diff --git a/FPCAcomponents/FPCA_Figure2.png b/FPCAcomponents/FPCA_Figure2.png new file mode 100644 index 0000000..7f48328 Binary files /dev/null and b/FPCAcomponents/FPCA_Figure2.png differ diff --git a/FPCAcomponents/FPCAcomponents b/FPCAcomponents/FPCAcomponents new file mode 100644 index 0000000..7c96116 --- /dev/null +++ b/FPCAcomponents/FPCAcomponents @@ -0,0 +1,110 @@ +% clear variables and close windows +clear all; +close all; +clc; + +%%% Start READ REAL DATA +load Results.mat % the workspace results are generated by the code FPCAreal_data.m +load('xData.txt','-ascii'); +load('Is.txt','-ascii'); +load('tickdatayear.txt','-ascii'); + +%%% End READ REAL DATA + +%%% Start PLOT FIGURE + +% define axis +axis_x=linspace(min(mx),max(mx),50); % maturity +axis_y=linspace(min(my),max(my),50); % moneyness +[Xa,Ya] = meshgrid(axis_x,axis_y); + +% interpolate data for the functional components +FFun1 = TriScatteredInterp(mx,my,V2b(:,1), 'linear'); +FFun2 = TriScatteredInterp(mx,my,V2b(:,2), 'linear'); +FFun3 = TriScatteredInterp(mx,my,V2b(:,3), 'linear'); +FFun4 = TriScatteredInterp(mx,my,V2b(:,4), 'linear'); +FFun5 = TriScatteredInterp(mx,my,V2b(:,5), 'linear'); +FFun6 = TriScatteredInterp(mx,my,V2b(:,6), 'linear'); +FFun7 = TriScatteredInterp(mx,my,V2b(:,7), 'linear'); +FFun8 = TriScatteredInterp(mx,my,V2b(:,8), 'linear'); + +Za1b=FFun1(Xa,Ya); +Za2b=FFun2(Xa,Ya); +Za3b=FFun3(Xa,Ya); +Za4b=FFun4(Xa,Ya); +Za5b=FFun5(Xa,Ya); +Za6b=FFun6(Xa,Ya); +Za7b=FFun7(Xa,Ya); +Za8b=FFun8(Xa,Ya); + +figure(2) +hFig = figure(2); +set(hFig, 'Position', 0.8*[500 500 1000 900]) + +subplot(3,2,1) +surfl(Xa,Ya,-Za1b); +set(gca,'XTick',[0.50 0.75 1 1.25 1.50]) +set(gca,'YTick',[0 0.25 0.50 0.75 1 ]) +xh=xlabel('Moneyness') +yh=ylabel('Maturity') +zh=zlabel('$$\hat{\gamma}^{(d)}_{1,T}$$') +set(zh,'Interpreter','latex') +set([xh,yh,zh],'fontsize',10) +set(gca, 'fontsize',10) + +subplot(3,2,2) +plot(xData,-loadsb(1,Is),'blue') +xlim([min(xData) max(xData)]) +zh=ylabel('$$\hat{\delta}_{1,T}$$') +set(zh,'Interpreter','latex') +set(gca,'XTick',tickdatayear([1,3,5,7,9,11])) +set(gca,'XTickLabel',[2002 2004 2006 2008 2010 2012]) +set(gca, 'LooseInset', get(gca, 'TightInset')); +set([xh,yh],'fontsize',10) +set(gca, 'fontsize',10) + +subplot(3,2,5) +surfl(Xa,Ya,-Za7b); +set(gca,'XTick',[0.50 0.75 1 1.25 1.50]) +set(gca,'YTick',[0 0.25 0.50 0.75 1 ]) +xh=xlabel('Moneyness') +yh=ylabel('Maturity') +zh=zlabel('$$\hat{\gamma}^{(d)}_{7,T}$$') +set(zh,'Interpreter','latex') +set([xh,yh,zh],'fontsize',10) +set(gca, 'fontsize',10) + +subplot(3,2,6) +plot(xData,-loadsb(7,Is),'blue') +xlim([min(xData) max(xData)]) +zh=ylabel('$$\hat{\delta}_{7,T}$$') +set(zh,'Interpreter','latex') +set(gca,'XTick',tickdatayear([1,3,5,7,9,11])) +set(gca,'XTickLabel',[2002 2004 2006 2008 2010 2012]) +set(gca, 'LooseInset', get(gca, 'TightInset')); +set([xh,yh],'fontsize',10) +set(gca, 'fontsize',10) + +subplot(3,2,3) +surfl(Xa,Ya,-Za3b); +set(gca,'XTick',[0.50 0.75 1 1.25 1.50]) +set(gca,'YTick',[0 0.25 0.50 0.75 1 ]) +xh=xlabel('Moneyness') +yh=ylabel('Maturity') +zh=zlabel('$$\hat{\gamma}^{(d)}_{3,T}$$') +set(zh,'Interpreter','latex') +set([xh,yh,zh],'fontsize',10) +set(gca, 'fontsize',10) + +subplot(3,2,4) +plot(xData,-loadsb(3,Is),'blue') +xlim([min(xData) max(xData)]) +zh=ylabel('$$\hat{\delta}_{3,T}$$') +set(zh,'Interpreter','latex') +set(gca,'XTick',tickdatayear([1,3,5,7,9,11])) +set(gca,'XTickLabel',[2002 2004 2006 2008 2010 2012]) +set(gca, 'LooseInset', get(gca, 'TightInset')); +set([xh,yh],'fontsize',10) +set(gca, 'fontsize',10) + +%%% End PLOT FIGURE diff --git a/FPCAcomponents/Is.txt b/FPCAcomponents/Is.txt new file mode 100644 index 0000000..0183c70 --- /dev/null +++ b/FPCAcomponents/Is.txt @@ -0,0 +1 @@ + 7.4000000e+01 1.5900000e+02 2.4400000e+02 4.9700000e+02 5.8400000e+02 6.7100000e+02 7.5500000e+02 8.3900000e+02 1.0920000e+03 1.1780000e+03 1.2650000e+03 1.3510000e+03 1.4350000e+03 1.6890000e+03 1.7740000e+03 1.8600000e+03 1.9460000e+03 2.0270000e+03 2.2670000e+03 2.3530000e+03 2.4330000e+03 2.5120000e+03 1.0000000e+00 2.5100000e+02 3.3700000e+02 4.2100000e+02 5.0500000e+02 5.9100000e+02 8.4600000e+02 9.3200000e+02 1.0160000e+03 1.1000000e+03 1.1850000e+03 1.4420000e+03 1.5270000e+03 1.6120000e+03 1.6970000e+03 1.7810000e+03 2.0340000e+03 2.1120000e+03 2.1900000e+03 2.2750000e+03 8.0000000e+00 2.5900000e+02 3.4400000e+02 4.2800000e+02 5.1200000e+02 5.9800000e+02 8.5400000e+02 9.3900000e+02 1.0230000e+03 1.1070000e+03 1.1920000e+03 1.4500000e+03 1.5340000e+03 1.6190000e+03 1.7040000e+03 1.7880000e+03 2.0420000e+03 2.1190000e+03 2.1970000e+03 2.2820000e+03 9.5000000e+01 1.8100000e+02 2.6700000e+02 3.5100000e+02 6.0500000e+02 6.9200000e+02 7.7700000e+02 8.6200000e+02 9.4600000e+02 1.1990000e+03 1.2860000e+03 1.3730000e+03 1.4580000e+03 1.5410000e+03 1.7950000e+03 1.8810000e+03 1.9670000e+03 2.0490000e+03 2.1260000e+03 2.3670000e+03 2.4470000e+03 1.0100000e+02 1.8700000e+02 4.4000000e+02 5.2700000e+02 6.1300000e+02 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'Functional Principal Component Analysis for Derivatives of High-Dimensional Spatial Curves' + +Description: 'It interpolates the estimated functional components at a common grid and plots them, together with the estimates loadings time series.'' + +Keywords: estimation, FPCA, call prices, derivative, density, state price density, risk neutral density, functional components, time series, loadings + +See also: FPCAgpu, FPCAepan, FPCAmultiloc, FPCAsimulate_input, FPCAindividual, FPCAvariance, FPCAexpiration, FPCAcomponents, FPCAloadings + +Author: Maria Grith + +Submitted: Maria Grith + +Input: + - Results.mat : Output of FPCAreal_data.m + - vdaxm.txt : VDAX index time series (same date as the loadings) + - xData.txt : date time series + - Is.txt : index for the time series of loadings + - tickdatayear.txt : tick years + +Output: 'It plots the functional components and the corresponding loadings.'' diff --git a/FPCAcomponents/Results.mat b/FPCAcomponents/Results.mat new file mode 100644 index 0000000..5c21d74 Binary files /dev/null and b/FPCAcomponents/Results.mat differ diff --git a/FPCAcomponents/tickdatayear.txt b/FPCAcomponents/tickdatayear.txt new file mode 100644 index 0000000..1157f57 --- /dev/null +++ b/FPCAcomponents/tickdatayear.txt @@ -0,0 +1 @@ + 7.3121800e+05 7.3158300e+05 7.3194800e+05 7.3231500e+05 7.3267900e+05 7.3304400e+05 7.3340900e+05 7.3377500e+05 7.3414200e+05 7.3450600e+05 7.3486700e+05 diff --git a/FPCAcomponents/vdaxm.txt b/FPCAcomponents/vdaxm.txt new file mode 100644 index 0000000..98a4da2 --- /dev/null +++ b/FPCAcomponents/vdaxm.txt @@ -0,0 +1 @@ + -6.0481032e-01 -1.3024810e+01 -9.5448103e+00 -1.1154810e+01 9.6518968e-01 -1.0148103e+00 -8.9148103e+00 -1.7848103e+00 -5.7248103e+00 -1.3234810e+01 -1.0574810e+01 -6.2848103e+00 -4.7448103e+00 -5.4848103e+00 2.1345190e+01 -2.7348103e+00 -1.3124810e+01 -2.4248103e+00 1.3205190e+01 -8.0848103e+00 -7.8648103e+00 -1.6948103e+00 -1.2474810e+01 -2.9048103e+00 -9.6548103e+00 5.3051897e+00 2.9151897e+00 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variables and close windows +clear all; +close all; +clc; + +%%% Start READ REAL DATA + +load Results.mat; % the workspace results are generated by the code FPCAreal_data.m +load('xData.txt','-ascii'); +load('Is.txt','-ascii'); +load('tickdatayear.txt','-ascii'); + +%%% End