% Example demonstrates how to hedge the target portfolio consisting of
% stock options by portfolio including indices, stocks, and indices options
% in optimal manner. 
% The function riskconstrparam is used for solving the problem.
% Problem is solved for 4 values of the parameter
% (CVaR constraint on the hedging error -- gamma):
% $525, $540, $550, and 600.

clear;
format long;

%Load the data for problem stored in mat file
load('problem_CS_Hedging_Portfolio_of_Options_5p25_data.mat');

%Specify a set of values of parameter (upper bound in the  CVaR constraint
%on the hedging error (CS.2) ) for which runs should be conducted
Parameters = [525 540 550 600];

%--------------------------------------------------------------------------
%Read point_price matrix and create point_price values array 
fulldata = deblank(textread('point_prices.txt', '%s','delimiter','\n', 'bufsize', 65535));

strdata_arr = [];
count = 1;
for j=2:1:length(fulldata)
    if ~isempty(fulldata{j})
        strdata_arr{count} = strread(fulldata{j},'%s','delimiter','\t');
        count = count+1;
    end
end
fulldata = [];
for j=1:1:length(strdata_arr)
    loc_arr = str2double(strdata_arr{j});
    data_arr(j, :) = loc_arr';
end 
point_price = data_arr(:,2);
clear strdata_arr;
%--------------------------------------------------------------------------

%Set solver options:
options.Solver = 'VAN';
options.Precision  = 5; 
%Set graph options:
stroptions.PlotGraph = 'On';
stroptions.PlotType = 1;

%Because riskconstrparam solves the problem with objective including risk function with minus sign ("-"),
%we change objective sign to compensate the standard objective statement for riskconstrparam
stroptions.ScaleObjective =-1;

%Solve the optimization problem for specified  values of the parameter gamma (CS.2)
[Objectives, Parameters, Points, GraphHandle]=riskconstrparam ([], risk2, [], [], [], [], w2, H2, c2, p2,...
d, r, [], [], [], [], lb, ub, 'r', [],[],[],...
[], [], Parameters, [], stroptions);

%Create string array for point labels.
%Point labels (p_1, p_2, p_3, p_4) present points for different values of
%parameter (CVaR constraint on the hedging error -- gamma)

for i=1:size(Parameters,2) 
    Point_label {i} = strcat('p_',int2str(i));
end
Point_label = Point_label';

%Sort components in lexicographical order
component_name_arr_sorted = sort(component_name_arr);

%Sort Points and Matrices in accordance with components order
for j=1:size(component_name_arr) 
    for i=1:size(component_name_arr) 
        k = strcmp(component_name_arr_sorted(i), component_name_arr(j));
        if k == true
                Points_sorted(:,i)= Points (:,j);
                H2_sorted (:,i) = H2 (:,j);
        end
    end
end
    
%Create string array for components. 
for i=1:size(component_name_arr_sorted) 
             comp_alias {i} = strcat('c_',int2str(i));
end
 comp_alias_sorted = comp_alias';
%--------------------------------------------------------------------------
%Calculating the avg_loss at the points pt_1...pt_4 
for i = 1:4
loss(:,i) = c2 - H2_sorted*Points_sorted(i,:)';
avg_loss(i) = p2'*loss(:,i);
end

%--------------------------------------------------------------------------
% Create plot for linear_initial_price, cvar_risk_Hedging_constraint, and avg_loss
% for points pt_1, pt_2, pt_3, and pt_4
clear x;
clear y1;
clear y2;
clear y3;

%Calculate value of the functions linear_initial_price,
%cvar_risk_Hedging_constraint, and avg_loss at the points pt_1...pt_4
for i=1:4
  x(i) = i;
  y1(i) = functionvalue('linear', [], -d', [], [], Points(i,:)');
  y2(i) = functionvalue('cvar_risk', 0.94999999, H2, c2, p2, Points(i,:)');
  y3(i) = avg_loss(i);
end 

% Create plot
figure;
 plot1 = plot(...
  x,y1,...
  'LineStyle','none',...
  'Marker','s',...
  'MarkerEdgeColor',[1 0 0],...
  'MarkerFaceColor',[1 0 0],...
  'MarkerSize',8);
fprintf('%5f', i);
  hold on;
  plot1 = plot(...
x,y2,...
  'LineStyle','none',...
  'Marker','d',...
  'MarkerEdgeColor',[0 1 0],...
  'MarkerFaceColor',[0 1 0],...
  'MarkerSize',8);
plot1 = plot(...
x,y3,...
  'LineStyle','none',...
  'Marker','^',...
  'MarkerEdgeColor',[0 0 1],...
  'MarkerFaceColor',[0 0 1],...
  'MarkerSize',8);
grid on;
set(gca,'XLim',[0 5]);
set(gca,'YLim',[-150 800]);
set(gca,'XTick',1:1:size(Point_label));
hAxes = gca;
set(hAxes, 'XTickLabel', Point_label);
  hold off;

xlabel('Points');
ylabel('Values of functions f1, f2, and f3');
title('Initial price (f1),CVaR (f2), and average loss (f3)');
h = gca;
legend1 = legend(h,{'f1', 'f2', 'f3'});

%--------------------------------------------------------------------------
% Create plot showing the contribution of each individual component of the
% point to the CVaR of the hedging error 

%%Calculate increment of the function cvar_risk_Hedging_constraint at the point pt_1
[Increments] = functionincrement('cvar_risk', 0.94999999, H2_sorted, c2, p2, Points_sorted (1,:)');

