%This m-file demonstrates the second setup simultaneously optimizing the
%CDO portfolio and credit tranching subject to a risk constraint assuring
%the rating of a tranche, a constraint on income spread payments,
%and a budget constraint.


clc
clear;

%Load data from file:
load('Data_for_Step-up_CDO_II_Toolbox.mat');
tbpsg_export_to_workspace(toolboxstruc_arr);

N_attach_points = 5;
%Specify the set of values of upper bound on probability that the
%cumulative collateral loss exceeds the tranche attachment point
%at least once in periods 1,…, T). Columns correspond to credit rating
%(BBB, A, AA, AAA)
Param_Mult_Prob = [0.0281 0.0071 0.0036 0.0012];

%Specify the set of values of lower bound on income spread payments
Param_lower_bound =[91 93 95 97];


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      Optimization Problem 6 (Example 4)    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Generate fragments of the problem description common for all parameter 
%values within Optimization Problem 6 (Example 4)
str1 = sprintf('Problem: problem_example_4, type = minimize'); 
str2 = sprintf('Objective: objective_linear_sum_of_x_5, linearize = 0');
str3 = sprintf('linear_sum_of_x_5(matrix_sum_of_x_5)');
str5 = sprintf('prmulti_pen_5_periods(0.00000000,matrix_example_4_1,matrix_example_4_2,matrix_example_4_3,matrix_example_4_4,matrix_example_4_5)');
str7 = sprintf('linear_spread(matrix_spread)');
str8 = sprintf('Constraint: constraint_budget, lower_bound = 1, upper_bound = 1, linearize = 0');
str9 = sprintf('linear_budget(matrix_budget)');
str10 = sprintf('Box_of_Variables: lowerbounds = point_lowerbounds, upperbounds = point_upperbounds');
str11 = sprintf('Solver: VAN, precision = 2, stages = 6');

%Begin two loops for Optimization Problem 6 (Example 4) over parameter values  
for i=1:1:length(Param_Mult_Prob)
   
%Generate parameter-specific fragment of the problem description
    str4 = sprintf('%s%.4f','Constraint: constraint_mult_prob, upper_bound =  ',Param_Mult_Prob(i));
    for j1=1:1:length(Param_lower_bound)
%Generate parameter-specific fragment of the problem description
        str6 = sprintf('%s%.0f','Constraint: constraint_spread, lower_bound =  ',Param_lower_bound(j1));
%Generate problem statement
        clear problem_statement;
        problem_statement = sprintf('%s\n', str1, str2, str3, str4, str5,...
            str6, str7, str8, str9, str10, str11);

%Uncomment the following line to open the problem in Toolbox Window:
%tbpsg_toolbox(problem_statement,toolboxstruc_arr);

%Optimize the problem      
        [solution_str, outargstruc_arr] = tbpsg_run(problem_statement, toolboxstruc_arr);
        
%Extract optimal solution
        point_variables = tbpsg_optimal_point_vars(solution_str, outargstruc_arr);
        loc = tbpsg_optimal_point_data(solution_str, outargstruc_arr);
        Points_Problem_6(:,j1,i)= loc';
        Sum_Attach_Points_Problem_1(j1,i) = tbpsg_objective(solution_str, outargstruc_arr); 
        constr_data = tbpsg_constraints_data(solution_str, outargstruc_arr);
        Multiple_Probabilities_Problem_1(j1,i) = constr_data(2);        
    end
end

warning('on', 'all');

str_ = ['BBB ' 'A ' 'AA ' 'AAA '];
ratings = strread(str_, '%s');
clear str_;

str_ = ['Attachment_Point_1 ' 'Attachment_Point_2 ' 'Attachment_Point_3 ' 'Attachment_Point_4 ' 'Attachment_Point_5 ' ];
attach_points_names = strread(str_, '%s');
attach_points_names = strrep(attach_points_names, '_', ' ');
clear str_;

str_ = ['Attach._Point_1 ' 'Attach._Point_2 ' 'Attach._Point_3 ' 'Attach._Point_4 ' 'Attach._Point_5 ' ];
attach_points_names_graph = strread(str_, '%s');
attach_points_names_graph = strrep(attach_points_names_graph, '_', ' ');
clear str_;

str_ = ['period_t=1 ' 'period_t=2 ' 'period_t=3 ' 'period_t=4 ' 'period_t=5 '];
period_names = strread(str_, '%s');
period_names = strrep(period_names, '_', ' ');
clear str_;