READ REAL DATA + +%%% Start PLOT FIGURE + +% define axis +axis_x=linspace(min(mx),max(mx),50); % maturity +axis_y=linspace(min(my),max(my),50); % moneyness +[Xa,Ya] = meshgrid(axis_x,axis_y); + +% interpolate data for the functional components +FFun1 = TriScatteredInterp(mx,my,V2b(:,1), 'linear'); +FFun2 = TriScatteredInterp(mx,my,V2b(:,2), 'linear'); +FFun3 = TriScatteredInterp(mx,my,V2b(:,3), 'linear'); +FFun4 = TriScatteredInterp(mx,my,V2b(:,4), 'linear'); +FFun5 = TriScatteredInterp(mx,my,V2b(:,5), 'linear'); +FFun6 = TriScatteredInterp(mx,my,V2b(:,6), 'linear'); +FFun7 = TriScatteredInterp(mx,my,V2b(:,7), 'linear'); +FFun8 = TriScatteredInterp(mx,my,V2b(:,8), 'linear'); + +Za1b=FFun1(Xa,Ya); +Za2b=FFun2(Xa,Ya); +Za3b=FFun3(Xa,Ya); +Za4b=FFun4(Xa,Ya); +Za5b=FFun5(Xa,Ya); +Za6b=FFun6(Xa,Ya); +Za7b=FFun7(Xa,Ya); +Za8b=FFun8(Xa,Ya); + +% define the crisis period +CRISIS=xData(1317:1650); + +% find the date with the most extreme value in the time series of loadings +% corresponding to the second functional component +aro=find(abs(loadsb(2,Is))==max(abs(loadsb(2,Is)))); +CRISIS(75)=xData(aro-1); +CRISIS(76)=xData(aro); + + +for i=75:76 + + % find day + indcall=find(datenum(days, 'dd/mm/yyyy')==CRISIS(i)); + tday=datenum(days(indcall), 'dd/mm/yyyy'); + select= find( day==tday ) ; + + c1=c1g(select); + c2=c2g(select); + c3=c3g(select); + c4=c4g(select); + c5=c5g(select); + c6=c6g(select); + c7=c7g(select); + + refdmy_c=datenum(c2, 'dd/mm/yyyy'); + cd=[refdmy_c, c4, c5, c6, c7]; + numdate=unique(refdmy_c); + + % compute maturities + clear tauc + clear aa + + for l=1:length(cd) + aa(l)=find(ye==c5(l) & me==c4(l)); + tauc(l)=(datenum(expdata(aa(l)),'dd-mmm-yy')-refdmy_c(l,1))/365; + end + + + % find stock index + dday=find(date_dax==numdate); + s=dax(dday); + + % find and interpolate interest rate + rday=find(date_ir==numdate); + R=IR(rday,:); + rc=interp1(T,R,tauc,'linear','extrap'); + + % date rescaled_strike call_price interest_rate maturity + cdd=[cd(:,1) cd(:,4)./(s*exp(rc'/100.*tauc')) cd(:,5)./(s*exp(rc'/100.*tauc')) rc'/100 tauc']; + + % delete observation with maturity outside of [0.02, 0.5] + cdd(find(tauc>0.5 & tauc<0.02),:)=[]; + + + % sort maturity + [cdd(:,5), Im] = sort( cdd(:,5) ); + cdd(:,2)=cdd(Im,2); + cdd(:,3)=cdd(Im,3); + + % sort moneyness + matu=unique(cdd(:,5)); + for l=1:length(matu) + Ik=find(cdd(:,5)==matu(l) ); + [cdd(Ik,2),Il] =sort(cdd(Ik,2)); + cdd(Ik,3)=cdd((min(Ik)-1)+Il,3); + end + + cdd(find(cdd(:,5)>1.5 |cdd(:,2)>1.5|cdd(:,2)<.5),:)=[]; + + % find call string with smallest maturity + gf=find(cdd(:,5)==min(cdd(:,5))); + + % plot figure + figure(1) + hFig = figure(1); + + if i==75 + set(hFig, 'Position', 0.8*[500 500 1000 600]) + subplot(2,2,1) + scatter3(cdd(:,5),cdd(:,2),cdd(:,3),'filled','k') + hold on + scatter3(cdd(gf,5),cdd(gf,2),cdd(gf,3),'ro') + set(gca,'YDir','reverse'); + ylim([0.5 1.5]) + xlim([0,1]) + zlim([0 0.5]) + set(gca,'YTick',[0.50 0.75 1 1.25 1.50]) + set(gca,'XTick',[0 0.25 0.50 0.75 1 ]) + yh=ylabel('Moneyness') + xh=xlabel('Maturity') + zh=zlabel('Call prices') + ti=title(num2str(datestr(tday))) + set([xh,yh,zh,ti],'fontsize',10) + set(gca, 'fontsize',10) + end + + if i==76 + subplot(2,2,2) + scatter3(cdd(:,5),cdd(:,2),cdd(:,3),'filled','k') + set(gca,'YDir','reverse'); + ylim([0.5 1.5]) + xlim([0,1]) + zlim([0 0.5]) + set(gca,'YTick',[0.50 0.75 1 1.25 1.50]) + set(gca,'XTick',[0 0.25 0.50 0.75 1 ]) + yh=ylabel('Moneyness') + xh=xlabel('Maturity') + zh=zlabel('Call prices') + ti=title(num2str(datestr(tday))) + set([xh,yh,zh,ti],'fontsize',10) + set(gca, 'fontsize',10) + end + + subplot(2,2,3) + surfl(Xa,Ya,Za2b); + set(gca,'XTick',[0.50 0.75 1 1.25 