Pricing Butterfly Spreads

oldmonk · Jul 31, 2018

I've been looking for information on how to price an ATM 1-2-1 butterfly spread, and I haven't been able to find anything useful so far. All else equal, I imagine you'd want to buy the spread when ATM implied vol is high relative to the wings (in other words, when skew is relatively low).

Skew appears to be quite volatile for short term spreads (< 2 weeks to expiry), as I've seen the spread's intraday price change dramatically in response to small changes in spot (I guess this also has to do with the gamma). This has worked both for/against me when I’ve traded these. So clearly timing matters a lot when entering/exiting these trades, even when you’re right on stat vol/direction.

What methodology do you use to price these spreads? Also, can you suggest any resources that provide a framework for butterfly spread pricing?

destriero · Jul 31, 2018

You're not going to find cheap wingspreads. Just saving you some time here. Butterflies are bimodal to most greeks but I don't want to go into the weeds. Spot at body strike if you're simply shorting vol, shotgun style; OTM if you want a pure play on gamma-modality and direction; ATM-ITM if you're after ddecay.

oldmonk · Jul 31, 2018

destriero said:
You're not going to find cheap wingspreads. Just saving you some time here. Butterflies are bimodal to most greeks and I don't want to go into the weeds. Spot at body strike if you're simply shorting vol, shotgun style; OTM if you want a pure play on gamma-modality and direction; ATM-ITM if you're after ddecay.

That makes sense, but what about timing? Even if it's impossible to find a cheap spread, I'm just trying to avoid buying these at an intraday high. Probably won't make much of a difference in the outcome of the trade, but could mean a 5% difference in returns. Does vertical skew play a role when you're placing these trades? Also, not sure what you mean by ddecay?

destriero · Jul 31, 2018

oldmonk said:
That makes sense, but what about timing? Even if it's impossible to find a cheap spread, I'm just trying to avoid buying these at an intraday high. Probably won't make much of a difference in the outcome of the trade, but could mean a 5% difference in returns. Does vertical skew play a role when you're placing these trades? Also, not sure what you mean by ddecay?

Sure, skew plays a role, but not as much as initial delta. Delta decay.

marameo · Jul 31, 2018

sle · Jul 31, 2018

destriero said:
Sure, skew plays a role, but not as much as initial delta. Delta decay.

You think? I'd say that ATM/OTM fly (especially on the put side) is a pure skew play, just a slightly safer version of a 1x2. Eventually it does decay into an explicit delta position, but early on delta is pretty small and most of your daily pnl would be coming from vega and skew, right?

PS. Sometimes when the skew is steep, you can find flys where you'd be long gamma and long theta... the "ultimate freebie"

PPS. Think of it this way, a barrier put is a ultimate lopsided fly and it's mostly a skew and (less so) vega play

destriero · Jul 31, 2018

Secret Santa said:
You think? I'd say that ATM/OTM fly (especially on the put side) is a pure skew play, just a slightly safer version of a 1x2. Eventually it does decay into an explicit delta position, but early on delta is pretty small and most of your daily pnl would be coming from vega and skew, right?

PS. Sometimes when the skew is steep, you can find flys where you'd be long gamma and long theta... the "ultimate freebie"

PPS. Think of it this way, a barrier put is a ultimate lopsided fly and it's mostly a skew and (less so) vega play

Yeah, I see your analogy of the barrier put delta inverse to vol; especially on the touches vs. digitals. Yeah, my primary trade is an ATM p-fly into steep skew.

destriero · Jul 31, 2018

Delta accounts for half, stickiness for half. I priced it QnD using the resulting deltas, so delta/local vol.

sle · Jul 31, 2018

destriero said:
Look at the following fly matrix.

Ugh, I see what you mean now. Given that all of these are expiring like tomorrow, I have to assume you are holding them to expiration. Now imagine doing a wider fly in something like Dec expiration, where you are packing up a bit of Vega and dVega/dSpot at different strikes.

destriero · Jul 31, 2018

Secret Santa said:
Ugh, I see what you mean now. Given that all of these are expiring like tomorrow, I have to assume you are holding them to expiration. Now imagine doing a wider fly in something like Dec expiration, where you are packing up a bit of Vega and dVega/dSpot at different strikes.

Yeah, agreed.