Fri, Feb 6, 2009 | Jared Woodard
The academic literature seems conflicted on whether backward-looking methods of forecasting volatility are superior to methods deriving forecasts from the volatility implied by options prices. This blog is intended for practitioners, not academics, so we’ll save ourselves and you, dear reader, the pain of a thorough literature review. For the truly geeky, here’s an anecdotal trawl of some relevant papers, in no particular order: Ogus 2005, Geske 2007, Yu 2008, Benavides 2004, Aguilar 1999, Brorsen 1998, Lehnert 2001.
We decided to see what some widely followed methods would forecast about S&P 500 volatility over the next several months.
In descending order, the lines above plot:
a) the at the money implied volatility of SPX options through September 2009;
b) the prices of VIX futures through the August 2009 contract;
c) a GARCH(1,1) forecast averaging the current and projected volatility n days out (which is intended to be more appropriate for pricing an option today that is n days out), using the past ten years of daily SPX closing prices;
d) a GARCH(1,1) forecast using the past ten years of daily SPX closing prices;
e) a GARCH(1,1) forecast using the past five years of daily SPX closing prices.
As with any analysis of this sort, the caveats are as important as the conclusions. None of these squiggly lines warrants a trading decision in and of itself, obviously. These are just projections – even the observed SPX option and VIX futures prices are just a snapshot. Think of these as moving averages for the future – even if one of these forecasts happened to be spot on, the real historical movement would be a lot noisier. For the forecast relying on five years of prices, the sample size is acceptable (n>1200), but intuitively, the fact that volatility is mean-reverting doesn’t mean we should expect it to revert to the sub-20 levels that were prevalent during the last bull market. Things have changed.
What we can say is that traders who actually stand to gain or lose from their forecasts are pricing volatility higher than any of these backward-looking methods would seem to warrant. Even if we shorten the examination window to include only the recent troubles (in the hopes of matching the historical data with the prices that real traders are viscerally aware of), a GARCH forecast relying on intraday data for the past two years (not pictured) has volatility staying about flat over the next 180 days.
The implied and historically-based forecasts can’t both be right. Index options are somewhat notorious for carrying an extra risk premium insofar as they’ve traditionally been used as hedging vehicles (the literature on this is quite good, for another time perhaps), and that may explain some of the disparity here. On the other hand, persistent elevated volatility is not to be trifled with, and keep in mind that a medium-term decline would be entirely consistent with periodic spikes and surprises.
Ultimately, for the near future we want to be net short options on indexes and long vega on individual equities.