1.50]) + set(gca,'YTick',[0 0.25 0.50 0.75 1 ]) + xh=xlabel('Moneyness') + yh=ylabel('Maturity') + zh=zlabel('$$\hat{ \gamma}^{(d)}_{2,T}$$') + set(zh,'Interpreter','latex') + zlim([-120,100]) + set([xh,yh,zh],'fontsize',10) + set(gca, 'fontsize',10) + + subplot(2,2,4) + LL2=loadsb(2,Is); + aro=find(abs(LL2)==max(abs(LL2))); + plot(xData,loadsb(2,Is),'blue') + hold on + scatter(xData(aro),LL2(aro),'ko','LineWidth',1, 'MarkerEdgeColor','k','MarkerFaceColor','red') + hold on + scatter(xData(aro-1),LL2(aro-1),'ko','LineWidth',1, 'MarkerEdgeColor','k','MarkerFaceColor','green') + ylim([-0.06,0.01]) + xlim([min(xData) max(xData)]) + xy=ylabel('$$\hat{\delta}_{2,T}$$') + set(xy,'Interpreter','latex') + ti=title(['Green: ', num2str(datestr(CRISIS(75))),'. Red: ',num2str(datestr(CRISIS(76)))]) + set(gca,'XTick',tickdatayear([1,3,5,7,9,11])) + set(gca,'XTickLabel',[2002 2004 2006 2008 2010 2012]) + set(gca, 'LooseInset', get(gca, 'TightInset')); + set([xh,yh,ti],'fontsize',10) + set(gca, 'fontsize',10) +end +%save2pdf(['Figure',num2str(i)],figure(1)) + +%%% End PLOT FIGURE diff --git a/FPCAexpiration/Is.txt b/FPCAexpiration/Is.txt new file mode 100644 index 0000000..0183c70 --- /dev/null +++ b/FPCAexpiration/Is.txt @@ -0,0 +1 @@ + 7.4000000e+01 1.5900000e+02 2.4400000e+02 4.9700000e+02 5.8400000e+02 6.7100000e+02 7.5500000e+02 8.3900000e+02 1.0920000e+03 1.1780000e+03 1.2650000e+03 1.3510000e+03 1.4350000e+03 1.6890000e+03 1.7740000e+03 1.8600000e+03 1.9460000e+03 2.0270000e+03 2.2670000e+03 2.3530000e+03 2.4330000e+03 2.5120000e+03 1.0000000e+00 2.5100000e+02 3.3700000e+02 4.2100000e+02 5.0500000e+02 5.9100000e+02 8.4600000e+02 9.3200000e+02 1.0160000e+03 1.1000000e+03 1.1850000e+03 1.4420000e+03 1.5270000e+03 1.6120000e+03 1.6970000e+03 1.7810000e+03 2.0340000e+03 2.1120000e+03 2.1900000e+03 2.2750000e+03 8.0000000e+00 2.5900000e+02 3.4400000e+02 4.2800000e+02 5.1200000e+02 5.9800000e+02 8.5400000e+02 9.3900000e+02 1.0230000e+03 1.1070000e+03 1.1920000e+03 1.4500000e+03 1.5340000e+03 1.6190000e+03 1.7040000e+03 1.7880000e+03 2.0420000e+03 2.1190000e+03 2.1970000e+03 2.2820000e+03 9.5000000e+01 1.8100000e+02 2.6700000e+02 3.5100000e+02 6.0500000e+02 6.9200000e+02 7.7700000e+02 8.6200000e+02 9.4600000e+02 1.1990000e+03 1.2860000e+03 1.3730000e+03 1.4580000e+03 1.5410000e+03 1.7950000e+03 1.8810000e+03 1.9670000e+03 2.0490000e+03 2.1260000e+03 2.3670000e+03 2.4470000e+03 1.0100000e+02 1.8700000e+02 4.4000000e+02 5.2700000e+02 6.1300000e+02 6.9700000e+02 7.8200000e+02 1.0350000e+03 1.1210000e+03 1.2070000e+03 1.2930000e+03 1.3780000e+03 1.6320000e+03 1.7170000e+03 1.8020000e+03 1.8880000e+03 1.9730000e+03 2.2100000e+03 2.2960000e+03 2.3750000e+03 2.4540000e+03 2.5270000e+03 1.9400000e+02 2.8100000e+02 3.6500000e+02 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9.1800000e+02 1.1700000e+03 1.2560000e+03 1.3420000e+03 1.4270000e+03 1.5130000e+03 1.7660000e+03 1.8510000e+03 1.9370000e+03 2.0220000e+03 2.1040000e+03 2.3450000e+03 2.4240000e+03 2.5030000e+03 7.3000000e+01 1.5800000e+02 4.1300000e+02 4.9600000e+02 5.8300000e+02 6.7000000e+02 7.5400000e+02 1.0080000e+03 1.0910000e+03 1.1770000e+03 1.2640000e+03 1.3500000e+03 1.6040000e+03 1.6880000e+03 1.7730000e+03 1.8590000e+03 1.9450000e+03 2.2660000e+03 2.3520000e+03 2.4320000e+03 2.5110000e+03 diff --git a/FPCAexpiration/Metainfo.txt b/FPCAexpiration/Metainfo.txt new file mode 100644 index 0000000..6fc28f5 --- /dev/null +++ b/FPCAexpiration/Metainfo.txt @@ -0,0 +1,21 @@ +Name of Quantlet: FPCAexpiration + +Published in: 'Functional Principal Component Analysis for Derivatives of High-Dimensional Spatial Curves' + +Description: 'Displays the effect of the