This paper presents an effective way of combining two popular, yet distinct approaches used in the hedging literature – dynamic programming (DP) and time-series (GARCH) econometrics. Theoretically consistent yet realistic and tractable models are developed for traders interested in hedging a portfolio. Results from a bootstrapping experiment used to construct confidence bands around the competi...

We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the Metropolis-Hastings algorithm and the parameters of the proposal density are determined adaptively by using the data sampled by the Markov chain Monte Carlo simulation...

Distributional theory for Quasi-Maximum Likelihood estimators in long memory conditional heteroskedastic models is not formally defined, even asympotically. Because of that, this paper analyses the performance of the Likelihood Ratio and the Lagrange Multiplier misspecification tests for Periodic Long Memory GARCH models. The real size and power of these tests are studied by means of Monte Carl...

Since their introduction by Engle (1982) and Bollerslev (1986), respectively, autoregressive conditional heteroscedastic (ARCH) and generalized autoregressive conditional heteroscedastic (GARCH) models have found extraordinarily wide use. The survey article by Bollerslev, Chou, and Kroner (1982) cited more than 300 papers applying ARCH, GARCH, and other closely related models. As they showed, A...

Recently, there has been a growing interest in the methods addressing volatility in computational finance and econometrics. Peiris et al. [8] have introduced doubly stochastic volatility models with GARCH innovations. Random coefficient autoregressive sequences are special case of doubly stochastic time series. In this paper, we consider some doubly stochastic stationary time series with GARCH ...