An Improved Volume Profile Chart with Levels

Without much ado, here is the code

## Copyright (C) 2020 dekalog
## 
## This program is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with this program.  If not, see
## .

## -*- texinfo -*- 
## @deftypefn {} {@var{retval} =} market_profile_plot (@var{cross}, @var{n_bars})
##
## Plot a Market Profile Chart of CROSS of the last N_BARS.
##
## @seealso{}
## @end deftypefn

## Author: dekalog 
## Created: 2020-05-11

function market_profile_plot( curr_cross , n_days )

pkg load statistics ; 
cd /path/to/data/folder ;
price_name = tolower( curr_cross ) ;

if ( strcmp( price_name , 'aud_jpy' ) || strcmp( price_name , 'eur_jpy' ) || strcmp( price_name , 'gbp_jpy' ) || ...
     strcmp( price_name , 'usd_jpy' ) )
 tick_size = 0.001 ;
 round_digit = 3 ;
elseif ( strcmp( price_name , 'xau_usd' ) )
 tick_size = 0.1 ;
 round_digit = 1 ;
elseif ( strcmp( price_name , 'xag_usd' ) )
 tick_size = 0.01 ;
 round_digit = 2 ; 
else
 tick_size = 0.0001 ;
 round_digit = 4 ;
endif

## get price data of *_ohlc_10m
unix_command = [ "wc" , " " , "-l" , " " , [ price_name , '_ohlc_10m' ] ] ;
## the 'wc' with '-l' flag command counts the number of lines in [ price_name , '_ohlc_20m' ] } 
[ ~ , system_out ] = system( unix_command ) ;
cstr = strsplit( system_out , " " ) ; 
lines_in_file = str2double( cstr( 1 , 1 ) ) ;

## read *_ohlc_10m file
price_data = dlmread( [ price_name , '_ohlc_10m' ] , ',' , [ lines_in_file - ( n_days * 144 + 18 ) , 0 , lines_in_file , 21 ] ) ;
## get the earliest London open on a Sunday, if any
sun_open_ix = find( ( price_data( : , 11 ) == 1 ) .* ( price_data( : , 9 ) == 22 ) .* ( price_data( : , 10 ) == 0 ) ) ;
## get weekday closes
end_ix = find( ( price_data( : , 15 ) == 16 ) .* ( price_data( : , 16 ) == 50  ) ) ;
delete_ix = unique( [ sun_open_ix ; end_ix ] ) ;
## delete uuwanted data
price_data( 1 : delete_ix( 1 ) , : ) = [] ; end_ix = end_ix .- delete_ix( 1 ) ; open_ix = end_ix .+ 1 ; 
end_ix( end_ix == 0 ) = [] ; end_ix( end_ix > size( price_data , 1 ) ) = [] ;
open_ix( open_ix == 0 ) = [] ; open_ix( open_ix > size( price_data , 1 ) ) = [] ;

## give names to data
open = price_data(:,18) ; high = price_data(:,19) ; low = price_data(:,20) ; close = price_data(:,21) ; vol = price_data(:,22) ;
high_round = floor( high ./ tick_size .+ 0.5 ) .* tick_size ;
low_round = floor( low ./ tick_size .+ 0.5 ) .* tick_size ;
max_tick_range = max( high_round .- low_round ) / tick_size ;
upper_val = high ; lower_val = low ;

## create y and x axes for chart
y_max = max( high_round ) + max_tick_range * tick_size ;
y_min = min( low_round ) - max_tick_range * tick_size ;
y_ax = ( y_min : tick_size : y_max )' ;
end_x_ax_freespace = 5 ;

## create container
all_vp = zeros( n_days , numel( y_ax ) ) ; all_mp = all_vp ;

if ( n_days == 1 )

[ all_vp(1,:) , vp_val ] = pcolor_background( y_ax , high , low , vol , tick_size ) ;
vp_z = repmat( all_vp( 1 , : ) , numel( high ) + end_x_ax_freespace , 1 ) ;
lower_val( : ) = vp_val( 1 ) ; upper_val( : ) = vp_val( 2 ) ; 

elseif ( n_days >= 2 )

vp_z = zeros( numel( high ) + end_x_ax_freespace , size( all_vp , 2 ) ) ;

 for ii = 1 : numel( end_ix ) 
 [ all_vp(ii,:) , vp_val ] = pcolor_background( y_ax , high(open_ix(ii):end_ix(ii)) , low(open_ix(ii):end_ix(ii)) , ...
                                                        vol(open_ix(ii):end_ix(ii)) , tick_size ) ;
 vp_z(open_ix(ii):end_ix(ii),:) = repmat( all_vp(ii,:)./max(all_vp(ii,:)) , numel( high(open_ix(ii):end_ix(ii)) ) , 1 ) ;
 lower_val( open_ix(ii) : end_ix(ii) ) = vp_val( 1 ) ; upper_val( open_ix(ii) : end_ix(ii) ) = vp_val( 2 ) ;
 endfor

