**Introduction.**

Most
of the indicators currently used by traders in the Forex market were created
for another market - the stock market and for another time, when there were
quite monotonous trends and quotes were not so volatile as at present, when
there are no trends as steady trends of unidirectional price movement. Therefore,
the entire existing arsenal of indicators is not very suitable for trading in
the Forex market and does not reflect the key moments of the state of this
market. To
assess the condition of the Forex market and its instruments, it is necessary
first of all to analyze statistical histories of their quotations, which allows
identifying patterns that are important for trade, which are latent for the
standard indicators (supplied with the MT4 trading platform). One of these,
providing a deep statistical analysis of instruments is the indicator **PDP**, which,
based on the analysis of the smaller time frames, calculates in real time the
probability distribution of the price for the larger time frames. The
visual control of probability distributions, which provides the indicator **PDP**, allows us
to achieve a deeper understanding of the modern market, namely:

statistically strictly identify the current price levels and assess the probabilities of the current (for the current moment) price in other segments of its fluctuations;

to reveal the microstructure of the true trend movement, as a sequence of such transitions from one price level to another, that have a certain shift in the balance of probabilities towards the growth of the price or its fall;

establish the beginning of a new trend movement based on the critical output of an non-lagging average beyond the current price level.

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**Principles of the indicator****. **

To calculate the probability distributions
on time frames М5-Н4, the data
of the minute chart - М1,
is used. For the daily is used time frame M5; for the weekly time frame and for the monthly time frame - M30. The
use of smaller time frames for estimating the probability distribution in these
large time frames is not advisable, and it is impossible not only because of
the braking of the program loaded with large arrays, but also because there is
not enough big of M1 history in (for
calculating probability densities) the scales of such graphs. Therefore, before
the indicator **PDP** is
installed on the chart of a tool, you first need to load the history (*Tools
/ History Center*) quotes for this tool, and also to increase to the limit
the options "*Max bars in history* " and "*Max bars in
the chart*" (*Tools /Options / Charts*). Note that if on some large-scale
timeframe of data for calculating the probability distribution is not enough,
on the "*Experts*" tab of the window of the term MT4 there will
be a message "*Download** **the** **quotation** **history** **of*… ". Indicator itself is resource-intensive
and requires at least a 4-core processor 2.8 GHz and 4.00 GB of RAM. If the indicator will brake the MT4
terminal, then in the indicator settings it is necessary to reduce the «*Number of countable bars of the current
chart* (<=200)», which is the
default 200.

The calculated probability distribution has
a sliding character, and the interval used for calculating the data is
determined by the input parameter «** The
averaging period in the bars of the current graph**», which
we denote IS; if, for example, IS =
15, and time frame H4, then the columns of probability values corresponding to
the time moments at H4 are calculated by 15 * 4 * 60 = 3600 points of the graph
M1, i.e. the last column (zero bar n = 0 to H4) -
over the last 3600 points of the time frame M1, the penultimate in the range of
values [241, 3840], .., nth in the interval [240 * n + 1, 3600 + 240 * n ]
minute chart. And,
if, say, IS = 1, then the last column is calculated
according to the last 240 values of the minute chart, the penultimate column is
calculated according to the values of the interval [241,480], etc., with the
mapping, of course, in all cases, to H4.

The program splits the total price fluctuation for a
given averaging period into **seven** equal intervals and calculates the
frequency of the price hits of historical data of already small timeframes in
that intervals. From these 7 intervals
for each moment of the analyzed large time frame, rectangles of the probability
mapping are formed (7 rectangles for
each, marked by a bar of a large time frame, time point). Calculated on the basis of the
statistical frequencies of the price (small timeframes) hit in the intervals
specified by the program, the probability columns can be displayed in the main
terminal window in two ways:

in the form of a color code, the type of the spectrum of visible light, when the most probable values are closer to the violet area, and the least probable values are close to the red, with the coloring of the intervals by the corresponding colors (the order of encoding the decreasing probability by means of the color scale is specified in the settings and can there be changed at the request of the user);

in the form of numerical values of the probability of hit in given intervals, with the corresponding colors.

**Modes of operation of the indicator
PDP. **

For the convenience of reading the color-coded probability values from the indicator prob_distrib, it is desirable to make a black background on the color scheme of the main window of the MT4 terminal and display prices also with a dark line or red and green bars, the template of which is attached to this indicator.

The
moving average, taken with the averaging period 2*n+1, is known to lag behind the "n" bars; the sliding
probability distribution that calculates the **first mode** of the **PDP** indicator
also lags behind, which in this case represents the data in such form (Fig. 1).

Fig. 1. Mode for calculating the sliding probability distribution of prices IS=15.

