In this paper, we derive a new application of fuzzy systems designed for a generalized autoregression conditional heteroscedasticity (GARCH) model. In general, stock market performance is time-varying and nonlinear, and exhibits properties of clustering. The latter means simply that certain large changes tend to follow other large changes, and in general small changes tend to follow other small...

We introduce a new family of processes that include the long memory (power law) in the volatility correlation. This is achieved by measuring the historical volatilities on a set of increasing time horizons and by computing the resulting effective volatility by a sum with power law weights. The processes have 2 parameters (linear processes) or 4 parameters (affine processes). In the limit where ...

We model the time series of the S&P500 index by a combined process, the AR+GARCH process, where AR denotes the autoregressive process which we use to account for the short-range correlations in the index changes and GARCH denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long-range correlations in the variance. We study the AR+GARCH process ...

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...