% this script search for cointegrated stat-arb strategies among swap contracts 
% see A. Meucci (2009) 
% "Review of Statistical Arbitrage, Cointegration, and Multivariate Ornstein-Uhlenbeck"
% available at ssrn.com

% Code by A. Meucci, April 2009
% Most recent version available at www.symmys.com > Teaching > MATLAB
% Adapted by R.M.Caloi


clear; clc; close all

trainingrange = 1:2564; %Training Set


%%%%%% estimation  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
load DB_SwapParRatesUSD_1995_2022
S=cov(Rates(trainingrange,:));
%If the statistical toolboox is available
%[E,Lam]=pcacov(S); 
%Otherwise
[E,D]=eig(S);
% rearrange D and E
Lam = diag(D);
Lam = Lam(end:-1:1);
E = E(:,end:-1:1);

% figure % set up dates ticks
% h=plot(Dates,Dates); 
% a=get(gca,'XTick');
% XTick = [];
% years = year(datetime(Dates(1),'ConvertFrom','excel')):year(datetime(Dates(end),'ConvertFrom','excel'));
% for n = years
%     XTick = [XTick datenum(n,1,1)];
% end
% a=min(Dates); 
% b=max(Dates); 
% X_Lim=[a-.01*(b-a) b+.01*(b-a)];
% close

Thetas =zeros(length(Lam),1);

for n=1:length(Lam)
    Y=Rates*E(:,n)*10000;
    [Mu,Theta,Sigma]=FitOU(Y(trainingrange),1/252); 
    Sd_Y=sqrt(Sigma/(2*Theta));
    Thetas(n)=Theta;
    
    figure
    current_line=ones(length(Y),1).*Y(end);
    Mu_line=ones(length(Y),1).*Mu;
    Z_line_up=Mu_line+Sd_Y;
    Z_line_dn=Mu_line-Sd_Y;
    

    plot(Dates,Y)
    hold on
    plot(Dates,Mu_line,'k','linewidth',1);
    hold on
    plot(Dates,Z_line_up,'r','linewidth',1)
    hold on
    plot(Dates,Z_line_dn,'r','linewidth',1)
    hold on
    plot(Dates,current_line,'g','linewidth',1)
    
    
%     set(gca,'xlim',X_Lim,'XTick',XTick);
%     datetick('x','yy','keeplimits','keepticks');
    grid off
    title(['eigendirection n. ' num2str(n) ',    theta = ' num2str(Theta)],'FontWeight','bold');
    xlabel('year','FontWeight','bold');
    ylabel('basis points','FontWeight','bold');
    
    pause
end

figure
plot(1:length(Lam),Thetas)
xlabel('eigendirection n. ','FontWeight','bold');
ylabel('theta','FontWeight','bold');