% display and save table with results of calculations
outfilename = 'Step-up_CDO_II_Output_Short.txt';
fid = fopen(outfilename, 'w');


fprintf('Table 1. Example 4: Attachment Points vs. Rating for Lower Bound on Income Spread Payments = 91\n');
fprintf(fid, 'Table 1. Example 4: Attachment Points vs. Rating for Lower Bound on Income Spread Payments = 91\n');
fprintf('Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
fprintf(fid, 'Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
for i=1:1:length(Param_Mult_Prob)
    fprintf('%5s',ratings{i});
    fprintf(fid,'%5s',ratings{i});
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            fprintf('%16f',Points_Problem_6(j,1,i));
            fprintf(fid,'%16f',Points_Problem_6(j,1,i));
        end
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');

fprintf('Table 2. Example 4: Attachment Points vs. Rating for Lower Bound on Income Spread Payments = 93\n');
fprintf(fid, 'Table 2. Example 4: Attachment Points vs. Rating for Lower Bound on Income Spread Payments = 93\n');
fprintf('Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
fprintf(fid, 'Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
for i=1:1:length(Param_Mult_Prob)
    fprintf('%5s',ratings{i});
    fprintf(fid,'%5s',ratings{i});
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            fprintf('%16f',Points_Problem_6(j,2,i));
            fprintf(fid,'%16f',Points_Problem_6(j,2,i));
        end
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');


fprintf('Table 3. Example 4: Attachment Points vs. Rating for Lower Bound on Income Spread Payments = 95\n');
fprintf(fid, 'Table 3. Example 4: Attachment Points vs. Rating for Lower Bound on Income Spread Payments = 95\n');
fprintf('Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
fprintf(fid, 'Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
for i=1:1:length(Param_Mult_Prob)
    fprintf('%5s',ratings{i});
    fprintf(fid,'%5s',ratings{i});
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            fprintf('%16f',Points_Problem_6(j,3,i));
            fprintf(fid,'%16f',Points_Problem_6(j,3,i));
        end
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');


fprintf('Table 4. Example 4: Attachment Points vs. Rating for Lower Bound on Income Spread Payments = 97\n');
fprintf(fid, 'Table 4. Example 4: Attachment Points vs. Rating for Lower Bound on Income Spread Payments = 97\n');
fprintf('Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
fprintf(fid, 'Rating  Attach.Point 1  Attach.Point 2  Attach.Point 3  Attach.Point 4  Attach.Point 5\n');
for i=1:1:length(Param_Mult_Prob)
    fprintf('%5s',ratings{i});
    fprintf(fid,'%5s',ratings{i});
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            fprintf('%16f',Points_Problem_6(j,4,i));
            fprintf(fid,'%16f',Points_Problem_6(j,4,i));
        end
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');


fprintf('Table 5. Structure of Optimal CDO Portfolio (rating BBB) for Different Lower Bounds on Income Spread Payments\n');
fprintf(fid, 'Table 5. Structure of Optimal CDO Portfolio (rating BBB) for Different Lower Bounds on Income Spread Payments\n');
fprintf('Instrument    Spread Payment = 91  Spread Payment = 93  Spread Payment = 95  Spread Payment = 97\n');
fprintf(fid, 'Instrument   Spread Payment = 91  Spread Payment = 93  Spread Payment = 95  Spread Payment = 97\n');
for j=1:1:size(Points_Problem_6,1)
    if size(findstr(point_variables{j}, 'attach'),1) == 0
            fprintf('%7s',point_variables{j});
            fprintf(fid,'%7s',point_variables{j});
            for j1=1:1:size(Param_lower_bound,2)
                fprintf('%21f',Points_Problem_6(j,j1,1));
                fprintf(fid,'%21f',Points_Problem_6(j,j1,1));
            end
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');



fprintf('Table 6. Structure of Optimal CDO Portfolio (rating A) for Different Lower Bounds on Income Spread Payments\n');
fprintf(fid, 'Table 6. Structure of Optimal CDO Portfolio (rating A) for Different Lower Bounds on Income Spread Payments\n');
fprintf('Instrument    Spread Payment = 91  Spread Payment = 93  Spread Payment = 95  Spread Payment = 97\n');
fprintf(fid, 'Instrument   Spread Payment = 91  Spread Payment = 93  Spread Payment = 95  Spread Payment = 97\n');
for j=1:1:size(Points_Problem_6,1)
    if size(findstr(point_variables{j}, 'attach'),1) == 0
            fprintf('%7s',point_variables{j});
            fprintf(fid,'%7s',point_variables{j});
            for j1=1:1:size(Param_lower_bound,2)
                fprintf('%21f',Points_Problem_6(j,j1,2));
                fprintf(fid,'%21f',Points_Problem_6(j,j1,2));
            end
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');


