I have essentially copied the code from the Matlab Example file BermudanSwaption.m in an effort to calibrate the Hull White one factor model to some given market data. As I use a subset about 30 or fewer swaptions for my calibration set, I am able to arrive at an interior solution. But when I use a larger set of instruments, I get a weird error:
Below is the code:
ValuationDate = '10-01-2014';
Settle = datenum(ValuationDate);
% Zero rate data is market data, bootstrapped from Bloomberg and Reuters quotes
CurveDates = [735874;
735882;
735906;
735936;
735950;
736040;
736133;
736224;
736314;
736424;
736606;
736788;
736971;
737153;
737336;
737518;
737701;
737884;
738069;
738251;
738433;
738615;
738797;
738979;
739162;
739345;
739528;
739710;
739893;
740075;
740260;
740442;
740624;
740806;
740989;
741171;
741354;
741536;
741719;
741901;
742084;
742269;
742451;
742633;
742815;
742997;
743180;
743362;
743545;
743728;
743911;
744093;
744278;
744460;
744642;
744824;
745006;
745189;
745372;
745554;
745737;
745919;
746102;
746284;
746469;
746651;
746833;
747015;
747198;
747380;
747563;
747745;
747928;
748111;
748296;
748478;
748660;
748842;
749024;
749206;
749389;
749572;
749755;
749937;
750120;
750302;
750487];
ZeroRates = 1.0e-03*[0.0172;
0.0188;
0.0191;
0.0221;
0.0249;
0.0244;
0.0269;
0.0333;
0.0423;
0.0571;
0.0789;
0.1021;
0.1253;
0.1435;
0.1617;
0.1749;
0.1881;
0.1973;
0.2064;
0.2158;
0.2253;
0.2311;
0.2370;
0.2429;
0.2488;
0.2547;
0.2607;
0.2640;
0.2672;
0.2706;
0.2738;
0.2772;
0.2807;
0.2842;
0.2877;
0.2913;
0.2948;
0.2964;
0.2979;
0.2995;
0.3011;
0.3026;
0.3043;
0.3060;
0.3077;
0.3095;
0.3112;
0.3118;
0.3125;
0.3132;
0.3138;
0.3146;
0.3152;
0.3160;
0.3167;
0.3175;
0.3183;
0.3186;
0.3189;
0.3192;
0.3196;
0.3199;
0.3202;
0.3206;
0.3209;
0.3213;
0.3217;
0.3217;
0.3216;
0.3216;
0.3216;
0.3216;
0.3216;
0.3216;
0.3216;
0.3216;
0.3216;
0.3217;
0.3217;
0.3218;
0.3218;
0.3219;
0.3219;
0.3220;
0.3220;
0.3221;
0.3221];
Compounding = 2;
RateSpec = intenvset('Compounding', 2,'ValuationDate', ValuationDate,'StartDates', ValuationDate,'EndDates', CurveDates,'Rates', ZeroRates);
InstrumentMaturity = datenum('12-Sep-2044');
% Swaption Vol data from Bloomberg
SwaptionBlackVol = [ 0.5940 0.5550 0.4450 0.3710 0.3400 0.3110 0.2910 0.2750 0.2630 0.2520 0.2250 0.2140 0.2080 0.2050;
0.5630 0.5470 0.4420 0.3690 0.3360 0.3090 0.2900 0.2740 0.2630 0.2520 0.2260 0.2150 0.2090 0.2060;
0.5760 0.5330 0.4400 0.3730 0.3410 0.3150 0.2970 0.2820 0.2700 0.2590 0.2330 0.2220 0.2170 0.2140;
0.5840 0.5020 0.4240 0.3730 0.3480 0.3240 0.3060 0.2920 0.2810 0.2710 0.2430 0.2300 0.2230 0.2190;
0.5630 0.4750 0.4100 0.3700 0.3450 0.3230 0.3070 0.2940 0.2830 0.2740 0.2470 0.2330 0.2260 0.2210;
0.5510 0.4520 0.3980 0.3660 0.3410 0.3220 0.3070 0.2950 0.2850 0.2760 0.2500 0.2360 0.2290 0.2240;
0.4630 0.4010 0.3660 0.3440 0.3250 0.3100 0.2990 0.2890 0.2790 0.2720 0.2470 0.2320 0.2260 0.2210;
0.4230 0.3750 0.3480 0.3290 0.3140 0.3030 0.2930 0.2840 0.2760 0.2690 0.2420 0.2300 0.2240 0.2190;
0.3700 0.3470 0.3280 0.3110 0.2960 0.2880 0.2800 0.2730 0.2680 0.2620 0.2360 0.2240 0.2190 0.2150;
0.3420 0.3250 0.3100 0.2970 0.2850 0.2770 0.2700 0.2640 0.2590 0.2540 0.2280 0.2180 0.2140 0.2110;
0.3230 0.3010 0.2900 0.2810 0.2720 0.2650 0.2590 0.2540 0.2500 0.2470 0.2230 0.2130 0.2090 0.2060;
0.3010 0.2860 0.2760 0.2670 0.2580 0.2530 0.2480 0.2450 0.2420 0.2390 0.2160 0.2060 0.2030 0.2000;
0.2850 0.2750 0.2650 0.2560 0.2480 0.2440 0.2400 0.2370 0.2350 0.2320 0.2100 0.2000 0.1970 0.1940;
0.2710 0.2600 0.2510 0.2440 0.2380 0.2340 0.2310 0.2290 0.2260 0.2240 0.2040 0.1940 0.1910 0.1890;
0.2580 0.2470 0.2400 0.2350 0.2300 0.2270 0.2240 0.2210 0.2190 0.2170 0.1980 0.1890 0.1860 0.1840;
0.2460 0.2370 0.2320 0.2270 0.2240 0.2210 0.2180 0.2150 0.2130 0.2110 0.1980 0.1840 0.1820 0.1800;
