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?

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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?

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.

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.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.

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.

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.

I think Shakone has beaten me to the punch here.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.

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.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.

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?

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.

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.