A new non-linear GARCH model

This dissertation contains four papers in the field of financial econometrics. In the first paper, A Smooth Transition ARCH Model for Asset Returns, a new class of ARCH models is introduced. The model class allows for non-linearity in the equation for the conditional variance. Two forms of non-linearity are considered: (i) asymmetry regarding the sign of residuals, and (ii) non-linearity regarding the size of residuals. Furthermore, specification tests for the models are presented. The second paper, Specification Tests for Asymmetric GARCH, presents two new Lagrange multiplier test statistics designed for testing the null of GARCH(1,1), against the alternative of asymmetric GARCH. Small sample properties for the statistics are presented and the power of both tests is shown to be superior to that of previously proposed tests. This is true for a large group of asymmetric GARCH models, providing that the proposed tests can detect general GARCH asymmetry. The third paper, Modeling Nordic Stock Returns with Asymmetric GARCH models, investigates the presence of asymmetric GARCH effects in a number of equity return series, and compares the modeling performance of seven different asymmetric GARCH models. The data consists of daily returns for 45 Nordic stocks, for the period July 1991 to July 1996. The paper also introduces three new procedures for asymmetry testing. The proposed LM tests allow for heterokurtosis under the null. The final paper, Discrete Time Hedging of OTC Options in a GARCH Environment: A Simulation Experiment, examines the effect of using the Black and Scholes formula for pricing and hedging options in a discrete time heteroskedastic environment using a simulation procedure. It is shown that the variance of the returns on the hedged position is considerably higher in a GARCH(1,1) environment than in a homoskedastic environment. The variance of returns is heavily dependent on the level of kurtosis in the returns process and on the first-order autocorrelation in centered and squared returns.Each paper is self-contained and can be read in an order chosen by the reader.In an introductory chapter, the reader is given a general summary of the ARCH literature and will gain a clear understanding of how the four essays relate to previous work in the econometrics and finance literature, and to practical considerations of econometric modeling.

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