[ all_vp(end,:) , vp_val ] = pcolor_background( y_ax , high(open_ix(end):end) , low(open_ix(end):end) , ...
                                                         vol(open_ix(end):end) , tick_size ) ;
vp_z( open_ix( end ) : end , : ) = repmat( all_vp( end , : ) ./ max( all_vp( end , : ) ) , ...
                                            numel( high( open_ix( end ) : end ) ) + end_x_ax_freespace , 1 ) ;
lower_val( open_ix( end ) : end ) = vp_val( 1 ) ; upper_val( open_ix( end ) : end ) = vp_val( 2 ) ;
endif

## create the background ( best choices - viridis and ocean? )
x_ax = ( 1 : 1 : numel( open ) + end_x_ax_freespace )' ;
colormap( 'viridis' ) ; figure( 10 ) ; pcolor( x_ax , y_ax , vp_z' ) ; shading interp ; axis tight ;

## plot the individual volume profiles
hold on ;

scale_factor = ( 1 / max(max(all_vp) ) ) * 72 ;
for ii = 1 : numel( open_ix )
figure( 10 ) ; fill( all_vp( ii , : ) .* scale_factor .+ open_ix( ii ) , y_ax' , [99;99;99]./255 ) ;
endfor

## plot candlesticks
figure( 10 ) ; candle_mp( high , low , close , open ) ;

## plot upper and lower boundaries of value area
hold on ; figure( 10 ) ; plot( lower_val , 'b' , 'linewidth' , 2 , upper_val , 'r' , 'linewidth' , 2 ) ; hold off ;

## Plot vertical lines for London open at 7am
london_ix = find( ( price_data( : , 9 ) == 7 ) .* ( price_data( : , 10 ) == 0 ) ) ;
if ( ~isempty( london_ix ) )
 for ii = 1 : numel( london_ix )
  figure( 10 ) ; vline( london_ix( ii ) , 'g' ) ;
 endfor
endif

endfunction

which calls this

## Copyright (C) 2020 dekalog
## 
## This program is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with this program.  If not, see
## .

## -*- texinfo -*- 
## @deftypefn {} {@var{vp_z}, @var{vp_val} =} pcolor_background (@var{y_ax}, @var{high}, @var{low}, @var{vol}, @var{tick_size})
##
## @seealso{}
## @end deftypefn

## Author: dekalog 
## Created: 2020-05-13

function [ vp_z , vp_val ] = pcolor_background ( y_ax , high , low , vol , tick_size )

vp_z = zeros( 1 , numel( y_ax ) ) ; ##tpo_z = vp_z ;
vol( vol <= 1 ) = 2 ; ## no single point vol distributions
vp_val = zeros( 2 , 1 ) ;

 for ii = 1 : numel( high )

 ## the volume profile, vp_z
 ticks = norminv( linspace(0,1,vol(ii)+2) , (high(ii) + low(ii))/2 , (high(ii) - low(ii))*0.25 ) ;
 ticks = floor( ticks( 2 : end - 1 ) ./ tick_size .+ 0.5 ) .* tick_size ;
 unique_ticks = unique( ticks ) ;

  if ( numel( unique_ticks ) > 1 )
  [ N , X ] = hist( ticks , unique( ticks ) ) ;
  [ ~ , N_ix ] = max( N ) ; tick_ix = X( N_ix ) ;
  [ ~ , centre_tick ] = min( abs( y_ax .- tick_ix ) ) ;
  vp_z(1,centre_tick-N_ix+1:centre_tick+(numel(N)-N_ix)) = vp_z(1,centre_tick-N_ix+1:centre_tick+(numel(N)-N_ix)).+ N ;
  elseif ( numel( unique_ticks ) == 1 )
  [ ~ , centre_tick ] = min( abs( y_ax .- unique_ticks ) ) ;
  vp_z( 1 , centre_tick ) = vp_z( 1 , centre_tick ) + vol( ii ) ;
  endif

 endfor

[ ~ , vp_val_centre_ix ] = max( vp_z ) ;
sum_vp_cutoff = 0.7 * sum( vp_z ) ;
count = 1 ;

while ( count ~= 0 )
 
 sum_vp_z = sum( vp_z( max( vp_val_centre_ix - count , 1 ) : min( vp_val_centre_ix + count , numel( vp_z ) ) ) ) ;
 if ( sum_vp_z >= sum_vp_cutoff )
  vp_val( 1 , 1 ) = y_ax( max( vp_val_centre_ix - count , 1 ) ) ;             ## lower
  vp_val( 2 , 1 ) = y_ax( min( vp_val_centre_ix + count , numel( vp_z ) ) ) ; ## upper
  count = 0 ;
 else
  count = count + 1 ;
 endif