0.2040 0.1980 0.1950 0.1920 0.1900 0.1890 0.1890 0.1880 0.1880 0.1870 0.1720 0.1660 0.1640 0.1620;
0.1790 0.1750 0.1740 0.1730 0.1730 0.1710 0.1710 0.1700 0.1690 0.1690 0.1530 0.1510 0.1500 0.1480;
0.1650 0.1650 0.1660 0.1670 0.1680 0.1670 0.1670 0.1680 0.1680 0.1680 0.1550 0.1580 0.1560 0.1530;
0.1530 0.1570 0.1590 0.1620 0.1640 0.1650 0.1660 0.1670 0.1680 0.1690 0.1560 0.1650 0.1620 0.1590];
% The tenors for the underlying swaps and the options on them
SwaptionExerciseDates = cellstr(['1M ';'2M ';'3M '; '6M ';'9M ';'1Y ';'18M';'2Y ';'3Y ';'4Y ';'5Y ';'6Y ';'7Y ';'8Y ';'9Y ';'10Y';'15Y';'20Y';'25Y';'30Y']);
SwaptionTenors = cellstr(['1Y ';
'2Y ';
'3Y ';
'4Y ';
'5Y ';
'6Y ';
'7Y ';
'8Y ';
'9Y ';
'10Y';
'15Y';
'20Y';
'25Y';
'30Y']);
testmat = zeros(length(SwaptionExerciseDates),1);
% Here I construct a matrix of exercise dates
for i = 1:length(SwaptionExerciseDates)
if SwaptionExerciseDates{i}(end)=='Y'
testmat(i) = addtodate(Settle,str2double(SwaptionExerciseDates{i}(1:end-1)),'year');
elseif SwaptionExerciseDates{i}(end)=='M'
testmat(i)=addtodate(Settle,str2double(SwaptionExerciseDates{i}(1:end-1)),'month');
end
end
EurExDates= testmat;
EurExDatesFull = repmat(testmat,1,length(SwaptionTenors));
testmat2 = zeros(length(SwaptionExerciseDates),length(SwaptionTenors));
% Here I construct a matix of maturity dates
for i = 1:size(EurExDatesFull,1)
for j = 1:size(EurExDatesFull,2)
if SwaptionTenors{j}(end)=='Y'
testmat2(i,j) = addtodate(EurExDatesFull(i,j),str2double(SwaptionTenors{j}(1:end-1)),'year');
elseif SwaptionTenors{j}(end)=='M'
testmat2(i,j)= addtodate(EurExDatesFull(i,j),str2double(SwaptionTenors{j}(1:end-1)),'month');
end
end
end
EurMatFull = testmat2;
% I construct an index of all the swaptions that I intend to use for calibration
relidx = find(EurMatFull <= InstrumentMaturity);
SwaptionBlackPrices = zeros(size(SwaptionBlackVol));
SwaptionStrike = zeros(size(SwaptionBlackVol));
% back out the swaption strikes and prices from the implied vol data.
for iSwaption=1:length(SwaptionExerciseDates)
for iTenor=1:length(SwaptionTenors)
[~,SwaptionStrike(iSwaption,iTenor)] = swapbyzero(RateSpec,[NaN 0],Settle, EurMatFull(iSwaption,iTenor),...
'StartDate',EurExDatesFull(iSwaption,iTenor),'LegReset',[1 2],'Basis',2);
SwaptionBlackPrices(iSwaption,iTenor) = swaptionbyblk(RateSpec,'call', SwaptionStrike(iSwaption,iTenor),Settle, ...
EurExDatesFull(iSwaption,iTenor), EurMatFull(iSwaption,iTenor),SwaptionBlackVol(iSwaption,iTenor));
end
end
TimeSpec = hwtimespec(Settle,daysadd(Settle,30*(1:370),6), 12);
% construct an index of some random collection of instruments
B = (214:224);
HW1Fobjfun4 = @(x) SwaptionBlackPrices(relidx(B)) - ...
swaptionbyhw(hwtree(hwvolspec(ValuationDate,testmat,x(2),testmat,x(1),'spline'), RateSpec, TimeSpec), 'call',SwaptionStrike(relidx(B)),EurExDatesFull(relidx(B)), 0,EurExDatesFull(relidx(B)), EurMatFull(relidx(B)),'Basis',2, 'SwapReset',12);
options = optimset('disp','iter','MaxFunEvals',1000,'TolFun',1e-5);
x0 = [.1 .01];
lb = [0 0];
ub = [1 1];
HW1Fparams = lsqnonlin(HW1Fobjfun4,x0,lb,ub,options)
In the results, when I just use instruments numbered 214:224, I am able to find a local minima: HW1Fparams(1) = 0.0801 , HW1Fparams(2) = 0.0002
however when I use instruments say 150:224 I get the following error:
"subscript indices must be real positive integers or logicals" error in cummswapcfbytrintree (line 23)
This is a Matlab created file. Does anyone know what's going wrong here? How do I go about diagnosing/debugging in the error is in some Matlab created file. The usual techniques of checking which variable or which index is being given a zero or double value are not at my disposal anymore. Thanks.
