VIX and Black-Scholes

OK, humor me here as I continue to think about volatility. Looking at the CBOE white paper on VIX, I see a plot (page 13) indicating very strong correlation between movements in the SP and the implied vol. A change in the SP of about 1% causes a 4% shift in the VIX, but with the opposite sign. Now, SP500 options are widely traded and liquid. They should provide one of the best tests of options pricing theory. But in the usual Black-Scholes model the volatility of the underlying security is a fixed input parameter - it certainly isn't supposed to be path (history) dependent. The simple log normal random walk model has its limitations - for example, there is no reason the vol shouldn't change in time (hopefully slowly) - but I'm surprised to see such clear path dependence. Of course, it's possible that the actual volatility (as opposed to implied volatility) doesn't exhibit the correlations we are discussing. But if so, there is an inefficiency in the behavior of options traders that should be arbed away!

...I've been informed that these issues are addressed using more sophisticated GARCH models. (GARCH = Generalised Autoregressive Conditional Heteroskedastic!)

This paper seems to conclude that implied vol is a good predictor of realized vol, so the correlation between market movements and vol is not a behavioral quirk of options traders (indeed, it is a quirk of the market itself).