 endwhile

endfunction

and this

function hhh=vline(x,in1,in2)
% function h=vline(x, linetype, label)
% 
% Draws a vertical line on the current axes at the location specified by 'x'.  Optional arguments are
% 'linetype' (default is 'r:') and 'label', which applies a text label to the graph near the line.  The
% label appears in the same color as the line.
%
% The line is held on the current axes, and after plotting the line, the function returns the axes to
% its prior hold state.
%
% The HandleVisibility property of the line object is set to "off", so not only does it not appear on
% legends, but it is not findable by using findobj.  Specifying an output argument causes the function to
% return a handle to the line, so it can be manipulated or deleted.  Also, the HandleVisibility can be 
% overridden by setting the root's ShowHiddenHandles property to on.
%
% h = vline(42,'g','The Answer')
%
% returns a handle to a green vertical line on the current axes at x=42, and creates a text object on
% the current axes, close to the line, which reads "The Answer".
%
% vline also supports vector inputs to draw multiple lines at once.  For example,
%
% vline([4 8 12],{'g','r','b'},{'l1','lab2','LABELC'})
%
% draws three lines with the appropriate labels and colors.
% 
% By Brandon Kuczenski for Kensington Labs.
% brandon_kuczenski@kensingtonlabs.com
% 8 November 2001
if length(x)>1  % vector input
    for I=1:length(x)
        switch nargin
        case 1
            linetype='r:';
            label='';
        case 2
            if ~iscell(in1)
                in1={in1};
            end
            if I>length(in1)
                linetype=in1{end};
            else
                linetype=in1{I};
            end
            label='';
        case 3
            if ~iscell(in1)
                in1={in1};
            end
            if ~iscell(in2)
                in2={in2};
            end
            if I>length(in1)
                linetype=in1{end};
            else
                linetype=in1{I};
            end
            if I>length(in2)
                label=in2{end};
            else
                label=in2{I};
            end
        end
        h(I)=vline(x(I),linetype,label);
    end
else
    switch nargin
    case 1
        linetype='r:';
        label='';
    case 2
        linetype=in1;
        label='';
    case 3
        linetype=in1;
        label=in2;
    end
    
    
    
    g=ishold(gca);
    hold on
    y=get(gca,'ylim');
    h=plot([x x],y,linetype);
    if length(label)
        xx=get(gca,'xlim');
        xrange=xx(2)-xx(1);
        xunit=(x-xx(1))/xrange;
        if xunit<0 .8="" code="" color="" else="" end="" g="=0" get="" h="" handlevisibility="" hhh="h;" hold="" if="" label="" nargout="" off="" set="" tag="" text="" vline="" x-.05="" x="" xrange="" y="">

and produces charts such as this,

which is a 10 minute ohlc chart of the last 3 days, including "today's" ongoing price action. The number of days is a function input, and the horizontal blue and red lines indicate the upper and lower extremes of the value area. The vertical green lines indicate the London opening bar (7am BST) and each set of levels ends at the New York closing bar (5pm EST).

Further examples are last 10 days

and last month

Enjoy!

A Volume Profile With Levels Chart

Just a quick post to illustrate the latest of my ongoing chart iterations which combines a levels chart, as I have recently been posting about, but with the addition of a refined methodology of creating the horizontal histograms to more clearly represent the volumes over distinct periods.

The main change is to replace the use of the Octave barh function with the fill function. A minimal working example of this plotting is given in the code box below.

## get price data of *_ohlc_10m
unix_command = [ "wc" , " " , "-l" , " " , [ price_name , '_ohlc_10m' ] ] ;
## the 'wc' with '-l' flag command counts the number of lines in [ price_name , '_ohlc_20m' ] } 
[ ~ , system_out ] = system( unix_command ) ;
cstr = strsplit( system_out , " " ) ; 
lines_in_file = str2double( cstr( 1 , 1 ) ) ;

## read *_ohlc_10m file
price_data = dlmread( [ price_name , '_ohlc_10m' ] , ',' , [ lines_in_file - n_bars , 0 , lines_in_file , 21 ] ) ;
open = price_data(:,18) ; high = price_data(:,19) ; low = price_data(:,20) ; close = price_data(:,21) ; vol = price_data(:,22) ;
high_round = floor( high ./ tick_size .+ 0.5 ) .* tick_size ;
low_round = floor( low ./ tick_size .+ 0.5 ) .* tick_size ;
max_tick_range = max( high_round .- low_round ) / tick_size ;

## create y and x axes for chart
y_max = max( high_round ) + max_tick_range * tick_size ;
y_min = min( low_round ) - max_tick_range * tick_size ;
y_ax = ( y_min : tick_size : y_max )' ;
end_x_ax_freespace = 5 ;

all_vp = zeros( 3 , numel( y_ax ) ) ;

all_vp( 1 , : ) = pcolor_background( y_ax , high(1:50) , low(1:50) , vol(1:50) , tick_size ) ;
all_vp( 2 , : ) = pcolor_background( y_ax , high(51:100) , low(51:100) , vol(51:100) , tick_size ) ;
all_vp( 3 , : ) = pcolor_background( y_ax , high(100:150) , low(100:150) , vol(100:150) , tick_size ) ;

vp_z = repmat( sum( all_vp , 1 ) , numel( high ) + end_x_ax_freespace , 1 ) ;

x_ax = ( 1 : 1 : numel( open ) + end_x_ax_freespace )' ;
colormap( 'viridis' ) ; figure( 20 ) ; pcolor( x_ax , y_ax , vp_z' ) ; shading interp ; axis tight ;

## plot the individual volume profiles
hold on ;
scale_factor = 0.18 ; 
fill( all_vp( 1 , : ) .* scale_factor , y_ax' , [99;99;99]./255 ) ; 
fill( all_vp( 2 , : ) .* scale_factor .+ 50 , y_ax' , [99;99;99]./255 ) ;
fill( all_vp( 3 , : ) .* scale_factor .+ 100 , y_ax' , [99;99;99]./255 ) ;

## plot candlesticks
candle_mp( high , low , close , open ) ;
hold off;

I hope readers find this new way of plotting profile charts useful - I certainly am pretty pleased with it.