fprintf('Table 7. Structure of Optimal CDO Portfolio (rating AA) for Different Lower Bounds on Income Spread Payments\n');
fprintf(fid, 'Table 7. Structure of Optimal CDO Portfolio (rating AA) for Different Lower Bounds on Income Spread Payments\n');
fprintf('Instrument    Spread Payment = 91  Spread Payment = 93  Spread Payment = 95  Spread Payment = 97\n');
fprintf(fid, 'Instrument   Spread Payment = 91  Spread Payment = 93  Spread Payment = 95  Spread Payment = 97\n');
for j=1:1:size(Points_Problem_6,1)
    if size(findstr(point_variables{j}, 'attach'),1) == 0
            fprintf('%7s',point_variables{j});
            fprintf(fid,'%7s',point_variables{j});
            for j1=1:1:size(Param_lower_bound,2)
                fprintf('%21f',Points_Problem_6(j,j1,3));
                fprintf(fid,'%21f',Points_Problem_6(j,j1,3));
            end
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');


fprintf('Table 8. Structure of Optimal CDO Portfolio (rating AAA) for Different Lower Bounds on Income Spread Payments\n');
fprintf(fid, 'Table 8. Structure of Optimal CDO Portfolio (rating AAA) for Different Lower Bounds on Income Spread Payments\n');
fprintf('Instrument    Spread Payment = 91  Spread Payment = 93  Spread Payment = 95  Spread Payment = 97\n');
fprintf(fid, 'Instrument   Spread Payment = 91  Spread Payment = 93  Spread Payment = 95  Spread Payment = 97\n');
for j=1:1:size(Points_Problem_6,1)
    if size(findstr(point_variables{j}, 'attach'),1) == 0
            fprintf('%7s',point_variables{j});
            fprintf(fid,'%7s',point_variables{j});
            for j1=1:1:size(Param_lower_bound,2)
                fprintf('%21f',Points_Problem_6(j,j1,4));
                fprintf(fid,'%21f',Points_Problem_6(j,j1,4));
            end
    end
    fprintf('\n');
    fprintf(fid,'\n');
end
fprintf('\n');
fprintf(fid,'\n');


% build graph showing attachment points for various ratings for Problem 6,
% (CS.42)-(CS.46), with the lower bound on received average spread
% payments = 91 in the constraint (CS.44).

clear Y;
for i=1:1:length(Param_Mult_Prob)
    j1 =0;
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            j1 = j1+1;
            Y(j1,i)= Points_Problem_6(j,1,i);
        end
    end
end

figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(attach_points_names_graph));
hAxes = gca;
set(hAxes, 'XTickLabel', attach_points_names_graph);
grid on;
legend(ratings, 'Location', 'NorthWest');
%xlabel('Names of Attachment Points');
ylabel('Values of Attachment Points');
title('Attachment Points for Problem 6 with the lower bound spread payments = 91 ');


% build graph showing attachment points for various ratings for Problem 6,
% (CS.42)-(CS.46), with the lower bound on received average spread
% payments = 93 in the constraint (CS.44).

clear Y;
for i=1:1:length(Param_Mult_Prob)
    j1 =0;
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            j1 = j1+1;
            Y(j1,i)= Points_Problem_6(j,2,i);
        end
    end
end

figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(attach_points_names_graph));
hAxes = gca;
set(hAxes, 'XTickLabel', attach_points_names_graph);
grid on;
legend(ratings, 'Location', 'NorthWest');
%xlabel('Names of Attachment Points');
ylabel('Values of Attachment Points');
title('Attachment Points for Problem 6 with the lower bound spread payments = 93 ');


% build graph showing attachment points for various ratings for Problem 6,
% (CS.42)-(CS.46), with the lower bound on received average spread
% payments = 95 in the constraint (CS.44).

clear Y;
for i=1:1:length(Param_Mult_Prob)
    j1 =0;
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            j1 = j1+1;
            Y(j1,i)= Points_Problem_6(j,3,i);
        end
    end
end

figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(attach_points_names_graph));
hAxes = gca;
set(hAxes, 'XTickLabel', attach_points_names_graph);
grid on;
legend(ratings, 'Location', 'NorthWest');
%xlabel('Names of Attachment Points');
ylabel('Values of Attachment Points');
title('Attachment Points for Problem 6 with the lower bound spread payments = 95 ');


