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.