A Comparison of Charts

Earlier in May I posted about Market Profile with some charts and video. Further work on this has made me realise that my earlier post should more accurately be described as Volume Profile, so apologies to readers for that.

Another, similar type of chart I have seen described as a TPO chart (TPO stands for 'That Price Occurred' or ticked) and it is a simple matter to extend the code in the above linked post to create a TPO chart and below is the Octave function I have written to produce the backgrounds for both types of plot

## Copyright (C) 2020 dekalog
## 
## This program is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with this program.  If not, see
## .

## -*- texinfo -*- 
## @deftypefn {} {@var{background} =} pcolor_background (@var{y_ax}, @var{high}, @var{low}, @var{vol}, @var{tick_size})
##
## Creates a matrix, BACKGOUND, to be used by Market Profile plotting functions,
## which need a colour background matrix to be plotted by pcolor.
## 
## @seealso{}
## @end deftypefn

## Author: dekalog 
## Created: 2020-05-13

function [ vp_background , mp_background ] = pcolor_background ( y_ax , high , low , vol , tick_size )

vp_z = zeros( 1 , numel( y_ax ) ) ; mp_z = vp_z ;
vol( vol <= 1 ) = 2 ; ## no single point vol distributions

for ii = 1 : numel( high )

## the volume profile, vp_background
ticks = norminv( linspace(0,1,vol(ii)+2) , (high(ii) + low(ii))/2 , (high(ii) - low(ii))*0.25 ) ;
ticks = floor( ticks( 2 : end - 1 ) ./ tick_size .+ 0.5 ) .* tick_size ;
unique_ticks = unique( ticks ) ;

if ( numel( unique_ticks ) > 1 )
[ N , X ] = hist( ticks , unique( ticks ) ) ;
[ ~ , N_ix ] = max( N ) ; tick_ix = X( N_ix ) ;
[ ~ , centre_tick ] = min( abs( y_ax .- tick_ix ) ) ;
vp_z(1,centre_tick-N_ix+1:centre_tick+(numel(N)-N_ix)) = vp_z(1,centre_tick-N_ix+1:centre_tick+(numel(N)-N_ix)).+ N ;
elseif ( numel( unique_ticks ) == 1 )
[ ~ , centre_tick ] = min( abs( y_ax .- unique_ticks ) ) ;
vp_z( 1 , centre_tick ) = vp_z( 1 , centre_tick ) + vol( ii ) ;
endif

## the market profile, mp_background
[ ~ , ix_high ] = min( abs( y_ax .- high( ii ) ) ) ;
[ ~ , ix_low ] = min( abs( y_ax .- low( ii ) ) ) ;
mp_z( 1 , ix_low : ix_high ) = mp_z( 1 , ix_low : ix_high ) .+ 1 ;

endfor

vp_background = repmat( vp_z , numel( high ) , 1 ) ;
mp_background = repmat( mp_z , numel( high ) , 1 ) ;

endfunction

I have elected to still call the TPO plot a Market Profile plot as, from what I can make out, the tick count of the TPO is intended to be a surrogate for the original, cleared volume of Market Profile.

The above function is intended to provide a matrix input for the pcolor function, which internally scales the matrix to 0-1. Another idea I have had is to multiply the Volume Profile matrix and the Market Profile matrix together to get a normalised Combined Profile matrix. The animated GIF below shows all three.

It can be seen that there are subtle differences between them but that, on the whole, the results are similar.

More in due course.

A Second Orderbook Visualisation Chart

Below is code for a second way of charting ohlc price with Oanda's order book levels. First, the function loads the relevant data and plots the order book levels with Octave's pcolor function and then plots the price ohlc as candlesticks over the pcolor plot. The candlestick part of the function reuses some of the code I wrote for the financial package's candle plotting function.

## Copyright (C) 2020 dekalog
## 
## This program is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with this program.  If not, see
## .

## -*- texinfo -*- 
## @deftypefn {} candle_with_order_levels (@var{cross}, @var{n_bars})
##
## Plots a 20 minute candlestick chart of the most recent N_BARS of currency CROSS with
## the background highlighted with Oanda's historical orderbook levels for
## this CROSS.
##
## @seealso{candle,snake_and_canyon_plot}
## @end deftypefn

## Author: dekalog 
## Created: 2020-05-06

function candle_with_order_levels ( curr_cross , n_bars )

price_name = tolower( curr_cross ) ;

## get price data of *_ohlc_20m
unix_command = [ "wc" , " " , "-l" , " " , [ price_name , '_ohlc_20m' ] ] ;
## the 'wc' with '-l' flag command counts the number of lines in [ price_name , '_ohlc_20m' ] } 
[ ~ , system_out ] = system( unix_command ) ;
cstr = strsplit( system_out , " " ) ; 
lines_in_file = str2double( cstr( 1 , 1 ) ) ;
## read *_ohlc_20m file
price_data = dlmread( [ price_name , '_ohlc_20m' ] , ',' , [ lines_in_file - n_bars , 0 , lines_in_file , 21 ] ) ;
open = price_data(:,18) ; high = price_data(:,19) ; low = price_data(:,20) ; close = price_data(:,21) ; vol = price_data(:,22) ;

