Monday, November 29, 2004

VIX thoughts

The VIX index tracks implied volatility, using a basket of options with expirations closest to +30 days to compute an implied probability distribution for values of the SP500 30 days hence. The VIX is often referred to as a "fear gauge" because it is anticorrelated with market performance: when the SP goes up the implied vol goes down, and vice versa.

To characterize the prob. dist. with a single volatility value, one fits to a Gaussian. Historically we know that outlier events are much more likely than implied by a log normal distribution. Deep out of the money options are included in the VIX computation as long as there are nonzero bids (and no intervening zero bids at more probable strikes). Looking at the current prices I see this only goes out about 2 sigma into the tail, so the distortion from mispricing of rare events is small. I know Nassim Taleb (author of Fooled By Randomness) makes his living buying mispriced deep out of the money options - I assume he has to buy these directly by calling up market makers, since the widely traded options don't go too far out on the tail.

Why is the VIX anticorrelated with market moves? I can understand why options traders might be psychologically disposed to expect more vol in a down market, but does the observed, historical vol exhibit this anticorrelation? We could check by crunching the data looking for up/down moves to see if the variation in the following 30 days is correlated with the sign of the move. To put it very simply, are downward moves of the market choppier than upward moves? If not, can't I arbitrage by selling vol when the market goes down and buying it when the market moves up?


Fan Yu said...

Nice to have come across this page. I was a physicist working on condensed matter theory before switching to economics - now I am teaching MBA students how to price options. The issue of negative correlation between the VIX and index level was first brought up by Fischer Black himself. He called this the "leverage effect". Basically, think of the whole market as if it were a firm. As the market drops, the amount of "assets" in the economy is less and less and it becomes closer to the "default threshold". And if you take the firm analogy literally, this means the leverage (or the debt to equity ratio) is going up. The equity being a call option on total asset value, its vol is proportional to the asset vol multiplied by the debt to equity ratio. So as the market drops, its vol goes up (assuming the vol of the asset stays constant of course). You could short straddles as the market falls and buy them as the market rises to take advantage of the mean reversion in vol, but as in any other type of "convergence trading", the correlation is not perfect, so you are not guaranteed to make money all of the time.

Fan Yu said...

Just to correct the previous post, Fischer Black came up with the "leverage effect" to refer to the negative correlation between the market level and the historical vol (not the VIX because the VIX didn't even exist back then).

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