We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics enhancing the model flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH ...

This study employed the Hinich portmanteau bicorrelation test (Hinich and Patterson, 1995; Hinich, 1996) as a diagnostic tool to determine the adequacy of the GARCH model in describing the returns generating process of Malaysia’s stock market, specifically the Kuala Lumpur Stock Exchange Composite Index (KLSE CI). The bicorrelation results demonstrated that, while GARCH model is commonly applie...

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...

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...

We model the power-law stability in distribution of returns for S&P500 index by the GARCH process which we use to account for the long memory in the variance correlations. Precisely, we analyze the distributions corresponding to temporal aggregation of the GARCH process, i.e., the sum of n GARCH variables. The stability in the power-law tails is controlled by the GARCH parameters. We model the ...

This paper introduces a unified model, which can accommodate both a continuoustime Itô process used to model high-frequency stock prices and a GARCH process employed to model low-frequency stock prices, by embedding a discrete-time GARCH volatility in its continuous-time instantaneous volatility. This model is called a unified GARCH-Itô model. We adopt realized volatility estimators based on hi...