%Set bound for components showing in the linear graph
bound_show_comp_linear = 6.9891e-003;

%Select components to be shown in the graph. These components are greater
%than bound_show_comp constant defined above.
clear i;
clear y;
others = 0;
k=0;
j = 1;
for i=1:1:size(component_name_arr_sorted(:,1)) 
    if abs(Increments(i)/y2(1)) >  bound_show_comp_linear
        comp_show(j) = comp_alias_sorted(i);
        y(j) = Increments(i)/y2(1);
        j = j+1;
        x(j) = j;
    else
        others = others + Increments(i)/y2(1);
          k = k + 1;
    end;
end;
others = others/k;
S = ['Others'];
comp_others = cellstr(S);

comp_show(length(comp_show)+1) = comp_others;
y(length(comp_show)) = others;

%Create Y-axis marks array
Ytick(1) = -0.025;
for i = 1:29
Ytick (i+1) = Ytick(i) + 0.001;
end

 % Create plot
figure;
plot1 = plot(...
  x,y,...
  'LineStyle','none',...
  'Marker','s',...
  'MarkerEdgeColor',[1 0 0],...
  'MarkerFaceColor',[1 0 0],...
  'MarkerSize',4);
grid on;
set(gca,'XLim',[0 length(comp_show)]);
set(gca,'YLim',[-0.025 0]);
set(gca,'XTick',1:length(comp_show));
set(gca,'YTick',Ytick);
hAxes = gca;
set(hAxes, 'XTickLabel', comp_show);
xlabel('Components');
ylabel('Values of Contribution to the CVaR of the Hedging Error ');
title('Contribution of Components of the Point p_1 to the CVaR of the Hedging Error');

%--------------------------------------------------------------------------
% Create pie diagram showing structure of the selected optimal point p_1

clear y;
others = 0;
%Set bound for component values to be displayed as different segments of the pie
bound_show_comp_pie = 14.9;
j = 1;
for i=1:1:size(component_name_arr_sorted(:,1)) 
    comp_pie(i) = Points_sorted(1,i)'* point_price(i);
    if comp_pie(i) >  bound_show_comp_pie
           comp_show_pie(j) = comp_alias_sorted(i);
        y(j) = comp_pie(i);
        j = j+1;
    else
        others = others + Points_sorted(1,i)'*point_price(i);
    end;
end;

comp_show_pie(length(comp_show_pie)+1) = comp_others;
y(length(comp_show_pie)) = others;

f = figure;
pie(y);
h = gca;

%Hide percent values on the pie
textObjs = findobj(h,'Type','text');
percent = get(textObjs,{'String'});
visibility = get(textObjs,{'Visible'});

for i = 1:length(comp_show_pie)
     visibility{i} = 'off';
end
set(textObjs,{'Visible'},visibility);

% Create annotation textbox
annotation1 = annotation(...
  f,'textbox',...
  'Position',[0.4625 0.8892 0.09107 0.05301],...
  'LineStyle','none',...
  'FitHeightToText','off',...
  'FontWeight','bold',...
  'String',{'X[pt\_1]'});

% Create title
title('Structure of the selected optimal point',...
  'FontSize',12,...
  'FontWeight','bold');

legend3 = legend(h,comp_show_pie,...
'AmbientLightColor',[0.7529 0.7529 0.7529],...
  'CLim',[1 12],...
  'Color',[0.8 0.8 0.8],...
  'DataAspectRatio',[10 1 1],...
  'Position',[0.7872 0.27 0.1732 0.5576],...
  'XColor',[0.7529 0.7529 0.7529],...
  'YColor',[0.7529 0.7529 0.7529],...
  'EdgeColor',[0.7529 0.7529 0.7529],...
  'Interpreter','none',...
  'Box','off');

%--------------------------------------------------------------------------
% Create histogram for Probability Density Function of Losses.
% Calculate the loss
loss = c2 - H2_sorted*Points_sorted(1,:)';
%Create Y-axis marks array
Xtick(1) = -150;
for i = 1:41
Xtick (i+1) = Xtick(i) + 25;
end
%Create the histogram:
figure
[bins,xout] = hist(loss,41);
bins = bins/sum(bins);
bar(xout,bins,'r',...
    'BarWidth',0.4);
h = gca;
set (h, 'YLim',([0.00 0.08]));
set (h, 'XLim',([-150 875]));
set(h,'XTick',Xtick);
set(h,'XTickLabel',Xtick);
set(h,'FontSize',7);
grid on;
set(h, 'YAxisLocation','left');
ylabel ('Probability','FontSize',9);
hold on;
xlabel('Losses (USD)','FontSize',9);
tit =sprintf('%s%','Probability Density Function of Losses: matrix\_Options\_scenarios\_small');
title(tit,'FontSize',9,...
    'FontWeight','bold');

%--------------------------------------------------------------------------
%Display the resultunt table
fprintf('\n%35s','CVaR constraint on the hedging error');
for i=1:1:length(Parameters)
    fprintf('%12.6f', Parameters(i));
end
fprintf('\n%35s','Initial price of the hedging');
fprintf('\n%35s','portfolio');
for i=1:1:length(Parameters)
    fprintf('%12.4f', Objectives(i));
end
fprintf('\n%35s','Optimal value of components');
for j=1:size(component_name_arr)
    fprintf('\n%30s', component_name_arr_sorted {j});
   for i=1:1:length(Parameters)
    fprintf('%12f', Points_sorted(i,j));
   end
end 
fprintf('\n');

%the last line of the code

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