Hi everyone,I am currently beginning to work on trading strategies on the VIX futures, but after a few days, I have this quite naive question: What the **** is the VIX Index ?Of course, I have done my researchs and read thorougly the White book on the CBOE website. And the more I learn about it, the more it feels to me it is a variance swap, and is finally not directly linked to volatility. The last proof of this being this paper I found: http://papers.ssrn.com/sol3/papers.cfm? ... =2030292Ok, I know, you will tell me, volatility - variance: not that much different! But actually, there are some quite huge difference I believe between variance swaps and volatility swaps. One of them being that, due to the convexity of the payoff, the actual strike of a variance swap tend to be implied vol of a 90% put (cf. http://pcj-gonfroy.com/PCJ_G%C3%A9Rant/ ... rSwaps.pdf)On the other hand, I keep reading articles saying that VIX is actually overpriced compared to consequently realized volatility. As those are using percentages (like for instance, in 80% of the cases, realized vol < VIX Index), it is completely wrong, isn't it? Given the payoff of the variance swap, I don't care if the VIX is only underestimating consequent volatility in 20% of the cases, as what really matter is the actual payoff of the equivalent variance swap.Or am I wrong and I really did not understand what the VIX actually was?Thank you for your help

If s underestimates sigma in 80% of cases, that is the same as saying that s^2 underestimates sigma^2 in 80% of cases, n'est ce pas?

Quotethere are some quite huge difference I believe between variance swaps and volatility swapsYes. And the same negative convexity relationship that exists between a vol swap and a variance swap also exists between a VIX future with maturity T and a 30-day forward starting (at T) variance swap. And this has to be taken into account in hedging one with the other.

QuoteIf s underestimates sigma in 80% of cases, that is the same as saying that s^2 underestimates sigma^2 in 80% of cases, n'est ce pas?Yes, I agree 100%. But it doesn't mean that sigma is a bad estimation of s in the end, because what is important is that sigma = E ?QuoteYes. And the same negative convexity relationship that exists between a vol swap and a variance swap also exists between a VIX future with maturity T and a 30-day forward starting (at T) variance swap. And this has to be taken into account in hedging one with the other.Do you mean that the VIX futures are actually forwards on vol swaps? and not forward on var swaps?Given that:QuoteVIX calculation uses a square root of total variance p E[WT ] which is more or equal to future realized volatility E[ p WT ]. (cf. first link in my previous message)I would have thought that the VIX futures would behave like futures on var swaps, and that the square root in the calculation was only there to get a value which in the end is coherent with the volatility that most investors know (or at least think they know).Thanks!

1. Under some well-known theory, VIX^2 is (essentially) the fair strike of an (uncapped) variance swap, quoted in same units. 2. Deviations of real world strikes from that theory may be negligble (Carr and Wu)3. They may be the only authors to have ever studied such deviations. 4. If so, that's pretty much the whole story at this point, regarding interpretation of VIX.

Last edited by Alan on March 31st, 2013, 10:00 pm, edited 1 time in total.

QuoteOk, I know, you will tell me, volatility - variance: not that much different! But actually, there are some quite huge difference I believe between variance swaps and volatility swaps. Correct - there is huge difference between volatility and variance swap. You are right - VIX is based on the variance swap value. It is then transformed in order to have the same units as vol swap. There will be systematic difference in price - as can be seen from Jensen's inequality.Variance swaps are easy to price using the static replication techniques. Vol derivatives - in general these have variance swap as an underlying. They are considerably more complex to price and were considered by a number of researchers in various set ups. For example: Howison, Rafailidis & Rasmussen, Javaheri, Wilmott & Haug (approximation to the vol swap convexity adjustment), Carr & Lee, Broadie & Jain, Carr & Wu, etc.

At a well known investment bank in the late 90s, the bank bought vol via vol swaps from loads of clients. They were centralised in one book, where the vol derivs trader then sold the replicating basket for the nearest equivalent var swap to the related single index book (FTSE, SPX, DAX, N225, etc).Then one day an internal email went out stating that there was a global trading halt in vol swaps. The reason given was that "vol swaps are negatively convex". Once people figured out that the vol swap book was bleeding money due to being short vol of vol at zero, and vol of vol not being zero, and found that all index option books were very long vol of vol, the global trading halt was quietly reversed... The index option books were up significant money, and the vol swap book was down about the same amount. Funny how that works...

- stampeding
**Posts:**7**Joined:**

(Deleted posting, after reading about VIX I realised I misunderstood Alan's posting...)/Samuel

Last edited by stampeding on July 29th, 2013, 10:00 pm, edited 1 time in total.