This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature, whereas they actually fall into the domain of nonconvex nonlinear programming. Our re...

This paper attempts to model the behavior of 1-minute high frequency exchange rate data of 5 currencies : the Japanese Yen, the Australian Dollar, the Canadian Dollar, the Euro, the Pound sterling against the US Dollar, on 21 July 2005 when the Chinese Yuan was revaluated. The data shows the following distinctive features: (1) There is a large jump at the time of the Yuan revaluation, (2) Large...

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...

Using a multivariate generalized autoregressive conditional heteroskedasticity (GARCH-M) model, we investigate volatility spillovers in six Southeast Asian stock markets around the time of the 1997 Asian crisis. We focus on interactions with the U.S. market as a world financial market, and with the Japanese market as a regional financial market. We also use bivariate GARCH-M models to examine t...

Starting from the Cholesky-GARCH model, recently proposed by Darolles, Francq, and Laurent (2018), paper introduces Block-Cholesky GARCH (BC-GARCH). This new model adapts in a natural way to asset pricing framework. After deriving conditions for stationarity, uniform invertibility beta tracking, we investigate finite sample properties of variety maximum likelihood estimators suited BC-GARCH mea...

The contribution of this paper is twofold. First, we exploit copula methodology, with two threshold GARCH models as marginals, to construct a bivariate copula-threshold-GARCH model, simultaneously capturing asymmetric nonlinear behaviour in univariate stock returns of spot and futures markets and bivariate dependency, in a flexible manner. Two elliptical copulas (Gaussian and Student’s-t) and t...

The main objective of this paper is to propose an alternative valuation framework for pricing foreign currency and cross-currency options, which is capable of accommodating existing empirical regularities. The paper generalizes the GARCH option pricing methodology of Duan (1995) to a two-country setting. Specifically, we assume a bivariate nonlinear GARCH system for the exchange rate and the fo...

The stylized facts of univariate high-frequency data in finance are well known; see Dacorogna et al. (2001). In Breymann et al. (2003) we analyzed bivariate high frequency forex data as a function of the sampling frequency, however treating the data as iid. In the present paper, using the data from Breymann et al. (2003), we model the dynamics as GARCH type processes and investigate the stylize...

This paper focuses on the diagnostic checking of vector ARMA (VARMA) models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This is different from the traditional approach that employs only the squared series of standard...