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 ...

Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our ne...

In this paper we propose a new multivariate GARCH model with timevarying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. While each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analogue. By impos...

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity ~ARMAGARCH! model+ The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established+ Consistency of the quasimaximum-likelihood estimator ~QMLE! is proved under only the second-order moment conditi...

The issue of finite-sample inference in GARCH-like models has seldom been explored in the theoretical literature, although its potential relevance for practitioners is self-evident. In some cases, asymptotic theory may provide a very poor approximation to the actual distribution of the estimators in finite samples. The aim of this paper is to propose the application of the socalled double lengt...

We consider the parameter restrictions that need to be imposed in order to ensure that the conditional variance process of a GARCH(p, q) model remains non-negative. Previously, Nelson and Cao (1992) provided a set of necessary and sufficient conditions for the aforementioned non-negativity property for GARCH(p, q) models with p ≤ 2, and derived a sufficient condition for the general case of GAR...

In this paper, we introduce a two−dimensional Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model for clutter modeling and anomaly detection. The one−dimensional GARCH model is widely used for modeling financial time series. Extending the one−dimensional GARCH model into two dimensions yields a novel clutter model which is capable of taking into account important characteris...

The paper aims to show methodology of parameter estimation of the stable GARCH(1,1) model. There are represented and compared 3 methods of finding estimates of their parameters. We assume that we have a stable GARCH(1,1) model with the stable symmetric innovation. We search for the estimates of parameters of the stable GARCH model under assumption that we don’t know anything about parameters, t...

We derive analytically the first four conditional moments of the integrated variance implied by the GARCH diffusion process. From these moments we obtain an analytical closed-form approximation formula to price European options under the GARCH diffusion model. Using Monte Carlo simulations, we show that this approximation formula is accurate for a large set of reasonable parameters. Finally, we...

The paper investigates the relationship between inflation and inflation uncertainty using the Iranian data over the period 1959:03 – 2008:02. GARCH models are used to examine this relationship. Granger methods are employed to provide statistical evidence for the relationship between average inflation and inflation uncertainty. Threshold GARCH (TGARCH) models are considered to investigate asymme...