expiration date on the level of estimated loadings corresponding to the second component.' + +Keywords: estimation, FPCA, call prices, derivative, density, state price density, risk neutral density, functional component, loadings + +See also: FPCAgpu, FPCAepan, FPCAmultiloc, FPCAsimulate_input, FPCAindividual, FPCAvariance, FPCAexpiration, FPCAcomponents, FPCAloadings + +Author: Maria Grith + +Submitted: Maria Grith + +Input: + - Results.mat : Output of FPCAreal_data.m + - xData.txt : date time series + - Is.txt : index for the time series of loadings + - tickdatayear.txt : tick years + +Output: 'It plots the call price strings on two consecutive trading days, as well as the second estimated non-orthonormal functional component of the state price density (SPD) and the corresponding loadings' diff --git a/FPCAexpiration/Results.mat b/FPCAexpiration/Results.mat new file mode 100644 index 0000000..5c21d74 Binary files /dev/null and b/FPCAexpiration/Results.mat differ diff --git a/FPCAexpiration/tickdatayear.txt b/FPCAexpiration/tickdatayear.txt new file mode 100644 index 0000000..1157f57 --- /dev/null +++ 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windows +clear all; +close all; +clc; + +%%% Start READ REAL DATA +load Results.mat % the workspace results are generated by the code FPCAreal_data.m +load('vdaxm.txt','-ascii') +load('xData.txt','-ascii'); +load('Is.txt','-ascii'); +load('tickdatayear.txt','-ascii'); + +%%% End READ REAL DATA + +%%% Start PLOT FIGURE + +% set size of the moving window +window=250; + +% initiate container to store the results +b=[]; +s=[]; +error=[]; +ASA=[]; +varcorra=[]; + +% sort loadings +xx=-loadsb([1,3,7],Is)'; + +% compute time varying standard deviations and correlations using a moving window +for i=window+1:N-1 + for j=1:3 + x=xx(i-window:i,j); + y=xx(i+1-window:i+1,j); + mdl = fitlm(x,y,'y ~ x1 -1 '); + R2ao(i)=mdl.Rsquared.Adjusted; + COF=mdl.Coefficients.Estimate; + ppv=mdl.Coefficients.pValue; + b(i,j)=COF(1); + error(:,j)=y-COF*x; + s(i,j)=std(error(:,j)); % standard deviation + end + ASA=corr(error); + varcorr(i-window,:)=[ASA(1,2) ASA(1,3) ASA(2,3)]; % pairwise correlation +end + +figure(3) +hFig = figure(3); +set(hFig, 'Position', 0.8*[500 500 1000 600]) +subplot(2,2,1) +plot(xData(window+1:N-1),b(window+1:N-1,1),'k-') +hold on +plot(xData(window+1:N-1),b(window+1:N-1,2),'r-') +hold on +plot(xData(window+1:N-1),b(window+1:N-1,3),'b-') +xlim([min(xData) max(xData)]) +zh=title('$$\hat{b}_{1}$$ (black), $$\hat{b}_{3}$$ (red) and $$\hat{b}_{7}$$ (blue)') +set(zh,'Interpreter','latex') +set(gca,'XTick',tickdatayear([1,3,5,7,9,11])) +set(gca,'XTickLabel',[2002 2004 2006 2008 2010 2012]) +set(gca, 'LooseInset', get(gca, 'TightInset')); +set(zh,'fontsize',10) +set(gca, 'fontsize',10) + +subplot(2,2,2) +plot(xData(window+1:N-1),s(window+1:N-1,1),'k-') +hold on +plot(xData(window+1:N-1),s(window+1:N-1,2),'r-') +hold on +plot(xData(window+1:N-1),s(window+1:N-1,3),'b-') +xlim([min(xData) max(xData)]) +zh=title('$$ \quad{ } \hat{\sigma}_{e1}$$ (black), $$\hat{\sigma}_{e3}$$ (red) and $$\hat{\sigma}_{e7}$$ (blue)') +set(zh,'Interpreter','latex') +set(gca,'XTick',tickdatayear([1,3,5,7,9,11])) +set(gca,'XTickLabel',[2002 2004 2006 2008 2010 2012]) +set(gca, 'LooseInset', get(gca, 'TightInset')); +set(zh,'fontsize',10) +set(gca, 'fontsize',10) + +subplot(2,2,3) +% define brewer map colors +sig1col = [0.1059 0.6196 0.4667; 0.8510 0.3725 0.0078; 0.4588 0.4392 0.7020; 0.9059 0.1608 0.5412; 0.4000 0.6510 0.1176; 0.9020 0.6706 0.0078; 0.6510 0.4627 0.1137; 0.4000 0.4000 0.4000]; +plot(xData(window+1:N-1),varcorr(:,1),'color',sig1col (1,:)) +hold on +plot(xData(window+1:N-1),-varcorr(:,3),'color',sig1col (4,:)) +xlim([min(xData) max(xData)]) +zh=title('$$corr(\hat{e}_{1}, \hat{e}_{3})$$ (green) and $$-corr( \hat{e}_{3}, \hat{e}_{7})$$ (magenta)') +ylim([-1 1]) +set(zh,'Interpreter','latex') +set(gca,'XTick',tickdatayear([1,3,5,7,9,11])) +set(gca,'XTickLabel',[2002 2004 2006 2008 2010 2012]) +set(gca,'YTick',[-1 0 1]) +set(gca, 'LooseInset', get(gca, 'TightInset')); +set(zh,'fontsize',10) +set(gca, 'fontsize',10) + +subplot(2,2,4) +vda=vdaxm(Is)'; +volv=[]; +% compute the volatility of volatility index +for i=251:N-1 + volv(i)=std(vda(i-250:i)); +end +[ax, h1, h2] = plotyy(xData(window+1:N-1),varcorr(:,2),xData(window+1:N-1),volv(window+1:N-1),'plot','plot','color', '#1f77b4','color', '#1f77b4'); +zh=title('$$ corr(\hat{e}_{1}, \hat{e}_{7})$$ (orange) and $$\hat{\sigma}_{IV}$$ (light blue)') +set(zh,'Interpreter','latex') +set(gca,'XTick',tickdatayear([1,3,5,7,9,11])) +set(gca,'XTickLabel',[2002 2004 2006 2008 2010 2012]) +set(zh,'fontsize',10) +set(gca, 'fontsize',10) +set(ax(1),'YColor',[0 0 0]); + +%%% End PLOT FIGURE diff --git a/FPCAloadings/Is.txt b/FPCAloadings/Is.txt new file mode 100644 index 0000000..0183c70 --- /dev/null +++ b/FPCAloadings/Is.txt @@ -0,0 +1 @@ + 7.4000000e+01 1.5900000e+02 2.4400000e+02 4.9700000e+02 5.8400000e+02 6.7100000e+02 7.5500000e+02 8.3900000e+02 1.0920000e+03 1.1780000e+03 1.2650000e+03 1.3510000e+03 1.4350000e+03 1.6890000e+03 1.7740000e+03 1.8600000e+03 1.9460000e+03 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'Functional Principal Component Analysis for Derivatives of High-Dimensional Spatial Curves' + +Description: 'Employs a moving window to estimate an AR(1) model for the loadings and to estimate standard deviation of the VDAX, and plots the results.' + +Keywords: estimation, FPCA, call prices, derivative, density, state price density, risk neutral density, autoregressive, time series + +See also: FPCAgpu, FPCAepan, FPCAmultiloc, FPCAsimulate_input, FPCAindividual, FPCAvariance, FPCAexpiration, FPCAcomponents, FPCAloadings + +Author: Maria Grith + +Submitted: Maria Grith + +Input: + - Results.mat : Output of FPCAreal_data.m + - vdaxm.txt : VDAX index time series (same date as the loadings) + - xData.txt : date time series + - Is.txt : index for the time series of loadings + - tickdatayear.txt : tick years + +Output: + - b : autoregressive coefficients + - s : standard deviation of the error + - varcorr : pairwise error correlation + - volv : standard deviation of the VDAX index diff --git a/FPCAloadings/Results.mat b/FPCAloadings/Results.mat new file mode 100644 index 0000000..5c21d74 Binary files /dev/null and b/FPCAloadings/Results.mat differ diff --git a/FPCAloadings/tickdatayear.txt b/FPCAloadings/tickdatayear.txt new file mode 100644 index 0000000..1157f57 --- /dev/null +++ b/FPCAloadings/tickdatayear.txt @@ -0,0 +1 @@ + 7.3121800e+05 7.3158300e+05 7.3194800e+05 7.3231500e+05 7.3267900e+05 7.3304400e+05 7.3340900e+05 7.3377500e+05 7.3414200e+05 7.3450600e+05 7.3486700e+05 diff --git a/FPCAloadings/vdaxm.txt b/FPCAloadings/vdaxm.txt new file mode 100644 index 0000000..98a4da2 --- /dev/null +++ b/FPCAloadings/vdaxm.txt @@ -0,0 +1 @@ + -6.0481032e-01 -1.3024810e+01 -9.5448103e+00 -1.1154810e+01 9.6518968e-01 -1.0148103e+00 -8.9148103e+00 -1.7848103e+00 -5.7248103e+00 -1.3234810e+01 -1.0574810e+01 -6.2848103e+00 -4.7448103e+00 -5.4848103e+00 2.1345190e+01 -2.7348103e+00 -1.3124810e+01 -2.4248103e+00 1.3205190e+01 -8.0848103e+00 -7.8648103e+00 -1.6948103e+00 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path here; genpath(folderName) returns a path string that includes folderName and multiple levels of subfolders below