This phenomenon might be due to the fact that inflation depends on a linear combination of econ...

In this paper we study a new class of nonlinear GARCH models. Special interest is devoted to models that are similar to previously introduced smooth transition GARCH models except for the novel feature that a lagged value of conditional variance is used as the transition variable. This choice of the transition variable is mainly motivated by the desire to find useful models for highly persisten...

How persistent is volatility? In other words, how quickly do financial markets forget large volatility shocks? Figure 1.1, Shephard (attached) shows that daily squared returns on exchange rates and stock indices can have autocorrelations which are significant for many lags. In any stationary ARCH or GARCH model, memory decays exponentially fast. For example, if {εt } are ARCH (1), the {εt} have...

This article applied GARCH model instead AR or ARMA model to compare with the standard BP and SVM in forecasting of the four international including two Asian stock markets indices.These models were evaluated on five performance metrics or criteria. Our experimental results showed the superiority of SVM and GARCH models, compared to the standard BP in forecasting of the four international stock...

We compare three methods of constructing confidence intervals for sample autocorrelations of squared returns modeled by models from the GARCH family. We compare the residual bootstrap, block bootstrap and subsampling methods. The residual bootstrap based on the standard GARCH(1,1) model is seen to perform best.

In this paper we introduce an exponential continuous time GARCH(p, q) process. It is defined in such a way that it is a continuous time extension of the discrete time EGARCH(p, q) process. We investigate stationarity, mixing and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous time GARCH(p, p) model.