Valuing Options with Flexible Volatility Estimators

Abstract

Since their introduction by Engle and Bollers1ev models with autoregressive, conditional heteroscedasticity (autoregressive conditional heteroscedasticity models or ARCH) have been successfully applied to financial market data. Thus it is natural to discuss option pricing models where the underlying instrument follows an ARCH process. From an empirical point of view the form of the news impact curve, which is defined as a function of the current volatility dependent on yesterday’s returns, is the dominant factor in determining the price. It is important, for example, to know whether the news impact curve is symmetric or asymmetric. In order to avoid inaccurate pricing due to asymmetries it is necessary to use flexible volatility models. In this way EGARCH models (see Section 12.2) can be used when stock prices and volatility are correlated. This model however has a weakness that the problem of the stationarity conditions and the asymptotic of the Quasi-Maximum-Likelihood-Estimator (QMLE) is not yet completely solved. Another Ansatz, as in the Threshold GARCH-Models, is to introduce thresholds in the news impact curve to create flexible asymmetry.