Hello . Does any one knows a reference for a probability of an asset to stay within a range ( low barrier / high barrier ) in a specific time frame and a known volatility in that time ? I guess the double barrier options models can be of use but i can't find closed forms . The purpose - if there's a better idea - is to try and model the probability of hitting a stop loss / take profit levels within a specific time frame of some asset ( a currency , stock , etc ...) .Thanks !

while the double barrier probabilities are not closed forms, they do have a relatively straightforward series summation

QuoteI guess the double barrier options models can be of use but i can't find closed forms The chances of closed forms decrease monotonically to zero as complexity increases, yes? It becomes impossible?One choice is to solve the first exit time pde. It's documented in PWQF books.

So - if i wanna estimate the probability of hitting either stop loss/ take profit in a predifined intraday time period ( say an hour ) - how do you recommend doing that ? - by monte carlo ? Thing is i cant allow myself to run a numeric calculation at each trade entry (technical reasons ...) so i thought about approximation of the situation by a 5d matrix of spot at entry , volatility at entry ,drift , stop loss level and take profit level - and do monte carlo ( instead of the infinite series approx for the double barrier solutions) simulations for several ( thousands ...) of different situations so when a entry is happening i look for the probability in this huge matrix , and get an approximation to the hitting probability . I"ll be happy to get more ideas on this problem ! Thanks.

The 'a predefined intraday time period' can be in a future or during an immediate future. First if you can try to develop approach of the GBM with constant coefficients. Write the explicit solution. Then represent needed probability of the asset being in tube with respect to Wiener process. Thus you arrive at the problem when W ( * ) belongs to some another tube area. Then you can approximate continuous time problem by the discrete. If you can derived something appropriate then you can see what it is possible to make to be closer to reality.I saw math papers regarding similar problem for general nonlinear SDE. They transform this problem to the study parabolic problem in the correspondent area. They studied asymptotic of the probability (= the solution of the parabolic equation) when area is a narrow ot when T tends to infinity. It seems that a similar problem also studied in the book Ikeda , Watanabe.

Here is article on first-time exit problem using PDE (1.5) and MC approaches. PDE is nice because you can solve fast and accurate using FDM. So, this is a particularly easy PDE on a bounded domain. And some FDM are very fast and can be parallelised. From (1.5) and the maximum principle the solution always <= 1 and the same will hold for good monotonic schemes. I reckon this solves the problem. QuoteFirst if you can try to develop approach of the GBM with constant coefficients. Write the explicit solution. Then represent needed probability of the asset being in tube with respect to Wiener process. Thus you arrive at the problem when W ( * ) belongs to some another tube area. Then you can approximate continuous time problem by the discrete. If you can derived something appropriate then you can see what it is possible to make to be closer to reality.list,do you have links to this algorithm?

"do you have links to this algorithm? "Cuchulainn, in http://papers.ssrn.com/sol3/papers.cfm? ... _id=500303 on pages 26-29 you can find something close. Though I think the method could cover the two sides estimate. I remember that in Kiev institute of mathematics 80-90 Vitaly Gasanenko studied such a problem for nonlinear SDE with coefficients which does not depend on t. He used eigenfunctions series to present a solution of the correspondent to our probability parabolic PDE. I saw his papers on Springer Website.