## How to find the probability of touching between two dates

This is a discussion on How to find the probability of touching between two dates within the Futures & Options forums, part of the Markets category; I'm trying to figure out how to calculate the probability of a stock touching a certain price target specifically between ...

 Nov 13, 2011, 8:57am #1 Joined Apr 2011 How to find the probability of touching between two dates I'm trying to figure out how to calculate the probability of a stock touching a certain price target specifically between two dates I choose, without it being touched before. For example, suppose I want to find the probability of a stock price touching some out the money target next week between Wednesday to Friday, without ever touching that target anywhere between now to Wednesday. How do I do it? Anyone has an idea?
 Nov 13, 2011, 11:16am #2 Joined Feb 2002 Re: How to find the probability of touching between two dates You might be able to guess this but I don't think I'd go so far as to say 'calculate'. Maybe there is another way to where you want to be - why do you want to be able to do this?
 Nov 13, 2011, 6:46pm #3 Joined Apr 2011 Re: How to find the probability of touching between two dates I think there should be something more than just guessing about it (given we assume certain value for future volatility) just as we can calculate the probability of touching somewhere between the current date and a future date as here: Monte Carlo Option Probability Calculator | Option Trading Probability Calculator The reason for getting the right idea about probability is because the time when a price reaches a target may make a big difference as to whether your options position is profitable or not.
 Nov 13, 2011, 9:50pm #4 Joined Feb 2009 Re: How to find the probability of touching between two dates If you have a few option prices for the two maturities, you may be able to calculate the *risk-neutral* probability of touching (under a variety of assumptions). __________________ "Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness."
Nov 13, 2011, 10:33pm   #5
Joined Sep 2009
Re: How to find the probability of touching between two dates

Quote:
 Originally Posted by Socratic I'm trying to figure out how to calculate the probability of a stock touching a certain price target specifically between two dates I choose, without it being touched before.
Last decade or so there always seems to be a short squeeze put in play by the invisible hand. Typical gambit is currency manipulation and sovereign devaluation right around option expiration time by Central Banks and so called Economic Advisory Boards known affectionately as the PPT.

You'd have to monitor the tick and / or review intraday histories to avoid the trade after the designated high or low water benchmark was "touched".

Sounds similar to so called stop loss floor strategies that trading systems based on optimized "back test" models use.

 Nov 13, 2011, 10:39pm #6 Joined Feb 2002 Re: How to find the probability of touching between two dates Well, yes, that's just what I was about to say.
 Nov 13, 2011, 11:02pm #7 Joined Apr 2011 Re: How to find the probability of touching between two dates Martinghoul: right, I can calculate the probability of touching at some point in between now and the the nearer date and I can calculate the probability of touching at some point in between now and the farther date. Yet what I want to calculate is the probability that the touching does not take place before the nearer date yet does take place sometime in between the two dates. Cadavre: It seems very complicated to do back-testing on complicated strategies, all the more so when the historical options prices aren't all available. What I need I guess is some mathematical formula or computer modeling designed to give probabilistic answer to such a question, much like the link referred to above purports to do.
 Nov 13, 2011, 11:45pm #8 Joined Feb 2009 Re: How to find the probability of touching between two dates I've probably misunderstood what you're trying to do, and the assumptions. If you know what the probability of it hitting before time T, then you also know the probability of it not hitting by that time. So if you know the prob of it hitting before T+whatever, and it not hitting before T, don't you already have the info you need?
Nov 14, 2011, 12:31am   #9

Joined Feb 2009
Re: How to find the probability of touching between two dates

Quote:
 Originally Posted by Socratic Martinghoul: right, I can calculate the probability of touching at some point in between now and the the nearer date and I can calculate the probability of touching at some point in between now and the farther date. Yet what I want to calculate is the probability that the touching does not take place before the nearer date yet does take place sometime in between the two dates.
I think Shakone has beaten me to the punch here.
__________________
"Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness."

Nov 14, 2011, 1:19am   #10
Joined Apr 2011
Re: How to find the probability of touching between two dates

Quote:
 Originally Posted by Shakone I've probably misunderstood what you're trying to do, and the assumptions. If you know what the probability of it hitting before time T, then you also know the probability of it not hitting by that time. So if you know the prob of it hitting before T+whatever, and it not hitting before T, don't you already have the info you need?