folderName. +%addpath(genpath('your path')); + +addpath(genpath('C:\Users\maria.grith\Documents\APROJECTS\Heiko\Quantanet Version_GPU2\FINAL CODES')); + +%%% Start READ REAL DATA + +% read expiration dates +fid = fopen('ExpirationDates.txt','rt'); +indata = textscan(fid, '%s %s', 'HeaderLines',1); +fclose(fid); +expdata = indata{1,1}; +[ye, me, de] = datevec(expdata,'dd-mmm-yy'); + +% read DAX index +[a1,a2]=textread('dax_index.txt','%s %f'); +dax=horzcat(a2); +date_dax=datenum(a1,'dd.mm.yyyy'); + +% read VDAX index +[a1v,a2v]=textread('vdax.txt','%s %f'); +vdax=horzcat(a2v); +date_vdax=datenum(a1v,'dd.mm.yyyy'); + +% read interest rate +[b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16]=textread('IRs.dat','%s %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f'); +date_ir=datenum(b1,'dd.mm.yyyy'); +IR=horzcat(b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16); + +% read call data +[c11,c12,c13,c14,c15,c16,c17]=textread('C_2002.txt', '%s %s %s %f %f %f %f'); +[c21,c22,c23,c24,c25,c26,c27]=textread('C_2003.txt', '%s %s %s %f %f %f %f'); +[c31,c32,c33,c34,c35,c36,c37]=textread('C_2004.txt', '%s %s %s %f %f %f %f'); +[c41,c42,c43,c44,c45,c46,c47]=textread('C_2005.txt', '%s %s %s %f %f %f %f'); +[c51,c52,c53,c54,c55,c56,c57]=textread('C_2006.txt', '%s %s %s %f %f %f %f'); +[c61,c62,c63,c64,c65,c66,c67]=textread('C_2007.txt', '%s %s %s %f %f %f %f'); +[c71,c72,c73,c74,c75,c76,c77]=textread('C_2008.txt', '%s %s %s %f %f %f %f'); +[c81,c82,c83,c84,c85,c86,c87]=textread('C_2009.txt', '%s %s %s %f %f %f %f'); +[c91,c92,c93,c94,c95,c96,c97]=textread('C_2010.txt', '%s %s %s %f %f %f %f'); +[c101,c102,c103,c104,c105,c106,c107]=textread('C_2011.txt', '%s %s %s %f %f %f %f'); + +c1g=[c11;c21;c31;c41;c51;c61;c71;c81;c91;c101]; +c2g=[c12;c22;c32;c42;c52;c62;c72;c82;c92;c102]; +c3g=[c13;c23;c33;c43;c53;c63;c73;c83;c93;c103]; +c4g=[c14;c24;c34;c44;c54;c64;c74;c84;c94;c104]; +c5g=[c15;c25;c35;c45;c55;c65;c75;c85;c95;c105]; +c6g=[c16;c26;c36;c46;c56;c66;c76;c86;c96;c106]; +c7g=[c17;c27;c37;c47;c57;c67;c77;c87;c97;c107]; + +% define maturies for the interest rates +T=[7/365 14/365 21/365 1/12 2/12 3/12 4/12 5/12 6/12 7/12 8/12 9/12 10/12 11/12 1]; + +days=unique(c2g); +day=datenum(c2g, 'dd/mm/yyyy'); +N=length(days); + +%initiate container to store the results +vdaxc=[]; +odax=[]; +R=[]; +daysa=[]; + +cgridx=[]; +cgridy=[]; + +x1minc=[]; +x2minc=[]; +x1maxc=[]; +x2maxc=[]; + +for d=2:(N+1) + tday=datenum(days((d-1)), 'dd/mm/yyyy'); + select= find( day==tday ) ; + + c1=c1g(select); + c2=c2g(select); + c3=c3g(select); + c4=c4g(select); + c5=c5g(select); + c6=c6g(select); + c7=c7g(select); + + refdmy_c=datenum(c2, 'dd/mm/yyyy'); + cd=[refdmy_c, c4, c5, c6, c7]; + numdate=unique(refdmy_c); + + % compute maturities + clear tauc + clear aa + + for i=1:length(cd) + aa(i)=find(ye==c5(i) & me==c4(i)); + tauc(i)=(datenum(expdata(aa(i)),'dd-mmm-yy')-refdmy_c(i,1))/365; + end + + % find stock price + dday=find(date_dax==numdate); + s=dax(dday); + odax=[odax,s]; + + if(s>0) + daysa=[daysa, dday ]; + + % find volatility index + vdday=find(date_vdax==numdate); + sv=vdax(vdday); + vdaxc=[vdaxc,sv]; + + % find interest rate + rday=find(date_ir==numdate); + R=IR(rday,:); + + % interpolate interest rate + rc=interp1(T,R,tauc,'linear','extrap'); + + % date rescaled_strike call_price interest_rate maturity + cdd=[cd(:,1) cd(:,4)./(s*exp(rc'/100.*tauc')) cd(:,5)./(s*exp(rc'/100.