In this paper, we propose a bounded influence estimation (BIE) and outlier detection procedure for GARCH models. Previous studies show that maximum likelihood estimates of GARCH models are sensitive to outliers and financial time series present a heavy tail due to outliers. The proposed BIE limits the influence of a small subset of the data and is asymptotically normal. Its robustness against o...

This paper proposes an efficient approach to compute the prices of American style options in the GARCH framework. Rubinstein’s (1998) Edgeworth tree idea is combined with the analytical formulas for moments of the cumulative return under GARCH developed in Duan et al. (1999, 2002) to yield a simple recombining binomial tree for option valuation in the GARCH context. Since the resulting tree is ...

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 the historical and the 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...

Several aspects of GARCH(p, q) models that are relevant for empirical applications are investigated. In particular, it is noted that the inclusion of dummy variables as regressors can lead to multimodality in the GARCH likelihood. This invalidates standard inference on the estimated coefficients. Next, the implementation of different restrictions on the GARCH parameter space is considered. A re...

We introduce a new framework, Realized GARCH, for the joint modeling of returns and realized measures of volatility. A key feature is a measurement equation that relates the realized measure to the conditional variance of returns. The measurement equation facilitates a simple modeling of the dependence between returns and future volatility. Realized GARCH models with a linear or log-linear spec...

In this paper we investigate the properties of the Lagrange Multiplier LM test for autoregressive conditional heteroskedasticity ARCH and generalized ARCH GARCH in the presence of additive outliers AO s We show an alytically that both the asymptotic size and power are adversely a ected if AO s are neglected the test rejects the null hypothesis of homoskedasticity too often when it is in fact tr...

We introduce a new semiparametric model, GARCH with Functional EX ogeneous Liquidity (GARCH-FunXL), to capture the impact of liquidity, as implied by a stock exchange’s complete electronic limit order book (LOB), on asset price volatility. LOB-implied liquidity can be viewed as a functional rather than scalar or vectorial stochastic process. We adopt recent ideas from the functional data analys...

There is a compelling need to accurately and efficiently compute option values. Existing literature shows that models based on constant stock volatilities have been widely used in option valuation. However, stock volatilities change constantly in real life situations. The introduction of the Auto Regressive Conditional Heteroskedasticity (ARCH) model and subsequently, the Generalized Auto Regre...

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...