Does anyone know how to replicate VIX using S&P options or futures?

[byroh]

Don't think it's too quantitative. I need a logical way (buy,sell) to replicate if there is one. Thank you for any input.

 

[Joy Pathak]

I have some ideas, but I will ask your question at the NY Options Conference going on right now that I am at. I will ask the makers of VIX index (although they might not be too happy about replication), about it after their presentation. I will post it here if I get a good answer, otherwise I will just give you what I think might be a good substitute.

 

[bob]

Simple enough: It's the square root of the par variance swap rate (and thus not an estimate of volatility per se):

http://www.cboe.com/micro/vix/vixwhite.pdf

 

[Joy Pathak]

Well, there is no way to do a static replication on VIX I think, just because of it's structure. You would have to do some sort of dynamic replication of variance swaps.

The simplest way to replicate a long VIX futures would be to short a strip of SPX options possibly.

Here is some more literature: http://www.cboe.com/micro/vix/vixtermstructure.pdf

Hopefully I get a better answer tomorrow.

 

[bob]

Spot VIX, no, but VXX is pretty much the only place anything like that is traded--and VXX is a weighted portfolio of the two front months of VIX futures, which is the real fundamental instrument. The futures can actually be replicated (in theory) because their maturity is a fixed time.

You should look into the literature on variance swaps if you want detail--it's a static hedge in OTM options combined with a dynamic hedge in the underlying. I wouldn't imagine it's particularly economical, however.

 

[Yike Lu]

Buy VIX call, short VIX put and you've got a synthetic VIX forward. Or you could just use VIX futures. Same delta, just a different theta exposure.

 

[byroh]

Thank you all; It was helpful.

@ Joy: Could you elaborate a bit more about shorting a strip of SPY options to replicate long VIX futures in words (business way)?

I read your paper, but quite not understanding an equation. (not sure which part of an equation indicating 'short' spy).

 

[tzimmerm]

If you are interested in more information about VIX Futures, check out this release:

CBOE.com


In October, with volume up 155% from a year earlier, VIX futures notched the 13th consecutive month of year-over-year volume increases.

 

[Jedison]

Realize I am quite late to this party but can't it be shown relatively easily that you can replicate vix futures using a strip of s&p options (using the same argument as in variance swap replication).

 

[euroazn]

It's trivial and canonical. People buy and sell the strip literally every VIX expiry (which is now weekly)