## get orderbook data of *_historical_orderbook_snapshots
unix_command = [ "wc" , " " , "-l" , " " , [ price_name , '_historical_orderbook_snapshots' ] ] ;
## the 'wc' with '-l' flag command counts the number of lines in [ price_name , '_historical_orderbook_snapshots' ] } 
[ ~ , system_out ] = system( unix_command ) ;
cstr = strsplit( system_out , " " ) ; 
lines_in_file = str2double( cstr( 1 , 1 ) ) ;
## read *_ohlc_20m file
orderbook_data = dlmread( [ price_name , '_historical_orderbook_snapshots' ] , ',' , [ lines_in_file - n_bars , 0 , lines_in_file , 87 ] ) ;
## combine buys and sell % and delete unnecessary data
orderbook_data( : , 7 : 47 ) = orderbook_data( : , 7 : 47 ) .+ orderbook_data( : , 48 : 88 ) ;
orderbook_data( : , 48 : 88 ) = [] ; ## col( : , 27 ) is the orderbook price level column

## create the backgound heatmap of levels
if ( strcmp( price_name , 'aud_jpy' ) || strcmp( price_name , 'eur_jpy' ) || strcmp( price_name , 'gbp_jpy' ) || ...
     strcmp( price_name , 'usd_jpy' ) )
 bucket_size = 0.05 ;
elseif ( strcmp( price_name , 'xau_usd' ) )
 bucket_size = 0.5 ;
else
 bucket_size = 0.0005 ;
endif

rounded_order_price = round( orderbook_data( : , 6 ) ./ bucket_size ) .* bucket_size ;

## create and fill image mesh for backgound plot
y_max = max( rounded_order_price .+ ( 20 * bucket_size ) ) ;
y_min = min( rounded_order_price .- ( 20 * bucket_size ) ) ;
y_ax = ( y_min - 5 * bucket_size : bucket_size : y_max + 5 * bucket_size )' ;
x_ax = ( 1 : 1 : numel( open ) + 3 )' ;

z = zeros( numel( x_ax ) , numel( y_ax ) ) ;

##for ii = 1 : size( z , 2 )
##[ ~ , ix ] = min( abs( y_ax .- rounded_order_price( ii ) ) ) ;
##z( ix - 20 : ix + 20 , ii ) = orderbook_data( ii , 7 : 47 )' ;
##endfor

[ ~ , ix ] = min( abs( y_ax .- rounded_order_price( 1 ) ) ) ;
z( 1 , ix - 20 : ix + 20 ) = orderbook_data( 1 , 7 : 47 ) ;
for ii = 2 : numel( x_ax ) - 3
z( ii , : ) = z( ii - 1 , : ) ;
[ ~ , ix ] = min( abs( y_ax .- rounded_order_price( ii ) ) ) ;
z( ii , ix - 20 : ix + 20 ) = orderbook_data( ii , 7 : 47 ) ;
endfor

for ii = numel( x_ax ) - 2 : numel( x_ax )
z( ii , : ) = z( ii - 1 , : ) ;
endfor

## For pcolor(), if x and y are vectors, then a typical vertex is (x(j), y(i), c(i,j)). 
## Thus, columns of c correspond to different x values and rows of c correspond to different y values.
## create the background ( best choices - viridis and ocean? ) 
colormap( 'ocean' ) ; figure( 20 ) ; pcolor( x_ax , y_ax , z' ) ; shading interp ; axis tight ;

hold on ; 

## plot candlesticks
wicks = high .- low ;
body = close .- open ;
up_down = sign ( body );
body_width = 20 ;
wick_width = 2 ;
doji_size = 10 ;
one_price_size = 15 ;

## plot the wicks
x = ( 1 : numel( close ) ) ;  # the x-axis
idx = x ;
high_nan = nan( size ( high ) ) ; high_nan( idx ) = high ; # highs
low_nan = nan( size ( low ) ) ; low_nan( idx ) = low ;     # lows
x = reshape( [ x ; x ; nan( size ( x ) ) ] , [] , 1 ) ;
y = reshape( [ high_nan( : )' ; low_nan( : )' ; nan( 1 , length ( high ) ) ] , [] , 1 ) ;
figure( 20 ) ; plot( x , y , 'w' , 'linewidth' , wick_width ) ; # plot wicks

## plot the up bar bodies
x = ( 1 : numel( close ) ) ; # the x-axis
idx = ( up_down == 1 ) ; idx = find ( idx ) ;                      # index by condition close > open
high_nan = nan( size ( high ) ) ; high_nan( idx ) = close( idx ) ; # body highs
low_nan = nan( size ( low ) ) ; low_nan( idx ) = open( idx ) ;     # body lows
x = reshape( [ x ; x ; nan( size ( x ) ) ] , [] , 1 ) ;
y = reshape( [ high_nan( : )' ; low_nan( : )' ; nan( 1 , length ( high ) ) ] , [] , 1 ) ;
figure( 20 ) ; plot( x , y , 'c' , 'linewidth' , body_width ) ; # plot bodies for up bars

