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# CBOE Variance Futures

Discussion in 'Options' started by sle, Dec 18, 2012.

1. ### sle

So, here they are. There is little volume there, but I already hear that hedgies want to get crossed on the exchange instead of OTC and there are two or three active market makers.

VAâS&P 500 Variance Futures

I will admit that this is pretty awesome. For all of us who who get our jollies playing with volatility, variance swaps is a pretty awesome product. If you like selling premium, selling variance is better (smoother P&L profile, better decay). If you think the world is going to end, variance swaps is probably one of the best instruments to play it - you are not tied to a particular strike. There are many, many more things you can do with variance swaps - against VIX futures, against SPX options, play around with it's term structure etc.

In this thread, I am going to, over the next few days, post the following:
(a) historical data for variance swaps - they trade very actively in OTC
(b) explanation and clarification on how these things trade and pay out
(c) some variance strategies and a conversion/payoff calculator

PS. No, I am not a shill for CBOE, but i really would love for these things to become popular

2. ### Random.Capital

If this thread lives up to its promise, it will go down in the Hall of Fame of ET Threads That Must Be Read And Understood.

Looking forward to the incoming installments...

3. ### sle

Lets start at what is a variance swap and how is it "GOOD".

Variance is a square of volatility. Historical variance can be calculated from daily closes using the following formula:

252 * Sum( 1 to N) { log(SPX[t]/SPX[t-1])/(N-1)

So, it's just an average of daily logarithmic returns that is annualized. To be anal and detail-oriented, variance for variance swap purposes is calculated from the close of the strike date (in case of futures, it is the listing date) to the SOQ print on the expiration date.

So far so good? Well, a variance swap pays the difference between the realized variance (as calculated above) and the variance strike:

payoff = variance units * (realized variance - variance strike)

To make things a bit easier in terms of quotation, usually variance strike is quoted as a volatility number, so it's a square root of variance strike:

K = sqrt(variance strike)

and variance units are calculated from "vega notional" and the variance strike as:

variance units = 1/(2*K)

So, if you have sold a 100k vega notional of a 1m variance swap struck at 15.57 (that's today VIX close, we will give there in my next post) and S&P realized 12% volatility, your P&L will be

-100000 * (.12^2 - .1557^2)/(2 * .1557) = 3160.723

Bingo. Not as simle as buying and selling stocks, but simple enough. More about variance and VIX in the next installment.

4. ### tayte

Hey SLE, how would you do the portfolio weighting if you wanted to trade the gamma spread between these futures and index options?

5. ### sle

The "atm vs var" switches trade fairly liquidity in the OTC broker market. The usual way is to trade them Vega neutral - so you trade vega notional of the variance swap equal to the SPX vega. In case of futures, you would want to take the variance units and back out the vega notional given the current variance level.

6. ### tayte

noted with much thanks!

7. ### sle

So, to continue about variance. Where does variance come from? Well, thats easy too.

Fair variance strike is determined almost exactly the same way as the level of VIX - it is an average of out of the money puts and call. The weights are determined by the strike step divided by the square of the strike level. So, the formula would be something along the lines of
put leg = Sum(all strikes from forward to zero) Put(strike) * strike step/ strike^2
call leg = Sum(all strikes from forward to infinity) call(strike) * strike step/ strike^2

fair variance strike = 2/T * (call leg + put leg)

Some discounting and forward corrections will apply, but for now, it's not important.

So, a bit of homework for the those who care - since VIX is more or less the fair variance strike, you can take the historical VIX data plus historical SPX data and calculate historical P&L for 1 month variance since 1990s. Assume that you do this every expiration month to next expiration month, VIX strike will be a close enough approximation. I will post the results next time, equity curve and all.

8. ### sle

Do you think this thread actually belongs in Index futures or somewhere else? Would it get better visibility there?

9. ### atticus

Less visibility in futures, IMO. ET could use a vola forum for stuff like this. I hope these do better than the "VT" did. My guess is that you'll be needed to provide liq!

10. ### atticus

VAA ticker for bbg, but cannot get it to quote on IBTWS. Anyone?

#10     Dec 18, 2012
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