The price as discrete stochastic variable

Hi all...

Just finnished the course Statistic Mathematics... is there anyone else that has any knowledge about probabilitys?

My question is, can't you see the price as as a discrete stochastic variable?
The days opening price can be seen as the wait value... and the daily range can be seen as the standard deviation?

Isn't there a way to use some binominial, exponential, hypergeometric formula that is used to calculate probabilitys to calculate where the price is probably is heading for?

Hope that you get my point, I can't all the english words for that math stuff...
I bet there are some mathgenius here to help...

Sounds like an interesting concept. I love math...though i never reached the level you are speaking of as far as personal knowledge with formulas. I'm wondering if some of the Neural Net computations aren't using similar algorithyms? Where are all our Mensa Members? Any takers?

: ) Thom

I seem to recall Twoblink being a math wiz. He still lurking around here?

J

Well lets say EURUSD daily differences are normaly distributed with some avarage and deviation (actualy it satisfys hypothesis about it when i checked it last time though i believe it's not realy the case. Maybe candles are noramly distributed, but the reason why it's not normal or random if you like is the way candles follow one another). So if we asume that this hypotesis is corect and the price is random and it has some distribution function (whatever it is) you cant actualy have any real so called edge and you still dont now where the price is going next moment (thats the whole idea of randomnes. If youy roll the dice 10 times and you get lets say 6 all the time the probability of which is 1.6538171687920201866246676489018e-8, you still dont now if its not going to be 6 11th time, it still has 1/6 probability. The same apllies if one asumes that price is random). Basicly what i'm trying to say is that if you see some article with words "statistics", "market", "profit" in the same sentance, theres a very high probablity that it's just some dude trying to pull of another one of those doctorial dissertations which has absolutely no practical use (noticed that it's especialy common with statistics). That apllies to all those funny time series models and etc.

Though for me as a mathematician it's pitty that theres no real way to aplly math to the markets (maybe except some geometry... ). Most of the models are just smoke around you, it missleads you from important things. All of that is just my own opinion.

The first mathematician with this idea was Bachelier, see http://en.wikipedia.org/wiki/Louis_Bachelier
You could read his articles (boring), but when you want to know more about trading and stochastics, you should read "the (mis)behavior of markets" by Mandelbrot. It not only describes fractals, but gives also a good description of the links between probabilitytheory and trading.

Yes, but does it make any difference if it's not random. There are formulas for that too, the hypergeometrics formulas where the probability depends on selections made before... For example, picking different coloured balls from a glass without puttin them back.


Sounds interesting, should give it a read tomorrow when I have time.

I don't want any hyperavanced, I just want some probabilty about the price reaching x pips from daily opening price...

According to the scientists, it can be best described as a normal distribution. The mean is the startvalue. The standarddeviation is almost equal to the average standard deviation of the last periods. An extra problem is that the standard deviation is dependent on the time of the day. When markets are open of closed they change that standard deviation.

But be careful, it has what they call "fat tails". That means that extreme situations are far more likely than according to that normal distribution. The chance on a rise/decline of 100 pips (or another big number) in a few hours is much greater than in a normal distribution.

Cynthia Kase is a trader and author who uses statistical reasoning in her methods.
An interesting topic from her is the Dev stop,
a stoploss tecnique which takes in account the variance of volatility (as ATR) and skewness (volatility is always>0).
This gives you a probability of price not reaching certain values (~ .85, .98, .999).
Interestingly, her entry-forecast methods are based on a simplified application of elliot wave principles along with ma's and stochastic (for divergences) on multiple (3) time frames (this is a concept she emphatizes much).

QG

Prices are most certainly not normally distributed, nor do they follow a binomial distribution. There might be stretches of time where it seems like they are, but they are not distributed that way in the long run.

Check out Mandelbrot's book, "The (mis)Behaviour of Makets," it's an interesting read. He has spent a considerable amount of time studying price changes in all kinds of markets (stocks, commodities, and currencies). He did some quick calculations to see if the stock market fits a normal distribution: He took the Dow Jones Industrial Average daily prices from 1916 to 2003 and plotted a frequenct distribution. If prices were normally distributed we should have seen only 58 days (from 1916 to 2003) where price moved more than 3.4% in a day, but in fact it happened 1001 times. Price swings of more than 7% should come only once every 300,000 years (if prices were normally distributed) but it happened 48 times in the stock market in only 87 years!

That's evidence enough for me to see that prices are not normally distributed...and the forex has much bigger swings on average than the stock market; it is much more volatile.

Despite this evidence, most of the financial models used today (and in the past) are based on the assumption that prices are normally distributed. Mandelbrot suggest that prices might better follow a Cauchy distribution, but actually he has his own model of price movements using fractals.

But none of this will help you make money in the markets, just help you save money. Knowing price distributions is probably most helpful for risk management, maybe so you could estimate how far to place your stops.

I personally think that we should look to develop psychological strategies. We could try to model the market in many ways using all kinds of fancy economics and mathematics...but in the end, it's people buying and selling that moves the market. If you could predict where others are buying/selling (especially the people with big money), then you might have something...