## plot the down bar bodies
x = ( 1 : numel( close ) ) ; # the x-axis
idx = ( up_down == -1 ) ; idx = find ( idx ) ;                    # index by condition close < open
high_nan = nan( size ( high ) ) ; high_nan( idx ) = open( idx ) ; # body highs
low_nan = nan( size ( low ) ) ; low_nan( idx ) = close( idx ) ;   # body lows
x = reshape( [ x ; x ; nan( size ( x ) ) ] , [] , 1 ) ;
y = reshape( [ high_nan( : )' ; low_nan( : )' ; nan( 1 , length ( high ) ) ] , [] , 1 ) ;
figure( 20 ) ; plot( x , y , 'r' , 'linewidth', body_width ) ; # plot bodies for down bars

## plot special cases
## doji bars
doji_bar = ( high > low ) .* ( close == open ) ; doji_ix = find ( doji_bar ) ;

if ( length ( doji_ix ) >= 1 )
  x = ( 1 : length ( close ) ) ; # the x-axis
  figure( 20 ) ; plot( x( doji_ix ) , close( doji_ix ) , '+k' , 'markersize' , doji_size ) ; # plot the open/close as horizontal dash
endif

## open == high == low == close
one_price = ( high == low ) .* ( close == open ) .* ( open == high ) ; one_price_ix = find ( one_price ) ;

if ( length ( one_price_ix ) >= 1 )
  x = ( 1 : numel( close ) ) ; # the x-axis
  figure( 20 ) ; plot ( x( one_price_ix ) , close( one_price_ix ) , '.k' , 'markersize' , one_price_size ) ; # plot as a point/dot
endif

hold off ;

endfunction

The 20 orderbook levels above and below the open of each candlestick are plotted and a typical looking chart output, with the "ocean" colourmap, is:

where the lighter colours show a higher proportion of accumulated orders.

The next little project I have set myself is to do the same as above, but to plot a different version of a market profile chart.

Recording Oanda's Streaming Prices

As a quick update following on from my previous post about Market Profile, with a bit of help I have written the following command line code to capture streaming prices to file

stdbuf -oL -eL curl -s -H "Content-Type: application/json" -H "Authorization: Bearer XXX..." "https://stream-fxtrade.oanda.com/v3/accounts/XXX-XXX-XXXXXX-XXX/pricing/stream?instruments=EUR_USD" | jq --raw-output --unbuffered '[.time, .bids[0].price, .asks[0].price] | @csv' | sed -u 's/["Z]//g' | sed -u 's/[-T:]/,/g' >> ~/path/to/append/to/output

In my previous post I mentioned that capturing streaming tick data would be a whole new infrastructure project, however it seems that the above one line of code in the command line would suffice. I still do not intend to routinely capture such streaming tick data for a host of reasons, but I am going to capture some data in order to calibrate the approach used in my previous post.

More in due course. 

Market Profile Chart in Octave

In a comment on my previous post, visualising Oanda's orderbook, a reader called Darren suggested that I was over complicating things and should perhaps use a more established methodology, namely Market Profile.

I had heard of Market Profile before Darren mentioned it, but had always assumed that it required access to data that I didn't readily have to hand, i.e. tick level data. With my recent work on Oanda's API in Octave that is no longer necessarily the case. However, downloading, storing and manipulating streams of tick data would be a whole new infrastructure project that I would have to implement in either R or Octave.

Instead of doing this I have done some research into Market Profile and come up with an alternative solution that can use the more readily available tick volume. One of the empirically observed assumptions of Market Profile is that on a "normal" day such volume is normally distributed and creates a "value area" that contains approximately 70% of the market action, which roughly corresponds to action falling within one standard deviation of the mean of said action, and this mean in turn roughly corresponds with what is termed the "point of control" (POC).

If one takes this at face value as being an accurate description of market action, it is possible to recreate the "normal" market profile with the following Octave code:

 ticks = norminv( linspace( 0 , 1 , vol( ii ) + 2 ) , ( high( ii ) + low( ii ) ) / 2 , ( high( ii ) - low( ii ) ) / 6 ) ;
 ticks = floor( ticks( 2 : end - 1 ) ./ tick_size .+ tick_size ) .* tick_size ;
 [ vals , bin_centres ] = hist( ticks , unique( ticks ) ) ;

What this does is create vol(ii)+2 linearly spaced tick values from 0 to 1, where vol(ii) is the tick volume for an aggregated period, i.e. an ohlc bar, and transforms these into normally distributed ticks with a mean of the midpoint of the bar and an assumed standard deviation of one sixth the high-low range, rounded to the nearest whole tick. The hist function then provides the counts of ticks per level (vals) at levels (bin_centres).

Below is a screen shot of recent EUR_USD forex prices at a resolution of 20 minute candlesticks from 17:00 EST on 28th April 2020 to end of week close at 17:00 EST 1st May 2020.

The silhouette chart at the bottom is the usual tick volume per bar and the horizontal histogram is the Market Profile of the 20 minute bars from the first bar to the first vertical green line, calculated as described above. All the visable vertical green lines represent the open at 07:00 BST, whilst the vertical red lines are the 17:00 EST closes. The horizontal blue line is the current POC at 07:00 BST, taking into account only the bars to the left of the first green line, i.e. the Asian overnight session.

