How reliable is delta as a probability of expiring ITM?

K

kartik_subbarao

It's often mentioned that "delta can also be viewed as a probability indicator of the option expiring in-the-money". Has anyone looked at this more closely? For instance, it's intuitive to think that delta is more accurate of an indicator during expiration week than say, for a LEAP option with 2 years to go. But has this ever been statistically (or otherwise) analyzed?

As a particular example, take all the options with 1 week left to expiration that have a delta of 0.75. Did 75% of them eventually expire in-the-money? And then repeat that same experiment with different time frames -- 2 weeks, 1 month, 3 months, etc. How off was delta as a predictor in each timeframe?

Here's where this could be applied. Take a spread with a 4 to 1 risk/reward ratio. Based on delta, if you can have statistical confidence greater than 80% (4/5) that the spread will expire favorably, then this strategy should be profitable over time.

Any pointers, comments, ideas?

-Kartik
 
Quote from kartik_subbarao:

It's often mentioned that "delta can also be viewed as a probability indicator of the option expiring in-the-money". Has anyone looked at this more closely? For instance, it's intuitive to think that delta is more accurate of an indicator during expiration week than say, for a LEAP option with 2 years to go. But has this ever been statistically (or otherwise) analyzed?

As a particular example, take all the options with 1 week left to expiration that have a delta of 0.75. Did 75% of them eventually expire in-the-money? And then repeat that same experiment with different time frames -- 2 weeks, 1 month, 3 months, etc. How off was delta as a predictor in each timeframe?

Here's where this could be applied. Take a spread with a 4 to 1 risk/reward ratio. Based on delta, if you can have statistical confidence greater than 80% (4/5) that the spread will expire favorably, then this strategy should be profitable over time.

Any pointers, comments, ideas?

-Kartik
More...

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Kartick;
Yes.

As a practical matter you may find a 3 month , more or less;
more profitable than 1 week or 2 years.

Delta =probability indicator more than predictor, and here is a big fly in the ointment last 2 weeks expiry.

Even if you dont have occasional tek trouble with your computer/back up system last 2 weeks;
slippage can be huge last 2 weeks, and limit orders could easily be rightly laughed at, due to price speed change.

And , dont confuse .75 delta /75% ITM , which may very well be accurate % over time;
with profitable position.Options dont move like leveraged stocks.

Wisdom is profitable to direct.:cool:
 
kartik_subbarao

Using the delta as a probability is very crude.

The delta will vary as a function of the implied volatility on the option - as option IV changes so does the deltas, and since option IV is skewed across the strikes, which IV figure would you use ?

Secondly, the delta or N(d1) as it's called in the BS model isn't the real probability. The real probability is actually N(d2), otherwise know as the probability to be called.

There is an interesting thread on probability calcuations here;

http://www.elitetrader.com/vb/showthread.php?s=&postid=675102&highlight=probability#post675102
 
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