Using VIX Signals to Trade SPX Implied Volatility

# VIX = Vega of S&P500 options?


# VIX = Vega of S&P500 options?












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?

## Answer by jlowin (score 4)

https://quant.stackexchange.com/a/4078

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.

## Answer by Brian B (score 1)

https://quant.stackexchange.com/a/4142

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.