Modelling asymmetric conditional heteroskedasticity in financial asset returns: an extension of Nelson’s EGARCH model

Recently, volatility modeling has been a very active and extensive research area in empirical finance and time series econometrics for both academics and practitioners. GARCH models have been the most widely used in this regard. However, GARCH models have been found to have serious limitations empirically among which includes, but not limited to; failure to take into account leverage effect in financial asset returns. As such so many models have been proposed in trying to solve the limitations of the leverage effect in GARCH models two of which are the EGARCH and the TARCH models. The EGARCH model is the most highly used model. It however has its limitations which include, but not limited to; stability conditions in general and existence of unconditional moments in particular depend on the conditional density, failure to capture leverage effect when the parameters are of the same signs, assuming independence of the innovations, lack of asymptotic theory for its estimators et cetera. This paper therefore is geared at extending/improving on the EGARCH model by taking into account the said empirical limitations. The main objective of this paper therefore is to develop a volatility model that solves the problems faced by the exponential GARCH model. Using the Quasi-maximum likelihood estimation technique coupled with martingale techniques, while relaxing the independence assumption of the innovations; the paper has shown that the proposed asymmetric volatility model not only provides strongly consistent estimators but also provides asymptotically efficient estimators