Registered: Dec 2011
Posts: 343

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Quote from cactiman:

If you're not a teacher already, you should become one!
Mucho Gracias.

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Just a regular guy trying to help out

Registered: Nov 2005
Posts: 568

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Quote from TskTsk:

5 delta strikes ... statistically they should've been hit only 5/100 = 5% of the time.

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Registered: May 2009
Posts: 1029

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Quote from Kevin Schmit:

Delta is N(d1). The risk-neutral probability of expiring ITM is approximately N(d2). Since d2 is strictly less than d1 (by sigma*sqrt(T-t)), delta will always overstate the true risk-neutral probability.

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Registered: Sep 2006
Posts: 48

If you use an Option Model to calculate Probabilities, then it will suffer from the same limitations and caveats that ALL Option Models do ... but at least it will be consistent with all the other Greeks that the Option Model generates ...

Espen Haug covers PROBABILITY GREEKS in his book 'Option Pricing Formulas' and suggests that the Greek he calls STRIKE DELTA can be interpreted as the discounted risk-neutral probability of the Strike ending up In the Money ... similar to the Delta Adjustment that Kevin mentioned above ....

Back to the real world .... in practice, I use one of three methods as rough and ready approximations ....

1. The absolute value of Delta approximates to the Strike finishing ITM ... the shorter the time frame / the lower the Vol / the more accurate the approximation.

2. ATM Straddle Price x 1.25 approximates to 1 Standard Deviation Move

3. Max Loss / Strike Width % for a Vertical Spread approximates to the Strike finishing ITM

Whereas 1. uses an Option Model ... 2. and 3. have the advantage of using Liquid Market Prices ...

Hope that helps
Cheers
James

Registered: Jul 2004
Posts: 179

I think the most interesting output is the probability of touch, which is approx TWICE the probability of the option finishing ITM. For example, if we assume the delta is approx the prob of finishing ITM, then a 30D option has a 30% chance of expiring ITM and a 60% chance of touching ATM during it's lifetime.

Registered: Oct 2012
Posts: 19

Trader13's statement: "probability of touch is approx TWICE the probability of the option finishing ITM" is a fairly accurate rule of thumb for Out-of-the-Money Options, but it does not apply very well for In-the-Money Options.

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