**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. |