Delta and probability question

Quote from nravo:

Does, for lack of a better term, delta-probability differ from the statistical probablity at a givven moment, and if so by how much, how often, et-cetera. Is the statistical probablity for the aforementioned option 22% versus the 20 delta? 18? Is this spread generally about the same? CAtch the drift of the original question?
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Yes, there is a differerence. Lookup an explanation of the BS-formula's, Natenberg is a good source but not online, and you will see that the probability-function (itself based on expected volatility) of the expiration-price is an input to the formula. Delta is an output. They are similar, but not the same. The difference will be more than 2% certainly. I think in some summaries they are called d1 and d2.
However, for practical purposes it will suffice unless you have very special intentions with it. Might one ask?
Remember that the difference between the actual realized probabiltity and the expected one is often far greater, so an accurate prediction is meaningless.

Ursa..
 
nravo, there is no easy answer to your Q and BTW your assumption about delta is shaky at best.

google this:

delta probability "in the money" site:wilmott.com

if you really want to know, but be careful what you wish for.....:)
 
Delta is close, within 5% generally. The formulas, however, are *different*.

d1 = ln(price/strike) + (interestRate + (volatility^2)/2) * timeLeft) / (volatility * sqrt(timeLeft))

Delta = Normalize(d1)

p1 = ln(targetPrice / price) / (volatility * sqrt(timeLeft))

Prob = Normalize(p1)

In other words, delta includes the interest rate:
(interestRate + (volatility^2)/2) * timeLeft)

but probability does not.

In a period with extremely high interest rates (or high volatility), the difference will become much more noticeable.

One other thing to keep in mind--if there is a dividend or some other corporate action coming, delta and probability will have absolutely nothing to do with each other. :-)
 
delta and probability will have absolutely nothing to do with each other. :-) [/B][/QUOTE]

Finally !!! Someone actually said it.

I was going crazy reading through this thread, although Spike500 gave a good explanation as well.

Think of delta as the number of shares the contract currently represents.

An ATM (50 delta) option represents 50 shares, therefore it will move .50 for each 1.00 that the underlying moves. (assuming the multiplier is 100)

However, considering ATM gammas, your deltas will have changed before the underlying has moved a dollar.
 
Quote from FullyArticulate:

Delta is close, within 5% generally. The formulas, however, are *different*.

d1 = ln(price/strike) + (interestRate + (volatility^2)/2) * timeLeft) / (volatility * sqrt(timeLeft))

Delta = Normalize(d1)

p1 = ln(targetPrice / price) / (volatility * sqrt(timeLeft))

Prob = Normalize(p1)

In other words, delta includes the interest rate:
(interestRate + (volatility^2)/2) * timeLeft)

but probability does not.

Thanks much for all the explanations, the last one was pretty much what I was looking for, and I assume that difference is indeed, as you state, 5 percent -- not percentage points. Thanks again.

In a period with extremely high interest rates (or high volatility), the difference will become much more noticeable.

One other thing to keep in mind--if there is a dividend or some other corporate action coming, delta and probability will have absolutely nothing to do with each other. :-)
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Quote from nravo:

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Someone asked why I asked this question initially and it was because I had done some hasty sales of way OTM currency futures options, based on probabilities based on deltas, rather than a probability calculator and I was wondering how off base I would be, not only in the actual trades I made but generally.
 
Quote from nravo:

Someone asked why I asked this question initially and it was because I had done some hasty sales of way OTM currency futures options....
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Then my answer isn't as helpful as you'd expect. :-)

Black-Scholes is the wrong pricing model to be using for currency futures--you should be looking at Garman-Kohlhagen. The relative interest rates of the pairs you're trading are more significant than in typical B-S.
 
Quote from FullyArticulate:

Then my answer isn't as helpful as you'd expect. :-)

Black-Scholes is the wrong pricing model to be using for currency futures--you should be looking at Garman-Kohlhagen. The relative interest rates of the pairs you're trading are more significant than in typical B-S.
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So the deltas as a makeshift probability calculator is even more imprecise? How much more?
 
Quote from nravo:

So the deltas as a makeshift probability calculator is even more imprecise? How much more?
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It depends on how wide the interest rates of each currency are spread. If they're equal, delta is exactly the probability. If they're wide apart, delta gets further away from the probability.

If you're doing the Real vs. Yen, it might matter quite a bit.

On the other hand, Dollar vs GBP will yield a delta exactly equal to the probability.
 
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