Discussion of article "Applying the probability theory to trading gaps"
Thanks!!! Read the article and the previous two - something to think about :)
great article, thanks... it's a shame I have to use third party software, I'll have to figure something out
Thanks. It seems to me that at the stage of preliminary analysis the use of something like excel, python or R is almost inevitable. The main thing is that the final result (trading EA) should be on pure mql.
Доказательство невозможности заработать на случайном блуждании довольно непростое, поскольку требует привлечения сложного математического аппарата теории случайных процессов (стохастическое исчисление Ито, марковские моменты времени и т.д.).
I think all of this is redundant. The impossibility of earning follows from the definition of SB. Since each future increment does not depend on anything (and therefore is unpredictable), any combination of future increments (=transaction) is unpredictable.
I think all of this is redundant. The impossibility of earning follows from the definition of SB. Since each future increment does not depend on anything (and therefore is unpredictable), any combination of future increments (=transaction) is unpredictable.
You are right in case of SB with discrete time - mathematical expectation of capital increment is equal to the product of expectation of volume and price increments (because of their independence). For continuous-time SB (Wiener process) everything is much more complicated, although the result is the same.
Wiener process is complicated and is applicable to the market only in a limiting sense (because of discreteness of prices and time), but it allows making calculations that are difficult for discrete SB. That is why it is often used in financial maths.
Interesting research - different types of gaps have been analysed from the point of view of probabilistic approaches.
I would like to add that trading based on gaps is inefficient - not only in the direction of the gap, but also in the opposite direction, because after a gap (of any type), in most cases, there is an increase in volatility (i.e. an uneven increase in the amplitude of price movement in both directions in relatively small time intervals). And this always increases investment risks.
Thank you for your great work!
Your article makes it sound as if we are talking about two US sessions.
The standard definition of a gap is a price gap between two consecutive price ticks. Such classic gaps are quite rare in Forex, so it was decided to generalise the gap concept - to abandon the requirement of a strict sequence of two ticks forming a tick. That is, any number of other ticks is allowed between these two ticks. Nothing prevents us from studying the closing of such generalised gaps similarly to the closing of classical gaps.
The problem is that there are a lot of generalised gaps and we should somehow limit their number. For this purpose we decided to limit ourselves to gaps between sessions. The concept of a session in the article is more formal and general than, for example, the concept of a trading session in the properties of a trading symbol in MT5. A session is defined by the length, period and shift of the very first session relative to the zero moment. For example, for sessions corresponding to minute bars, the period and length are equal to one minute, and the shift is zero. For regional trading sessions on Forex, the period is equal to a day, the shift is the time from midnight to the start of trading in the region, and the length is the length of the working day in the region. Each separate session has its own number.
When fixing an intersession gap, ticks that do not belong to any session are ignored. When the first tick from a new session arrives, it is compared with the last tick from the previous session and if the gap between them is large enough, the gap is fixed. When further investigating the closing of this gap, all ticks are taken into account - both those belonging to sessions and those not.
The article contains a figure illustrating, however, the concept of session and not the gap between them. I hope that its presence together with the explanations will be enough.
Frankly speaking, I don't remember, and the data for three years have already been lost. I only remember that I checked with several relevant Internet services, somehow struggled with time translation to summer/winter time, and picked the time for the end of the session by brute force (they have several large cities in different time zones). I remember that there was a lot of fiddling with it, but I don't remember the specific numbers. Now I would probably distinguish the sessions by the minutes volatility chart - there they can be seen quite clearly.
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New article Applying the probability theory to trading gaps has been published:
In this article, we will apply the probability theory and mathematical statistics methods to creating and testing trading strategies. We will also look for optimal trading risk using the differences between the price and the random walk. It is proved that if prices behave like a zero-drift random walk (with no directional trend), then profitable trading is impossible.
Let's test the EA on the year of 2017 and define the risk value for trading in 2018 based on its results. The balance/equity graph based on test results of 2017 is provided below.
I have to make a few clarifications before proceeding to the risk calculation. First, we need to justify the need to determine the correct level of risk. Second, it is necessary to explain the advantage of applying our theory for this purpose.
Speculative trading is always associated with uncertainty. Any trading system sometimes makes losing trades. For this reason, the risk should not be too large. Otherwise, the drawdown will be excessive. On the other hand, the market may change at any time turning a profitable system into a losing one. Therefore, the system's "lifetime" is finite and is not known precisely. For this reason, the risk should not be too small. Otherwise, you will not be able to obtain all possible profit from your trading system.
Author: Aleksey Nikolayev