However, since the information on the frequencies of the price hit in
given intervals is obtained on the basis of a large amount of data extracted
from the lower time frames, it is possible to obtain algorithmically the **without delay**** probability distribution**,
the calculation of which constitutes the **second mode** of operation of the
indicator. In this case, the previous type of distribution is
shifted to bars "n" to the past, and information
about the distribution on the n-1 bar is found on the bars 2*(n-1)+1 of a large time frame, i.e. on
the points (2*(n-1)+1)*TL/TS, where TL - the duration of a large time
frame, a TS - the duration of a small time
frame, that detailing a large, the "n-k" bar on the 2*(n-k)+1 bars of a large time frame, i.e.
on (2*(n-1)+1)*TL/TS points, and about a zero bar on
on it himself, more precisely, on an array of the prices equal quantity TL/TS ; at the same time, the
probability distribution is calculated not on a bar that may be incomplete, but
on the last such number of points of a small time frame that forms a full bar,
which allows obtaining distributions for individual bars (Figure 2.1). By the same principle of using small, detailing time frames for
analyzing large time frames, the** average** **without
delay** is also calculated, which is also displayted by the indicator
(blue-purple line or asterisks).

Fig. 2. The mode of calculating the without delay probability distribution and the mean without delay IS=15.

Fig. 2.1. Probability distribution over bars IS=1.

In
the **third mode**, the algorithm for calculating the without delay
probability distribution is even more complicated and, firstly, the current
price channels corresponding to the averaging period are calculated at the end
of the history, and secondly, by a special one (reminiscent of exponential
smoothing with varying coefficients depending on the varying statistics
calculation of smoothing points), suitable for this period, the filtering
mean without delay (Fig. 3).

Fig. 3. The mode of calculating the without delay distribution with channels and adjusted mean IS=15.

In each of the above modes (1-3), the probability density mapping can be changed from its color coding (colors can be customized by the user) to the numerical presentation (Fig.4).

Fig. 4. The third mode with numerical probability mapping IS=15.

In the third mode, based on the calculated channel limits (which then need to place stops), the deposit and the specified risk level, you can also calculate the lot size for the trade within this channel, the lot information is displayed in the main window where its location is configured and can be selected, both at the bottom of the channel and at the top (Fig. 5).

Fig. 5. The third mode with the calculation of the lot.

The indicator is resource-intensive and
calculates a small number of bars, but to search for possible new channels, the
calculation area can be moved deep into history, for which the «*Shifting the
calculation area of the indicator*» parameter is set in the settings.

The current mode of operation and all its characteristics are printed on
the "*Experts*" tab of the window of the terminal MT4.

Fig. 6. Information about the indicator mode.

**The
indicator settings****. **

The indicator settings are
shown in Fig. 7, where they are described in the terminal window “*inputs*”.

Fig. 7. Indicator settings.

The indicator settings are divided into:

**Algorithm settings:**

- The averaging period in the bars of the current graph (2n+1) - averaging period (1-99).
- Number of countable bars of the current chart (<=200) - number of calculated indicator graph bars (1-200).
- Shifting the calculation area of the indicator - global indicator shift (0-100).
- The non-lagging distribution is calculated - calculate a non-lagging distribution.
- The channel and the non-late mean is calculated - calculate the current channel and non-lagging mean.
- Show the values of the probabilities of zones - display area probability values.

**Color and display settings: **

Colors in probability density descending order.

- Color of the maximum probability zone (0);
- Color of zone (1);
- Color of zone (2);
- Color of the zone of average probability (3);
- Color of zone (4);
- Color of zone (5);
- Color of the minimum probability zone (6);
- Color of the moving average line; - average color
- Show line average stars; - display average line as stars (false - as a line)

**Trading mode settings:**

- Calculate the lot size from the risk, deposit and channel
- Deposit in $
- Allowable losses in %
- The channel strategy is used - true - intra-channel strategy (false - channel breakthrough strategy)
- Color of message about the size of the lot
- Information about the lot at the bottom of the channel (false - information at the top of the channel)

**Identified
by the ****PDP**** indicator of the laws of the market and how to use them for
successful trading****. **

Looking at
the color maps of the probability distribution, it is easy to notice that the
places where the price "trampled on" the most, form on all time
frames rather extensive horizontal bands (Figure 8-9), which are similar to
discrete energy levels, when the price from one level to another passes jump,
almost avoiding intermediate points, in which the probability density of its hit
are sometimes minimal. And,
if the averages move smoothly, falling into such zones of maximum probability
by passing through all intermediate points (and otherwise can not be) and do
not distinguish similar probability concentration bands, these zones are easily
identifiable by the indicator **PDP**, since they really form are constant levels that are
essentially discrete or torn apart from each other.

Fig. 8. The bands of the maximum probability concentration on H4.

