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ok, so let assume I can predict the daily change in the VIX itself (in points) every day. what would be the best way to play this with OPTIONS? well, obviously VIX options, but if I can look at the VIX as the implied volatility of the S&P (?) can I now project from that on the change in Vega of the SPX options? so if my prediction tells me VIX is going down today, I should be able to make money by selling both call and put of the S&P (same strike and expiration) to maintain a Delta-neutral position, and being "short Vega", making money on the decline in the implied volatility of these options.

Am I right?

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2 Answers

Generally speaking, volatilities at all points of the vol surface are (positively) correlated in both empirical and theoretical models. So if you feel you have a prediction strategy for the VIX, you have an associated directional prediction for other volatilities, and you can take advantage of that.

Directional volatility bets are most often expressed (as you infer in your question) by buying/selling both a call and a put. This is called a straddle. If you want to spend less time hedging, you might instead trade a few more options at the same time.

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If he can predict the level of VIX, he is not necessarily predicting the level of fixed strike volatility (which is going to determine your straddle or strangle PnL) but rather is predicting a joined performance of S&P and some (fairly small) fixed strike vol component. If his prediction algo is robust (which I doubt), he should be trading VIX futures or if he found a way to predict changes in SPX (easy to check what explains variance in predictions) he should be trading S&P futures. –  Strange Sep 19 '12 at 4:15
    
Good point, Strange. It shouldn't be hard to check if there is any S&P prediction component there. –  Brian B Sep 20 '12 at 14:56
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The VIX is designed to "represent the implied volatility of a hypothetical at-the-money [SPX] option with exactly 30 days to expiration." (via the CBOE) The calculations are available from the CBOE in this white paper.

Note that your question is wrong -- it is the implied volatility, not the vega. Moreover, you wouldn't predict a change in vega (which is a second derivative...), you'd predict the change in volatility and seek to profit through vega.

Replacing your use of vega with implied volatility, your assumption becomes correct in theory -- but it's a tough theory to put into practice... even if we suppose for a moment that you can in fact predict the VIX. It is extremely rare that you can actually purchase an ATM option with 30 days to maturity, meaning your proxy security necessarily deviates from the VIX calculation. Moreover, the transaction costs of maintaining a delta-neutral position are not insignificant (you can't just sell a put and a call, it won't stay delta-neutral).

You wouldn't do it with VIX options because they reflect the forward value of the VIX at maturity, and if you look at the term structure of VIX futures you'll see that forward values, even one month out, are far less volatile than spot.

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Actually, you do not need to have changes in fixed strike implied volatility to have changes in VIX. In fact, sometimes you see an increase in VIX with a concurrent decrease in fixed strike volatility and vice versa. Most changes in VIX come from the delta "embedded" in the variance swap calculation. –  Strange Sep 3 '12 at 19:57
    
If you look at the index calculation methodology in the VIX white paper: Couldn't you just try to replicate the index by using (part of) the option strips used for index replication? I would try to calculate the index myself and then try to evaluate which options to drop (p.e. by regression or maybe pca)... so basically it would be all about S&P-Options in that case... –  vanguard2k Sep 4 '12 at 6:38
    
@Strange that makes sense because VIX references a hypothetical floating strike (ATM), not fixed. –  jlowin Sep 4 '12 at 21:19
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@vanguard2k You could try, but there are quite a few hurdles to replicating VIX with available SPX options: first, it would have be a very dynamic replication; the required options (not to mention quantities thereof) change every minute and rebalancing on any timescale would be difficult and expensive. Second, compounding the first, note that the calculation uses mid prices, and even half the bid/ask spread can have a meaningful impact on implied vol. –  jlowin Sep 4 '12 at 21:32
    
@jlowin sorry, not sure how to post it as a comment: (a) VIX is NOT a estimate of a hypothetical floating ATM strike, but rather a fair strike for a theoretical variance swap. (b) You could statically replicate it just like you would replicate a variance swap, though it's a fair amount of pain since in this case you have to buy two options strips to match the 30-day maturity (c) A better way would usually be to buy a front month variance swap in the IDB market and just live with the tiny amount of the term structure risk –  Strange Sep 5 '12 at 22:06
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