Asymmetry with respect to the memory in stock market volatilities

The empirically most relevant stylized facts when it comes to modeling time varying financial volatility are the asymmetric response to return shocks and the long memory property. Up till now, these have largely been modeled in isolation though. To more flexibly capture asymmetry also with respect to the memory structure we introduce a new model and apply it to stock market index data. We find that, although the effect on volatility of negative return shocks is higher than for positive ones, the latter are more persistent and relatively quickly dominate negative ones.