CBOE Variance Futures

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

  1. quite truthfully..i watch the oi, vol etc in the other new cfe curves , somehow i never looked at VA...promising oi it seems.

    of course i cannot get ib to quote the curve yet. if someone knows the correct symbol i'm interested.

    sle, guys like you mostly trade these against another product? btw, i did note no feb oi.

    my interest in these will be to see if they trade differently than vix futures.
    #11     Dec 18, 2012
  2. I did not read carefully, but it strikes me that maybe something is wrong in the formulas (I looked only at the first one).

    In variance formula, shouldn't you square the returns, and center them if using N-1, or divide by N instead of N-1 if no centering?
    #12     Dec 18, 2012
  3. Jgills


    i havent looked on IBTWS yet, but i see it on bbg. any idea why it shows the jan settlement at 764.16 (27.64 vol strike) but shows quotes at 16.15/16.45 25k x 5k?

    when would it even have traded with a 27.64 strike if it was listed dec 10?
    #13     Dec 18, 2012
  4. Lean on the bid!
    #14     Dec 18, 2012
  5. sle


    You are right, for some reason (formating?) it deleted my square rooting (lets see - ^2). Thank you for pointing out! Can a moderator correct this please, it's been too long?

    PS. I also see that a multiplier is missing from my variance P&L calculation, but that I think is my error.
    #15     Dec 18, 2012
  6. sle


    No, initial strike is specified by the exchange using a variance calculation, I think (have not looked) it would be with 19 handle

    edit - yes, initial strike is printed as 396.41, so square root of that is 19.9. i'll get to how these things are quoted in the next post. For now, think that, for practical purpose, they are quoted as fresh variance swap and settled (EOD) as seasoned variance swap vs the original strike.
    #16     Dec 18, 2012
  7. so what this value just floats on speculation .... its striked at a certain date as you specified then as variance starts to be realized it moves around.. wow i need to read more.. seems like your sort of trading against a snap shot of the implieds.. "strike"
    #17     Dec 18, 2012
    stevenk85 likes this.
  8. #18     Dec 18, 2012
  9. sle


    First of all, thank you all for participating. Also, if you see any errors, please let me know right away (thank you, tj!). Obviously, I try to be as correct as I can, but I am in bed with fever and my attention span is rather low.

    Anyway, I promised that I'd post a simple short variance strategy (the "homework answer") but I figured I'd go through how the futures are quoted and settled first, given that it is super-confusing at first.

    The way this works:

    * day one, when these things are listed, the exchange specifies an initial strike, K0 using a variance swap calculation (as I described above). So, for example, Jan13 futures were listed on Aug 20th, 2012 (they back-dated the calc based on the options listing) and the initial variance strike is 396.41, which is 19.9^2.

    * now, next day comes and the market makes make the fair variance at 16.75 @ 17. This is spot starting variance. Now, lets assume that you hit 16.75 bid in $100,000 vega notional, so your Vt = 16.75. You settlement will be determined as follows. First, some important inputs:

    DF = a discount factor provided by the exchange, given the level of OIS rates, it's equal to 1 more or less

    N = also known as N-effective, a number of business days between the contract listing and contract expiration.

    n = number of business days elapsed on which variance was observed

    K0 = initial variance strike as specified by the exchange (e.g. in our case of Jan13 futures, 396.41)

    X = interest accrued on margin. again, given the interest rates, you can safely assume it is going to be somewhere around zero

    First, we convert the price into "effective variance strike", call it Kt

    Kt = [ Vt^2 * (N-1-n)/252 + 10000 * Sum(1 to n) log(Si/Si-1)^2 ] * 252/(N-1)

    What did we do here? We combined current implied variance from now to expiry with already realized variance and annualized the result. So, now, we can calculate the "price" of the variance futures as

    Futures "Price" = DF * (Kt - K0) - X + 1000

    I will provide a numerical example in a sec.
    #19     Dec 18, 2012
  10. sle


    I will take a theoretical numerical example, but something close to reality:

    Lets assume that
    -- you hit the Jan 13 futures today for 16.75 in 100k vega
    -- since Aug 20th, S&P500 volatility has been about 0.65% per day

    If you do the legwork, you will see that
    -- N = 106
    -- n = 70
    For simplicity, we assume discount and accrued value as zero

    realized portion = 70*10000*(0.65%^2) = 29.575

    implied portion = (16.75^2)*(106-1-70)/252 = 38.9670

    Kt = (realized portion + implied portion)*252/(106-1) = 165.50

    Now, all thats left to do is to calculate the futures value:

    futures settlement = (165.50 - 396.41) + 1000 = 768.1

    CBOE, in their never-ceasing kindness, provides daily calculation of discount factor, realized variance, etc, so you don't have to deal with it and just plug in the numbers.
    #20     Dec 18, 2012