Next is a video of the progression through time along the above chart: as time progesses the Market Profile histogram changes and new, blue POC lines are plotted, with the time progression being marked by the advancing green lines. During subsequent Asian sessions the histogram colour is plotted in red, and new POC lines formed in the Asian session are also plotted in red.

For easier viewing, this is a screen shot of the chart as it appears at the end of the video

For comparative purposes this is a screen shot of the same as above, but using 10 minute ohlc bars and 10 minute updates to the Market Profile

Readers should note that the scaling of the silhouette charts and histograms are not the same for both - they are hand scaled by me for visualisation purposes only.

For completeness, here is the Octave script used to produce the above

clear all ;
pkg load statistics ;

## load data
cd /home/dekalog/Documents/octave/oanda_data/20m ;
oanda_files_20m = glob( "*_ohlc_20m" ) ;
ix = 7 ;##input( 'Tradable? ' ) ;
data = dlmread( oanda_files_20m{ ix } ) ;
data( 1 : 146835 , : ) = [] ;

tick_size = 0.0001 ;

open = data( : , 18 ) ; high = data( : , 19 ) ; low = data( : , 20 ) ; close = data( : , 21 ) ; vol = data( : , 22 ) ;
## Create grid for day
max_high = max( high ) + 0.001 ; min_low = min( low ) - 0.001 ; grid = ( min_low : tick_size : max_high + 0.0001 ) ;
grid_ix = floor( grid ./ tick_size .+ tick_size ) .* tick_size ; 
market_profile = [ grid_ix ; zeros( 1 , size( grid_ix , 2 ) ) ] ;
asian_market_profile = [ grid_ix ; zeros( 1 , size( grid_ix , 2 ) ) ] ;
 
figure( 20 ) ; 
candle( high , low , close , open ) ; 
vline( 27 , 'g' ) ; vline( 72 , 'r' ) ; vline( 99 , 'g' ) ; vline( 144 , 'r' ) ; vline( 174 , 'g' ) ;
xlim( [ 0 size( open , 1 ) ] ) ;
ylim( [ grid_ix(1) grid_ix(end) ] ) ;
hold on ; plot( ( vol .* 0.0000004 ) .+ grid_ix( 1 ) , 'b' , 'linewidth' , 2 ) ; 
area( ( vol .* 0.0000004 ) .+ grid_ix( 1 ) , 'facecolor' , 'b' ) ; hold off ;

for ii = 1 : 27
 ticks = norminv( linspace( 0 , 1 , vol( ii ) + 2 ) , ( high( ii ) + low( ii ) ) / 2 , ( high( ii ) - low( ii ) ) / 6 ) ;
 ticks = floor( ticks( 2 : end - 1 ) ./ tick_size .+ tick_size ) .* tick_size ;
 [ vals , bin_centres ] = hist( ticks , unique( ticks ) ) ;
 vals_ix = find( ismember( grid_ix , bin_centres ) ) ;
 market_profile( 2 , vals_ix ) += vals ;
endfor

[ max_mp_val_old , max_mp_ix ] = max( market_profile( 2 , : ) ) ;

hold on ; figure( 20 ) ; H = barh( market_profile( 1 , : ) , market_profile( 2 , : ).*0.005 , 'c' ) ; hold off ;
hline( market_profile( 1 , max_mp_ix ) , 'b' ) ;

for ii = 28 : 72
 ticks = norminv( linspace( 0 , 1 , vol( ii ) + 2 ) , ( high( ii ) + low( ii ) ) / 2 , ( high( ii ) - low( ii ) ) / 6 ) ;
 ticks = floor( ticks( 2 : end - 1 ) ./ tick_size .+ tick_size ) .* tick_size ;
 vals = hist( ticks , unique( ticks ) ) ;
 vals_ix = find( ismember( grid_ix , unique( ticks ) ) ) ;
 market_profile( 2 , vals_ix ) += vals ;
 [ max_mp_val , max_mp_ix ] = max( market_profile( 2 , : ) ) ;
 hold on ; figure( 20 ) ; barh( market_profile( 1 , : ) , market_profile( 2 , : ).*0.005 , 'c' ) ; hold off ;
 vline( ii , 'g' ) ; 
 if ( max_mp_val > max_mp_val_old )
  hline( market_profile( 1 , max_mp_ix ) , 'b' ) ;
  max_mp_val_old = max_mp_val ;
 endif
 pause(0.01) ;
endfor

for ii = 73 : 99
 ticks = norminv( linspace( 0 , 1 , vol( ii ) + 2 ) , ( high( ii ) + low( ii ) ) / 2 , ( high( ii ) - low( ii ) ) / 6 ) ;
 ticks = floor( ticks( 2 : end - 1 ) ./ tick_size .+ tick_size ) .* tick_size ;
 vals = hist( ticks , unique( ticks ) ) ;
 vals_ix = find( ismember( grid_ix , unique( ticks ) ) ) ;
 market_profile( 2 , vals_ix ) += vals ;
 asian_market_profile( 2 , vals_ix ) += vals ;
 [ max_mp_val , max_mp_ix ] = max( market_profile( 2 , : ) ) ;
 hold on ; figure( 20 ) ; barh( market_profile( 1 , : ) , market_profile( 2 , : ).*0.005 , 'c' ) ; 
 figure( 20 ) ; barh( asian_market_profile( 1 , : ) , asian_market_profile( 2 , : ).*0.005 , 'r' ) ;
 hold off ;
 vline( ii , 'g' ) ; 
 if ( max_mp_val > max_mp_val_old )
  hline( market_profile( 1 , max_mp_ix ) , 'b' ) ;
  max_mp_val_old = max_mp_val ;
 endif
 pause(0.01) ;
endfor

