In Duan, Gauthier and Simonato (1999), an analytical approximate formula for European options in the GARCH framework was developed. The formula is however restricted to the nonlinear asymmetric GARCH model. This paper extends the same approach to two other important GARCH specifications GJR-GARCH and EGARCH. We provide the corresponding formulas and study their numerical performance. keywords: ...

This paper examines the forecasting performance of four GARCH(1,1) models (GARCH, EGARCH, GJR and APARCH) used with three distributions (Normal, Student-t and Skewed Student-t). We explore and compare different possible sources of forecasts improvements: asymmetry in the conditional variance, fat-tailed distributions and skewed distributions. Two major European stock indices (FTSE 100 and DAX 3...

Empirical Mode Decomposition (EMD), recently proposed by Huang et al. [12], appears to be a novel data analysis method for nonlinear and non-stationary time series. By decomposing a time series into a small number of independent and concretely implicational intrinsic modes based on scale separation, EMD explains the generation of time series data from a novel perspective. This paper presents an...

This study investigates the time series beaviour of daily stock returns of four firms listed in the Nigerian StockMarket from 2nd January, 2002 to 31st December, 2006, using three different models of heteroscedastic processes, namely: GARCH (1,1), EGARCH (1,1) and GJR-GARCHmodels respectively. The four firms whose share prices were used in this analysis are UBA, Unilever, Guiness and Mobil. All...

For a GJR-GARCH(1, 1) specification with generic innovation distribution we derive analytic expressions for the first four conditional moments of forward and aggregated returns variances. Moments most commonly used GARCH models are stated as special cases. We also limits these time horizon increases, establishing regularity conditions to converge normal moments. A simulation study using produce...

The financial market is the core of national economic development, and stocks play an important role in market. Analyzing stock prices has become focus investors, analysts, people related fields. This paper evaluates volatility Apple Inc. (AAPL) returns using five generalized autoregressive conditional heteroskedasticity (GARCH) models: sGARCH with constant mean, GARCH sstd, GJR-GARCH, AR(1) GJ...

The present study aims at applying different methods i.e GARCH, EGARCH, GJRGARCH, IGARCH & ANN models for calculating the volatilities of Indian stock markets. Fourteen years of data of BSE Sensex & NSE Nifty are used to calculate the volatilities. The performance of data exhibits that, there is no difference in the volatilities of Sensex, & Nifty estimated under the GARCH, EGARCH, GJR GARCH, I...

We propose a new approach to density forecast optimisation and apply it to Value-at-Risk estimation. All existing density forecasting models try to optimise the distribution of the returns based solely on the predicted density at the observation. In this paper we argue that probabilistic predictions should be optimised on more than just this accuracy score and suggest that the statistical consi...

In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). For purposes of deriving the mathematical regularit...