The profitability of trading volatility using real-valued and symbolic models

Essentially, there are two notions of volatility in literature: historical volatility and implied volatility. While measures of the former notion are derived from historical returns by (weighted) averaging over a time window, measures of the latter are estimated from observed option prices. Whatever particular volatility measure one is willing to apply, a central question is that of predictability of volatility1. In particular, predictability in a statistical sense and economically meaningful predictability must be distinguished. In this paper we concentrate on the latter by analyzing the profitability of a pure volatility trading strategy which is delta-neutral and independent of an option pricing model, for the German stock index DAX. Several very different methods ranging from linear and non-linear, real-valued models to symbolic models of volatility changes2 are applied to predict the change in volatility to the next trading day and to gain profits by buying or selling straddles accordingly. The trading performance is evaluated for one historical and one implied volatility measure. The results are carefully evaluated concerning transaction costs, stationarity issues, and statistical significance. The main contribution of this paper is that, for the first time, the trading performance of models based on different modelling paradigms (real-valued versus symbolic) is compared. Furthermore, it is shown that the combination of different models can lead to improved performance, i.e., higher profits. 1There is yet another approach where historical returns are described by heteroskedastic time series models (e.g. by a GARCH model). In this case the volatility predictions are determined by the model specification. 2Symbolic sequences of volatility changes are obtained by quantizing volatility differences in a preprocessing step.