[ ~ , max_mp_ix ] = max( asian_market_profile( 2 , : ) ) ;
hline( asian_market_profile( 1 , max_mp_ix ) , 'r' ) ;

for ii = 100 : 144
 ticks = norminv( linspace( 0 , 1 , vol( ii ) + 2 ) , ( high( ii ) + low( ii ) ) / 2 , ( high( ii ) - low( ii ) ) / 6 ) ;
 ticks = floor( ticks( 2 : end - 1 ) ./ tick_size .+ tick_size ) .* tick_size ;
 vals = hist( ticks , unique( ticks ) ) ;
 vals_ix = find( ismember( grid_ix , unique( ticks ) ) ) ;
 market_profile( 2 , vals_ix ) += vals ;
 [ max_mp_val , max_mp_ix ] = max( market_profile( 2 , : ) ) ;
 hold on ; figure( 20 ) ; barh( market_profile( 1 , : ) , market_profile( 2 , : ).*0.005 , 'c' ) ;
 figure( 20 ) ; barh( asian_market_profile( 1 , : ) , asian_market_profile( 2 , : ).*0.005 , 'r' ) ; 
 hold off ;
 vline( ii , 'g' ) ; 
 if ( max_mp_val > max_mp_val_old )
  hline( market_profile( 1 , max_mp_ix ) , 'b' ) ;
  max_mp_val_old = max_mp_val ;
 endif
 pause(0.01) ;
endfor

[ max_mp_val , max_mp_ix ] = max( market_profile( 2 , 101 : end ) ) ;
max_mp_val_old = max_mp_val ;
hline( market_profile( 1 , max_mp_ix + 100 ) , 'b' ) ;

for ii = 145 : 174
 ticks = norminv( linspace( 0 , 1 , vol( ii ) + 2 ) , ( high( ii ) + low( ii ) ) / 2 , ( high( ii ) - low( ii ) ) / 6 ) ;
 ticks = floor( ticks( 2 : end - 1 ) ./ tick_size .+ tick_size ) .* tick_size ;
 vals = hist( ticks , unique( ticks ) ) ;
 vals_ix = find( ismember( grid_ix , unique( ticks ) ) ) ;
 market_profile( 2 , vals_ix ) += vals ;
 asian_market_profile( 2 , vals_ix ) += vals ;
 [ max_mp_val , max_mp_ix ] = max( market_profile( 2 , 101 : end ) ) ;
 hold on ; figure( 20 ) ; barh( market_profile( 1 , : ) , market_profile( 2 , : ).*0.005 , 'c' ) ; 
 figure( 20 ) ; barh( asian_market_profile( 1 , : ) , asian_market_profile( 2 , : ).*0.005 , 'r' ) ;
 hold off ;
 vline( ii , 'g' ) ; 
 if ( max_mp_val > max_mp_val_old )
  hline( market_profile( 1 , max_mp_ix + 100 ) , 'b' ) ;
  max_mp_val_old = max_mp_val ;
 endif
 pause(0.01) ;
endfor

[ ~ , max_mp_ix ] = max( asian_market_profile( 2 , 101 : end ) ) ;
hline( asian_market_profile( 1 , max_mp_ix + 100 ) , 'r' ) ;

for ii = 175 : size( open , 1 )
 ticks = norminv( linspace( 0 , 1 , vol( ii ) + 2 ) , ( high( ii ) + low( ii ) ) / 2 , ( high( ii ) - low( ii ) ) / 6 ) ;
 ticks = floor( ticks( 2 : end - 1 ) ./ tick_size .+ tick_size ) .* tick_size ;
 vals = hist( ticks , unique( ticks ) ) ;
 vals_ix = find( ismember( grid_ix , unique( ticks ) ) ) ;
 market_profile( 2 , vals_ix ) += vals ;
 [ max_mp_val , max_mp_ix ] = max( market_profile( 2 , 101 : end ) ) ;
 hold on ; figure( 20 ) ; barh( market_profile( 1 , : ) , market_profile( 2 , : ).*0.005 , 'c' ) ; 
 figure( 20 ) ; barh( asian_market_profile( 1 , : ) , asian_market_profile( 2 , : ).*0.005 , 'r' ) ;
 hold off ;
 vline( ii , 'g' ) ; 
 if ( max_mp_val > max_mp_val_old )
  hline( market_profile( 1 , max_mp_ix + 100 ) , 'b' ) ;
  max_mp_val_old = max_mp_val ;
 endif
 pause(0.01) ;
endfor

As just noted above for the scaling of the charts/video, readers should also be aware that within this script there are a lot of magic numbers that are unique to the data and scaling being used; therefore, this is not a plug in and play video script.

My thanks to the reader Darren, who suggested that I look into Market Profile. More in due course.