I would like to generate a set of forward yield curve matrix of size 1000 x 100. First I defined my SparseArray of 1000 x100:
(forwardYieldCurve=Normal[SparseArray[{{1,1}->0,{1000,100}-> 0}]])//MatrixForm;
then initial first row of forwardYieldCurve using:
Table[forwardYieldCurve[[1,j]]=tenor0[[1,j]]+driftM[[1,j]]tstep+
(volFit1[[1,j]]dX[[1,1]]+volFit2[[1,j]]dX[[1,2]]+volFit3[[1,j]]dX[[1,3]])Sqrt[tstep]
+((tenor0[[1,j+1]]-tenor0[[1,j]])/(dateArray[[1,j+1]]-dateArray[[1,j]]))tstep,{j,99}];//AbsoluteTiming
then for the second row and iterate with i (in BOLD) up to 100 rows of the forwardYieldCurve matrix:
Table[forwardYieldCurve[[i+1,j]]=forwardYieldCurve[[i,j]]+driftM[[1,j]]tstep+
(volFit1[[1,j]]dX[[i+1,1]]+volFit2[[1,j]]dX[[i+1,2]]+volFit3[[1,j]]dX[[i+1,3]])Sqrt[tstep]+
((forwardYieldCurve[[i+1,j+1]]-forwardYieldCurve[[i+1,j]])/(dateArray[[1,j+1]]-dateArray[[1,j]]))tstep,{j,99},{i,**100**}];//AbsoluteTiming
takes around 4 minutes to do to obtain results of 100 x 100, which will be projected take it to around 40 minutes to run when I eventually set i to iterate up to 1000 x 100, and furthermore, I will run this many times to get a statistically monte carlo simulation of distributions. How to optimize this to reduce run time.
My input data dimensions:
forwardYieldCurve -> {1000,100}
tenor0={{0.0050399,0.00537318,0.00578648,0.00614997,0.00633987,0.00637105,0.00632311,0.00625459,0.00622594,0.00631663,0.0065289,0.00679745,0.00706621,0.00731132,0.0075159,0.00766905,0.00778107,0.00786696,0.00793966,0.00800508,0.00806759,0.00813158,0.00820143,0.00828151,0.00837543,0.00848368,0.00860596,0.00874199,0.00889147,0.00905412,0.00922964,0.00941775,0.00961814,0.00983054,0.0100546,0.0102902,0.0105368,0.0107941,0.0110615,0.0113385,0.0116248,0.0119197,0.0122228,0.0125336,0.0128516,0.0131763,0.0135073,0.013844,0.0141859,0.0145327,0.0148838,0.0152389,0.0155975,0.0159592,0.0163236,0.0166903,0.0170588,0.0174287,0.0177995,0.0181709,0.0203931,0.0225666,0.0246436,0.0265946,0.0283977,0.0300428,0.0315247,0.0328461,0.0340124,0.035033,0.0359187,0.0366814,0.0373332,0.0378862,0.0383519,0.0387395,0.0390575,0.0393143,0.0395184,0.0396782,0.0398011,0.0398898,0.0399458,0.0399704,0.0399652,0.0399316,0.039871,0.0397848,0.0396746,0.0395418,0.0393879,0.0392142,0.0390222,0.0388134,0.0385892,0.0383511,0.0381006,0.037839,0.0375678,0.0372885}}
driftM = {{4.29874*10^-6,8.59748*10^-6,0.0000128962,0.000017195,0.0000214937,0.0000257924,0.0000300912,0.0000343899,0.0000386887,0.0000429874,0.0000472861,0.0000515849,0.0000558836,0.0000601824,0.0000644811,0.0000687798,0.0000730786,0.0000773773,0.000081676,0.0000859748,0.0000902735,0.0000945723,0.000098871,0.00010317,0.000107468,0.000111767,0.000116066,0.000120365,0.000124663,0.000128962,0.000133261,0.00013756,0.000141858,0.000146157,0.000150456,0.000154755,0.000159053,0.000163352,0.000167651,0.00017195,0.000176248,0.000180547,0.000184846,0.000189144,0.000193443,0.000197742,0.000202041,0.000206339,0.000210638,0.000214937,0.000219236,0.000223534,0.000227833,0.000232132,0.000236431,0.000240729,0.000245028,0.000249327,0.000253626,0.000257924,0.000283717,0.000309509,0.000335302,0.000361094,0.000386886,0.000412679,0.000438471,0.000464264,0.000490056,0.000515849,0.000541641,0.000567433,0.000593226,0.000619018,0.000644811,0.000670603,0.000696396,0.000722188,0.000747981,0.000773773,0.000799565,0.000825358,0.00085115,0.000876943,0.000902735,0.000928528,0.00095432,0.000980113,0.0010059,0.0010317,0.00105749,0.00108328,0.00110907,0.00113487,0.00116066,0.00118645,0.00121224,0.00123804,0.00126383,0.00128962}}
tstep = 0.01
volFit1={{0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226,0.00718226}}
