Probability of Touch (POT)

[Trader13]

The common rule-of-thumb is that an estimate of POT for a strike is the delta of its option x 2. For example, a 25 delta OTM option has a 50% POT.

When you have a steep put/call skew that is reflected in the deltas, an equivalent POT for puts and calls will be at different strike distances from ATM, which doesn't seem quite right. Especially when the skew is the result of a risk premium to one side, or supply/demand based on collar strategies, and other reasons that are not predictive of price movement.

Are there better estimates of POT than the quick-and-dirty delta calculation?

 

[nooby_mcnoob]

The common rule-of-thumb is that an estimate of POT for a strike is the delta of its option x 2. For example, a 25 delta OTM option has a 50% POT.

When you have a steep put/call skew that is reflected in the deltas, an equivalent POT for puts and calls will be at different strike distances from ATM, which doesn't seem quite right. Especially when the skew is the result of a risk premium to one side, or supply/demand based on collar strategies, and other reasons that are not predictive of price movement.

Are there better estimates of POT than the quick-and-dirty delta calculation?

Not sure if better but you can use Bayesian statistics to get a second estimate.

 

[tommcginnis]

Are there better estimates of POT than the quick-and-dirty delta calculation?

Nope. The best rule-of-thumb is the one is use. (Skew and all.)
But these days, with multi-core processors in our pockets, I'm hoping that efficient P(Touch) calculations will start popping up with regularity. It's going to happen.

[EDIT]
From an off-line conversation, a further realization on my part: the timeliness of the P(Touch) ≈ |δ*2| rule-of-thumb beats accuracy-of-calculation gains from other, current, methods at this time, and by a good bit. The δ comes from option market-makers, who are privy to and have calculated a boatload more of timely data/news/market impacts, than are available to any P(Touch) calculation I might make, no matter how grand the equation. That's the end of the story right there. "A good estimate from timely data beats a great estimate from stale data."

(IMO , YMMV, OIMMBCTTA.)

 

[Trader13]

... The δ comes from option market-makers, who are privy to and have calculated a boatload more of timely data/news/market impacts, than are available to any P(Touch) calculation I might make, no matter how grand the equation. That's the end of the story right there...

That certainly makes sense for skews on stocks that are pre-earnings. Probably also true for commodities with seasonal tendencies. They have a directional tilt.

But for equity indexes where Puts had a positive skew over the last three years of a bull market, it's been wrong almost every day.

 

[destriero]

A white paper to be published this week will show that McGinnis is still an abject moron.

 

[Trader13]

I should be "careful what I ask for" because a better solution for POT is quite a bit more complex than 2*delta. I'm currently reading about one-touch barrier options where their pricing addresses this topic in a more robust way.

There are some similarities to delta with differences in breaching upper barriers or lower barriers, and there are other considerations like continuous pricing with crossing/touching a boundary vs. jumping over it with a price gap. Rather than try to master the heavy math of barrier option pricing, I'll probably devise a DIY approach based on ATR or some other simplified measure of realized volatility.

 

[destriero]

Vanna Volga.

 

[Stamamarti]

Nope. The best rule-of-thumb is the one is use. (Skew and all.)
But these days, with multi-core processors in our pockets, I'm hoping that efficient P(Touch) calculations will start popping up with regularity. It's going to happen.

[EDIT]
From an off-line conversation, a further realization on my part: the timeliness of the P(Touch) ≈ |δ*2| rule-of-thumb beats accuracy-of-calculation gains from other, current, methods at this time, and by a good bit. The δ comes from option market-makers, who are privy to and have calculated a boatload more of timely data/news/market impacts, than are available to any P(Touch) calculation I might make, no matter how grand the equation. That's the end of the story right there. "A good estimate from timely data beats a great estimate from stale data."

(IMO , YMMV, OIMMBCTTA.)

Well, in case you do have already a reliable evaluation/estimation of δ, you may get a somewhat more accurate approximation of the P(Touch)=2*P(ITM) (for the standard BSM option pricing model) using: P(Touch) = -2* [callPrice-spotPrice*δ]/strike