% build graph showing attachment points for various ratings for Problem 6,
% (CS.42)-(CS.46), with the lower bound on received average spread
% payments = 97 in the constraint (CS.44).

clear Y;
for i=1:1:length(Param_Mult_Prob)
    j1 =0;
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            j1 = j1+1;
            Y(j1,i)= Points_Problem_6(j,4,i);
        end
    end
end

figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(attach_points_names_graph));
hAxes = gca;
set(hAxes, 'XTickLabel', attach_points_names_graph);
grid on;
legend(ratings, 'Location', 'NorthWest');
%xlabel('Names of Attachment Points');
ylabel('Values of Attachment Points');
title('Attachment Points for Problem 6 with the lower bound spread payments = 97 ');


% build graph showing attachment points (rating BBB) for optimal points of Problem 6,
% (CS.42)-(CS.46) on different values of the lower bound on received 
% average spread payments (91,93,95,97) in the constraint (CS.44).

clear Y;
for j1=1:1:length(Param_lower_bound)
    j2 =0;
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            j2 = j2+1;
            Y(j1,j2)= Points_Problem_6(j,j1,1);
        end
    end
end

figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(Param_lower_bound));
hAxes = gca;
set(hAxes, 'XTickLabel', Param_lower_bound');
grid on;
legend(attach_points_names_graph, 'Location', 'NorthWest');
xlabel('Lower Bound on Income Spread Payments');
ylabel('Values of Attachment Points');
title('Attachment Points (rating BBB) vs. Lower Bound on Income Spread Payments');



% build graph showing attachment points (rating A) for optimal points of Problem 6,
% (CS.42)-(CS.46) on different values of the lower bound on received 
% average spread payments (91,93,95,97) in the constraint (CS.44).

clear Y;
for j1=1:1:length(Param_lower_bound)
    j2 =0;
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            j2 = j2+1;
            Y(j1,j2)= Points_Problem_6(j,j1,2);
        end
    end
end

figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(Param_lower_bound));
hAxes = gca;
set(hAxes, 'XTickLabel', Param_lower_bound');
grid on;
legend(attach_points_names_graph, 'Location', 'NorthWest');
xlabel('Lower Bound on Income Spread Payments');
ylabel('Values of Attachment Points');
title('Attachment Points (rating A) vs. Lower Bound on Income Spread Payments');



% build graph showing attachment points (rating AA) for optimal points of Problem 6,
% (CS.42)-(CS.46) on different values of the lower bound on received 
% average spread payments (91,93,95,97) in the constraint (CS.44).

clear Y;
for j1=1:1:length(Param_lower_bound)
    j2 =0;
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            j2 = j2+1;
            Y(j1,j2)= Points_Problem_6(j,j1,3);
        end
    end
end

figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(Param_lower_bound));
hAxes = gca;
set(hAxes, 'XTickLabel', Param_lower_bound');
grid on;
legend(attach_points_names_graph, 'Location', 'NorthWest');
xlabel('Lower Bound on Income Spread Payments');
ylabel('Values of Attachment Points');
title('Attachment Points (rating AA) vs. Lower Bound on Income Spread Payments');


% build graph showing attachment points (rating AAA) for optimal points of Problem 6,
% (CS.42)-(CS.46) on different values of the lower bound on received 
% average spread payments (91,93,95,97) in the constraint (CS.44).

clear Y;
for j1=1:1:length(Param_lower_bound)
    j2 =0;
    for j=1:1:size(Points_Problem_6,1)
        if size(findstr(point_variables{j}, 'attach'),1)>0
            j2 = j2+1;
            Y(j1,j2)= Points_Problem_6(j,j1,4);
        end
    end
end

figure
bar(Y,'group');
  set(gca,'XTick',1:1:length(Param_lower_bound));
hAxes = gca;
set(hAxes, 'XTickLabel', Param_lower_bound');
grid on;
legend(attach_points_names_graph, 'Location', 'NorthWest');
xlabel('Lower Bound on Income Spread Payments');
ylabel('Values of Attachment Points');
title('Attachment Points (rating AAA) vs. Lower Bound on Income Spread Payments');

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%Copyright ©American Optimal Decisions, Inc. 2007-2016.                 |
%American Optimal Decisions (AOD) retains copyrights to this material.  |
%                                                                       |
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