Yes, both the probabilities "not hitting before T" and "hitting before T+whatever" are known. Yet I can't just multiply the two, because the events are not independent. Whether or not it hits by T has a probabilistic effect on whether or not it hits by T+whatever. If it hits by T the probability of it hitting by T+whatever is 1, and if it doesn't hit by T then the probability is unknown to me: sometime not hitting means it went far away from the target and sometimes it means it used the time to approach the target.

 Nov 14, 2011, 2:46am #11 Joined Sep 2009 Re: How to find the probability of touching between two dates An accurate forward priced Call / Put Probability surface?
Nov 14, 2011, 3:02am   #12

Joined Feb 2009
Re: How to find the probability of touching between two dates

Quote:
 Originally Posted by Socratic Yes, both the probabilities "not hitting before T" and "hitting before T+whatever" are known. Yet I can't just multiply the two, because the events are not independent. Whether or not it hits by T has a probabilistic effect on whether or not it hits by T+whatever. If it hits by T the probability of it hitting by T+whatever is 1, and if it doesn't hit by T then the probability is unknown to me: sometime not hitting means it went far away from the target and sometimes it means it used the time to approach the target.
You don't multiply them, you subtract one from the other. Because one event is a subset of the other.

Think of it another way. Suppose you simulate 100 paths. The paths you're interested in are those that do hit the level before T+whatever, but not the ones that have hit it before T. So you count the number of ones that hit by T+whatever and subtract all those that have hit by T. This leaves you with those paths that hit between T and T+. Doesn't it?

Nov 14, 2011, 6:32am   #13
Joined Apr 2011
Re: How to find the probability of touching between two dates

Quote:
 Originally Posted by Shakone You don't multiply them, you subtract one from the other. Because one event is a subset of the other. Think of it another way. Suppose you simulate 100 paths. The paths you're interested in are those that do hit the level before T+whatever, but not the ones that have hit it before T. So you count the number of ones that hit by T+whatever and subtract all those that have hit by T. This leaves you with those paths that hit between T and T+. Doesn't it?

Considering you example, it seems intuitively right. I'm not yet sure though, because according to probability theory, non-mutually exclusive events satisfy the following formula

p(A or B) = p(A) + p(B) - p(A and B)

If the events are mutually exclusive then the term p(A and B) becomes 0 and the equation remains

p(A or B) = p(A) + p(B)

This is equivalent to

p(A) = p(A or B) - p(B)

Now your suggestion seems to correspond to this as follows

p(hitting only between T and T+whatever) = p(hitting before T+whatever) - p(hitting before T)

where

A=hitting only between T and T+whatever.
B=hitting before T.

This is because p(A or B) simply covers all possible events in which the target is reached before T+whatever.

The problem seems to me to be that the probability number given for p(hitting before T) doesn't subtract from it the cases where the same sample that hits before T also hits in between T and T+whatever and so do not represent a mutually exclusive event. So as long as p(hitting before T) isn't in itself restricted to merely the cases where it hit the level before T and NOT between T+whatever, we seem to be missing a tern in the formula. Obviously, the probability calculators I use do not look forward to subtract the cases it hits the same target in the future.

 Nov 14, 2011, 7:06am #14 Joined Feb 2009 Re: How to find the probability of touching between two dates If A is a subset of B, then P("B but not A") written as P(B\A) is equal to P(B)-P(A) let B be the event that we hit before T+whatever. Let A be the event that we hit before T. Then every case where we hit before T, we have also hit by T+whatever. Obvious right, because we hit it early. This means that A is a subset of B. Any outcome that is in A, is also in B. So the probability that we hit between T and T+whatever, is the probability that we hit before T+whatever, but not before T, i.e. P(B\A)=P(B)-P(A). It's late for me, I may be losing my mind...I don't understand your last paragraph. It's irrelevant whether it hits before T and also hits between T and T+whatever. It hit. It's an outcome that hit before T, and an outcome that hit before T+. It's been accounted for.
 Nov 14, 2011, 7:08am #15 Joined Feb 2009 Re: How to find the probability of touching between two dates You know what. The best way to deal with these thigns (in my opinion) is that you simulate the sample paths. Give some dynamics, Monte Carlo the thing, and you can get the probabilities straight out. Hard to argue with those