The existence of such zones can be explained from a
psychological standpoint, as a consequence of the habit of key market
participants, which determines pricing,
when they are confident in the adequacy of certain price values determined at a
given moment. This key market participants try set this price for some time,
which continues until important events occur. Such levels, imprinted in the
memory of these participants, acquire a strong tendency to repeat, which can
also be seen on the color distribution of the probability and should be used in
the game. Namely,
if a trend has been signify, say, to an increase in the price, then necessary
(by examining the probability distribution on history, for which it may be
necessary to shift the indicator calculation area in the past by the *«**Shifting** **the** **calculation** **area** **of** **the** **indicator**» *option) to identify maximum probability zone
above current price, where to place the take-profit, since it is possible that
the direction of price motion will change after this zone, but price will reach
its with a high probability. From the analytical point of view, the existence
of such price zones and their isolation from each other is also understandable,
since highly nonlinear equations, in principle, describe such complex systems
as the market, have huge sets of sharply differing solutions that jump and
unpredictably replace each other in points of bifurcation, after which the
price only fluctuates around such solutions until the next bifurcation.

The very tendency to change the level of maximum probability is expressed (Fig. 9) in the intersection of the moving average and the band with a fairly low probability (from gold to red-orange), which should be identified by probability distribution without delay and moving average without delay to avoid signal lag.

Fig. 9. The bands of maximum probability concentration and the order of their change to D1.

**Successful
trading strategies using only ****PDP**** indicator****.**

*Preliminary actions.*

First, on the timeframe chosen by you for trading (M30-D1), roughly estimate the average length of the white bands <l>=(l1+l2+...lN)/N, where N - the number of bands visible on the chart, li - their extent.

The
indicator for both strategies is used in the **third mode**, where
are calculated channels,
probability distributions and mean without lag. The
indicator channel and, accordingly, is intended mainly for trading through
channels.

*1. **In-channel
strategies**. *

The indicator **PDP** allows you to reliably trade
in ** channel strategies**. Such trade
should be carried out on the already well-drawn (but not too long compared to
their average lengths) white bands <l>/4 < l < <l>/2 and, of course, beforehand (at
least 2 hours for trading on H1 and H4) before

**that may shift the price level to the new channel. In this case, the opening of positions should be done when the current price is either in the yellow or green sectors, and take the take-profit in the middle of the white line. The stops are placed slightly further than the full distribution channel (Figure 10). The value of the lot is calculated by the indicator itself, if in the indicator settings "**

*important news**Is channel strategy used?*" set true.

Fig. 10. Channel strategy.

*2. **Strategies
for channel breakdown.*

The bands of maximum probability jump discontinuously at the
intersection of the without lagging mean of the red strip, which is the band
with the minimum probability. Therefore, with the PDP indicator, the channel
breakdown strategy can also be implemented in the form of a breakdown of the
lowest possible level in an absolutely established channel l~ <l>, namely: put a pending order in the middle of the
current red band (Buy_stop - if the red band is above the white and Sell_stop -
if the red band is below white). A profitable order is closed manually when the
price reaches a new established white band
l~ <l>/4. Stoploss is also placed a little further than the full probability
distribution channel (Fig. 11). To calculate the lot, the option "*Is
channel strategy used?*" must be set to false.

Fig. 11. Channel breakdown strategy.

With this indicator, you can also use the classic
form of the channel breakdown strategy by placing a pair of pending orders (**Buy_stop**
and **Sell_stop**) and their stops just below both boundaries of the
established channel.

*3. **Trend
strategy*.

For currency pairs, the trend strategy in pure form is realized only on
very large-scale charts. If the trend and, most importantly, the high
probability of its continuation in the same direction are established
(fundamental analysis together with other indicators), then the **PDP** indicator can be used for the trend strategy
for order placement and *Stop Loss*, more precisely, (3.1) the **Buy Stop** order for the uptrend (and **Sell stop** for the downtrend) and **Stop Loss** are set as in the channel breakdown
strategy. It is possible (3.2) also to open an order as in the case of an
in-channel strategy, i.e. when rolling back, when the price falls in the green
or yellow sectors, separated from the white in the direction opposite to the
trend (Fig. 12). In this case, the lot is calculated
according to the appropriate types of channel strategies. Then, when the price
steadily <l>/4 < l < <l>/2 takes a new price level, **Stop Loss** is transferred in accordance with the
boundaries of the new channel, etc.,
with a profitable closing of the **Stop Loss**
order, when the price starts to unfold. In this case, if the trend is
identified, for example, by MN, then the channel is determined by W1, if the
trend is identified by W1, then the channel by D1, the trend is identified
by D1, the channel by H4.

Fig. 12. Trend strategy with opening of
a warrant on rollback and iteration of modifications**
Stop Loss**.** **

** Download or buy the indicator you can by reference PDP. **

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