Hello all ! In order to analyze a stop loss / take profit policy , i wanna build a tool (calculator or some matrix ) that for a specific market situation - namely volatility - and specific stop loss and take profit levels , i could estimate the probability that stop loss will be touched in a predefined time interval ( of course i"m assuming volatility will remain fix in that interval ) . I wonder what is the best way to do that - should i use monte carlo or some other method (maybe from the one touch options area ... ) and if so - what's the best tool to do that in a reasonable time : MATLAB , C++ , some statistical software ? (this will take alot of simulations for each and every market/ SL-TP conditions ) . Thank you people ! Tom .

No need to double post. What's the underlying?

Hi . Underlyings are indices and currencies pairs .Thanks

Take the spx and stop loss at some K < S0. I think, as a first shot, I would calibrateMerton's jump-diffusion model to a chain containing all the options (weeklies, monthly, and quarterlies) expiringwithin a month or two. Then, it should be relatively straightforward to use that model, with the calibratedparameters, to deduce the probability that the level K will ever be crossed.* That's becausethe MJD model is a Levy process, and ultimate crossing probs should not be a hard calculation.You can also calculate the probability that K will be crossed prior to T, but that may involve considerablemore analytics: fourier inversions, etc. If you can do that math, good -- otherwise maybe a Monte Carlo.Technically, these answers are "risk-adjusted" probabilities -- and so an over-estimate (since K < S0).However, the over-estimate may compensate for neglected micro-structure effects.-----------------------------------------------------------------------------------------------------------------------------------------* Note added: to make the ultimate crossing prob non-trivial (i.e., not equal to 1), you need to set the drift of log S(t) to a small positive value consistent with very long-run history.

Have you thought about using survival analysis?

I would use what I used to call a "back-sampling" monte carlo for a similar time period. Suppose I want to know probability distribution for the next 10 minutes. I sample 10 1-minute moves taken at random from the previous say 30 minutes. If there was a net up or down move in the previous 30 minutes of, say, 30 ticks, and I want to remove that, I can add one up tick to each of the 30 moves, and sample at random from that. Or if my profit is usually 5 ticks, I can adjust to expect 5 ticks. This process may underestimate the probability of novel outlier moves, and is not perfect in other ways. But it is a simple way to be probably more accurate than some crazy interpolation.

There are forex traders who uses ATR indictor to "measure" volatlity - if i have to "talk" in ATR values - is there a way of stop loss / take profit probability estimation for that ? And if so and i"m talking about 1 hour intervals - what model would you prefer to use for the underlying - i guess one with jumps for the Brwonian samples ...I must say i thought this to be more straight forward but it seems a little more involved Thanks!

Well - still i"m looking for some idea about this problem which is more down to the ground : say i look at the EUR/USD or other pair / commodity , and at a specific time say it's traded at 1.5EUR/USD ,and i put a stop loss at 1.4 and take profit at 1.55 . Based on the calculated volatility at entering - how can i compute the probability of touching the stop loss / take profit in a specific time period e.g - an hour ? This is intraday trading so i guess i have to consider some jump model (?) - but in general - what's the best way to use - Monte carlo ? Trinomial trees ? other ? Thank you very much ! Tom.

stop = 1.4;percenthit = 0;timeperiod = 60;adjustor=1;movebias = (close[1] - close[timeperiod*adjustor])/(timeperiod*adjustor);for (montes = 0; montes < 100; ++ montes){theorclose = close[0];for (i=0;i<timeperiod*adjustor;++i){samplebar = random(1,timeperiod) ;theorclose = theorclose + (close[samplebar]-close[samplebar+1])-movebias;if (theorclose < stop){percenthit++;i=9999999;}}//add random moves proportional to time period}//100 monte runs

Thanks ! As i see you do not simulate Brownian motion paths as i"ve considered ... Can you please explain that ? Tom .

QuoteOriginally posted by: tomericoAs i see you do not simulate Brownian motion paths as i"ve considered ... Can you please explain that ?Why would I simulate Brownian motion when I already have a whole chart full of random ticks of the right volatility and texture?If anything, you could increase the timeframe of the back-sampling search, and narrow down the subset of searched to bars after a bar that looks like the current bar, if only in tick direction. This would give you downticks after upticks, simulating the bid ask spread with almost no programming. Going in the opposite direction, you could remove skew by reversing up and down and random.

This is what i don't get - what in your building process - is refering to the volatility ? as you wrote - you sample the values randomly - but where does the volatility comes in ? I will expand my need - it's some matrix of probabilities such that for every market condition of soecific asset (namely volatility , stop and take profit values , and the time frame i wanna monitor ) - i will have a probability value in this matrix for stop loss and/ or take profit hit in this time frame.It's the random sampling without volatility consideraion at your proposal i do not understand Thank you ! Tom

QuoteOriginally posted by: tomericowhat in your building process - is refering to the volatility ?I don't turn ticks into volatility, and then volatility into ticks. I just use the ticks, meaning the bar-to-bar changes. The assumption that the volatility is the sum of random ticks, and dictated by their size - which is captured pretty well over a pretty small sample - is flawed. But this same sort of assumption is used in any monte carlo.You could say it is a weakness or a strength that I don't have to come up with some single volatility number, and then translate that into the various jump sizes you actually see. I just use the types of jumps we have seen recently, at the frequency they have occurred recently.You could use other simple enhancements, like sample at random from a pool limited to bars were in the past preceded by bars of the current jump size. This would create intervals of autocorrelated volatility, whether high or low, like in real life. But without having to come up with some crazy model and plug in parameters that are totally made up.The only fitting you might want to do is the adjustor, which increase or decreased volatility by adding jumps to the monte carlo. In theory, there is a possibility of bigger jumps than occured in the sample interval. But you can run a backtest to find a general adjustor. Perhaps stringing together 130 moves from the last 100 bars generally predicts volatility over the next 100 bars.Also, this simple program is designed to self adjust to fast and slow times of day. But you could really easily say well it is late afternoon, and I think the next hour will be less volatile than the last hour, and use and adjustor of .8. You might say hey, that is not real quanting, that .8 you just pulled out of the sky. But nothing is real, it is as good as anything else, this is the tragic nature of the world.

Thanks very much for all of your answers ! Tom .

As mentioned, number of approaches are possible, with varying degrees of sophistication. A simple approximate solution could be based on first passage time properties of a Brownian motion with no drift which starts at zero.Property 1. Suppose there is a fixed barrier b > 0. How long will it take before the BM reaches the level b? It has been shown that this waiting time tau_b has the following distribution: Prob( tau_b <= t) = 2[ 1 - phi[ b / (sigma*sqrt(t))]] where phi is the cumulative normal function. Property 2. There are two barriers a and b such that a < 0 < b. Then it has been shown that the probability that the BM hits the level b before the level a is given by a/(a-b).From this (and related results) it should be possible to solve your problem.