*tauc')) rc'/100 tauc']; + + % remove observations with maturity larger than one year + cdd(find(tauc>1),:)=[]; + + % sort maturities + [cdd(:,5), Im] = sort( cdd(:,5) ); + cdd(:,2)=cdd(Im,2); + cdd(:,3)=cdd(Im,3); + + % sorting moneyness + matu=unique(cdd(:,5)); + for l=1:length(matu) + Ik=find(cdd(:,5)==matu(l) ); + [cdd(Ik,2),Il] =sort(cdd(Ik,2)); + cdd(Ik,3)=cdd((min(Ik)-1)+Il,3); + end + + % interpolate data for FPCA + F = TriScatteredInterp(cdd(:,5),cdd(:,2),cdd(:,3), 'linear'); + % store interpolated curves + Fc{d-1}=F; + + + % find smallest common grid + x1minc=[ x1minc min(cdd(:,5))]; + x2minc=[ x2minc min(cdd(:,2))]; + x1maxc=[ x1maxc max(cdd(:,5))]; + x2maxc=[ x2maxc max(cdd(:,2))]; + + cgridx=union(cgridx,cdd(:,5)); + cgridy=union(cgridy,cdd(:,2)); + c5unil{d-1}= cdd(:,5); % maturity + c2unil{d-1}=cdd(:,2); % moneyness + c3unil{d-1}=cdd(:,3); % call price + end +end +%%% End READ REAL DATA + +%%% Start ESTIMATION + + +x1min =median( x1minc ); +x2min =median( x2minc ); +x1max =median( x1maxc ); +x2max =1.4; % or use median( x2maxc ); + +% construct common grid +my =x1min + ( x1max-x1min ).*rand( 512 , 1 ); % maturity +mx =x2min + ( x2max-x2min ).*rand( 512 , 1 ); % moneyness + +% estimate the variances +sigma=zeros(N,1); +parfor i=1:N + sigma(i)=FPCAvariance(cell2mat( c5unil(i) ),cell2mat( c2unil(i) ),cell2mat( c3unil(i) ) ); +end + +L=3; % low dimensional space parameter +method=1; % decomposition of the dual covariance matrix of the observed curves +% estimation using FPCAgpu +[hX2b, V2b, loadsb,Meansmo2bb,Db]=FPCAgpu(L,Fc,x1minc,x2minc,x1maxc,x2maxc,cgridx,cgridy,c5unil,c2unil,c3unil,c3unil,N,mx,my,method,'cpu',sigma,1); + +%%% End ESTIMATION diff --git a/FPCAreal_data/IRs.dat b/FPCAreal_data/IRs.dat new file mode 100644 index 0000000..3ee9406 --- /dev/null +++ b/FPCAreal_data/IRs.dat @@ -0,0 +1,3078 @@ +15.10.2001 3.8510 3.8280 3.8020 3.7760 3.6760 3.6360 3.5780 3.5340 3.5010 3.4800 3.4580 3.4440 3.4340 3.4776 3.4270 +16.10.2001 3.8440 3.8250 3.8000 3.7690 3.6700 3.6260 3.5620 3.5180 3.4850 3.4590 3.4340 3.4190 3.4100 3.4533 3.4050 +17.10.2001 4.1250 3.9700 3.8880 3.8210 3.6930 3.6450 3.5780 3.5290 3.4980 3.4690 3.4410 3.4250 3.4160 3.4573 3.4080 +18.10.2001 3.9910 3.9010 3.8380 3.7820 3.6780 3.6330 3.5670 3.5200 3.4830 3.4580 3.4310 3.4170 3.4080 3.4492 3.3990 +19.10.2001 3.9380 3.8510 3.8170 3.7610 3.6580 3.6070 3.5390 3.4870 3.4510 3.4210 3.3900 3.3730 3.3630 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0000000..982f4df --- /dev/null +++ b/FPCAreal_data/Metainfo.txt @@ -0,0 +1,29 @@ +Name of Quantlet: FPCAreal_data + +Published in: 'Functional Principal Component Analysis for Derivatives of High-Dimensional Spatial Curves' + +Description: 'Estimates state price densities (SPD) from a sample of discretely observed and noisy call price curves at different time to maturity and strike prices. Use FPCA decomposition of the dual covariance matrix and estimate functional components of the SPD and their corresponding loadings.' + +Keywords: estimation, FPCA, call prices, derivative, density, state price density, risk neutral density + +See also: FPCAgpu, FPCAepan, FPCAmultiloc, FPCAsimulate_input, FPCAindividual, FPCAvariance, FPCAexpiration, FPCAcomponents, FPCAloadings + +Author: Maria Grith + +Submitted: Maria Grith + +Input: + - ExpirationDates.txt : Expiration dates for the call prices + - dax_index.txt : DAX 30 index time series + - vdax.txt : VDAX index time series + - IRs.dat : EURIBOR interest rates multivariate time series + - C_2002.txt : Call prices 2002 + +Output: + - hX2b : Low dimensional SPD curves (using L dimensions) + - V2b : Second derivative w.r.t. moneyness of the eigenfunctions + - loadsb : Loadings corresponding to the eigenfunction + - Meansmo2bb : Mean curve + - Db : Eigenvalues + - mx : Output Grid Monetary axis + - my : Output Grid Maturity axis diff 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