volFit2={{-5.97435*10^-6,-5.77847*10^-6,-5.58514*10^-6,-5.39435*10^-6,-5.20606*10^-6,-5.02029*10^-6,-4.83699*10^-6,-4.65618*10^-6,-4.47782*10^-6,-4.3019*10^-6,-4.12841*10^-6,-3.95734*10^-6,-3.78867*10^-6,-3.62238*10^-6,-3.45846*10^-6,-3.2969*10^-6,-3.13768*10^-6,-2.98078*10^-6,-2.8262*10^-6,-2.67392*10^-6,-2.52391*10^-6,-2.37618*10^-6,-2.23069*10^-6,-2.08745*10^-6,-1.94643*10^-6,-1.80762*10^-6,-1.671*10^-6,-1.53656*10^-6,-1.40429*10^-6,-1.27417*10^-6,-1.14618*10^-6,-1.02032*10^-6,-8.9656*10^-7,-7.74893*10^-7,-6.55303*10^-7,-5.37775*10^-7,-4.22296*10^-7,-3.08849*10^-7,-1.97421*10^-7,-8.79963*10^-8,1.94392*10^-8,1.249*10^-7,2.28402*10^-7,3.29958*10^-7,4.29584*10^-7,5.27294*10^-7,6.23103*10^-7,7.17026*10^-7,8.09077*10^-7,8.9927*10^-7,9.87622*10^-7,1.07415*10^-6,1.15886*10^-6,1.24177*10^-6,1.3229*10^-6,1.40226*10^-6,1.47986*10^-6,1.55573*10^-6,1.62987*10^-6,1.7023*10^-6,2.10178*10^-6,2.44338*10^-6,2.73027*10^-6,2.96562*10^-6,3.1526*10^-6,3.29436*10^-6,3.39409*10^-6,3.45494*10^-6,3.4801*10^-6,3.47271*10^-6,3.43596*10^-6,3.37301*10^-6,3.28703*10^-6,3.18118*10^-6,3.05863*10^-6,2.92256*10^-6,2.77613*10^-6,2.6225*10^-6,2.46485*10^-6,2.30635*10^-6,2.15015*10^-6,1.99943*10^-6,1.85736*10^-6,1.72711*10^-6,1.61183*10^-6,1.51471*10^-6,1.43891*10^-6,1.38759*10^-6,1.36392*10^-6,1.37108*10^-6,1.41223*10^-6,1.49054*10^-6,1.60917*10^-6,1.77129*10^-6,1.98008*10^-6,2.2387*10^-6,2.55031*10^-6,2.91809*10^-6,3.3452*10^-6,3.83481*10^-6}}
volFit3={{1.85601*10^-6,1.86013*10^-6,1.8634*10^-6,1.86583*10^-6,1.86742*10^-6,1.8682*10^-6,1.86815*10^-6,1.86729*10^-6,1.86563*10^-6,1.86316*10^-6,1.85991*10^-6,1.85587*10^-6,1.85105*10^-6,1.84546*10^-6,1.8391*10^-6,1.83199*10^-6,1.82412*10^-6,1.81551*10^-6,1.80616*10^-6,1.79608*10^-6,1.78528*10^-6,1.77375*10^-6,1.76152*10^-6,1.74858*10^-6,1.73494*10^-6,1.72062*10^-6,1.70561*10^-6,1.68992*10^-6,1.67356*10^-6,1.65653*10^-6,1.63885*10^-6,1.62052*10^-6,1.60154*10^-6,1.58193*10^-6,1.56169*10^-6,1.54082*10^-6,1.51934*10^-6,1.49724*10^-6,1.47454*10^-6,1.45125*10^-6,1.42737*10^-6,1.4029*10^-6,1.37786*10^-6,1.35224*10^-6,1.32607*10^-6,1.29933*10^-6,1.27205*10^-6,1.24422*10^-6,1.21586*10^-6,1.18697*10^-6,1.15756*10^-6,1.12763*10^-6,1.09719*10^-6,1.06625*10^-6,1.03481*10^-6,1.00289*10^-6,9.70481*10^-7,9.37598*10^-7,9.04246*10^-7,8.70433*10^-7,6.58225*10^-7,4.31082*10^-7,1.90459*10^-7,-6.21896*10^-8,-3.25408*10^-7,-5.97743*10^-7,-8.77739*10^-7,-1.16394*10^-6,-1.45489*10^-6,-1.74914*10^-6,-2.04524*10^-6,-2.34172*10^-6,-2.63713*10^-6,-2.93002*10^-6,-3.21893*10^-6,-3.50241*10^-6,-3.77901*10^-6,-4.04726*10^-6,-4.30572*10^-6,-4.55292*10^-6,-4.78742*10^-6,-5.00776*10^-6,-5.21248*10^-6,-5.40014*10^-6,-5.56927*10^-6,-5.71842*10^-6,-5.84613*10^-6,-5.95096*10^-6,-6.03144*10^-6,-6.08613*10^-6,-6.11356*10^-6,-6.11228*10^-6,-6.08084*10^-6,-6.01778*10^-6,-5.92165*10^-6,-5.791*10^-6,-5.62436*10^-6,-5.42028*10^-6,-5.17731*10^-6,-4.894*10^-6}}
randomWalkPCA[n_]:= RandomVariate[NormalDistribution[0,1],n];
RandVarPCA[mcRun_]:=Table[randomWalkPCA[3],{mcRun}];
(dX:=RandVarPCA[1000])//MatrixForm;
dateArray={{0.0833333,0.166667,0.25,0.333333,0.416667,0.5,0.583333,0.666667,0.75,0.833333,0.916667,1.,1.08333,1.16667,1.25,1.33333,1.41667,1.5,1.58333,1.66667,1.75,1.83333,1.91667,2.,2.08333,2.16667,2.25,2.33333,2.41667,2.5,2.58333,2.66667,2.75,2.83333,2.91667,3.,3.08333,3.16667,3.25,3.33333,3.41667,3.5,3.58333,3.66667,3.75,3.83333,3.91667,4.,4.08333,4.16667,4.25,4.33333,4.41667,4.5,4.58333,4.66667,4.75,4.83333,4.91667,5.,5.5,6.,6.5,7.,7.5,8.,8.5,9.,9.5,10.,10.5,11.,11.5,12.,12.5,13.,13.5,14.,14.5,15.,15.5,16.,16.5,17.,17.5,18.,18.5,19.,19.5,20.,20.5,21.,21.5,22.,22.5,23.,23.5,24.,24.5,25.}}