It's something I developed early in the '00s as a "risk on" alternative to a risk-reversal for isolating skew. It's not the first time I've devoted a thread to the subject, but I figure it has performed well over nearly ten years and deserved updating. I ran a hypo portfolio as well as real$ in a public (HF) account which was documented and did well even in the credit crisis.
The Pitchfork combo (PF) is a quick 'n dirty method of analyzing $-skew and/or a potential trade setup in index skew. Obviously you're selling down and out strikes.
The raw PF-premium won't tell you anything w/o some sort of historical-context, so I run a rolling 30-day OTC straddle-vol based upon SPX CBOE ATM straddle vols. Each day I calc the 30-day OTC straddle premium with a vol-input from a blended tenor of SPX ATM *listed* straddles. That's the input for the average.
I price the first strike that is outside of the straddle range. SPX 1345; ATM combo 54; (1345 - 54 =1291). I'd look to Jul20 strikes at 1290 or lower.
Here we have the 40 and 45 straddles represented by their mids (fairval figure). Using 54.00 as the premium in the Jul20 ATM listed straddle.
The PF combo is the 1290 weighted straddle, 3:1 favoring puts. You're a seller of three 1290P against one short 1290C.
($12.95*3) + ($63.70*1) = $102.55 PF credit
Then you simply solve for risk of a strike touch under a flat vol-surface/gain to sticky delta
You take the (2*ATM straddle) value as an assumption of an immediate strike touch of 1290. In this case it's (2*$54) = $108. The value related to a pinned straddle value at 1290 spot under a flat vol/sticky assumption. If 1290 is touched you would be short four ATM options. Hence the "2*ATM straddle" value. You're massively long delta at a touch of 1290, but you're analyzing a risk of strike-touch, not your cum-delta position.
PF credit = $102.55
ATM combo*2 = 108
Risk of strike touch under flat vol = $5.45 per pitchfork contract (3x1)
Obviously the flat-vol is as realistic as flat-Earth, but it's a data-point for further mining and can give you a premium-value on skew if you're running some the OTC/theoretical calc. There can be some gains from symmetry on a lower notional spot value, but it's normally overwhelmed by the vol-jump. You can hedge these off as pseudo-flies to trade them bounded.
Dude you give a ton to this place without much (if anything) in return. Thanks.
Couple questions if you don't mind:
Quote from atticus:
Each day I calc the 30-day OTC straddle premium with a vol-input from a blended tenor of SPX ATM *listed* straddles. That's the input for the average.
Just to clarify, if it was 10 days before July expiration (40 before Aug), the vol input for the OTC straddle would be = (1/3) * July_ATM_Vol + (2/3) * Aug_ATM_Vol ? (Similar to VXO...I think)
There can be some gains from symmetry on a lower notional spot value
Gains from symmetry...what's that referring to?
You can hedge these off as pseudo-flies to trade them bounded.
I'm sure it varies from trade to trade, but do you use a generic game plan for trade management after the risk is on ? (fly it off if (synthetic) vol comes in, sell deltas on 1/x sigma moves lower, etc)
After normalizing by strike, ever use the PF risk to put on pair-ish / rel val type trade between indices? I'm assuming the idiosyncratic risk makes that a no-go for single names.
I would use some form of regression but that is ok.
I suppose the best explanation is to use a heuristic;
Price spot at 1400; 1400-straddle for 30D at zero rates: 64
Price spot at 1300; 1300-straddle " .... ": 59
These don't really play well with 1:1 wing hedging. Let me go back and look at the initial delta and gamma position.
Edit: As expected, the 1290 PF is nearly dead-neutral on delta, as is usually the case when you go one-strike OTM of the ATM straddle range. There is an order to it that I am sure can be solved rather simply, but it holds to the top and bottom deciles on SPX volatilities.
The 1:1 1290 straddle (the call and one put) gammas are offsets; leaving you naked on a two-lot put gamma, as far as dissection goes. The combo is reduced, so no further dissection is possible.
I am not recommending people go shit-crazy in naked PFs. These should be traded conservatively; cash-secured isn't a bad idea. They perform well over a couple sigmas due to the vol-edge. You're trading vol-edge for gamma risk.
Nutshell: Earn on skew (vol "box" ATM/OTM swap), symmetry; stickiness if the move is gradual. Risk to gamma, vega, and their downstream moments. You're not buying a condor which may benefit from the changes in strips.
After normalizing by strike, ever use the PF risk to put on pair-ish / rel val type trade between indices? I'm assuming the idiosyncratic risk makes that a no-go for single names.
That's a good idea if you could pair two correlated names that were somehow exhibiting opposing skews. Obviously that would be extremely hard if not impossible to find. I've done these a lot on the 2x ETFs.
