Probability of Default Calibration

Description

Implementation of most popular approaches to PD (probability of default) calibration: Quasi Moment Matching approach, M.van der Burgt algorithm, K.Pluto and D.Tasche's most prudent estimate methodology.

Details

The package implements three most popular among practitioners approaches to PD calibration:

1. Quasi Moment Matching approach proposed by D.Tasche (see QMMRecalibrate).

2. M. van der Burgt algorithm based on CAP curve smoothing (see VDBCalibratePD).

3. K.Pluto and D.Tasche "most prudent" estimate methodology (see PTOnePeriodPD,PTMultiPeriodPD).

Author(s)

Denis Surzhko <densur@gmail.com>

References

Pluto, K. and Tasche, D. (2005) Thinking Positively. Risk, August, 72-78.
Van der Burgt, M. (2008) Calibrating low-default portfolios, using the cumulative accuracy profile. Journal of Risk Model Validation, 1(4):17-33.
Tasche, D. (2009) Estimating discriminatory power and PD curves when the number of defaults is small. Working paper, Lloyds Banking Group.
Tasche, D. (2013) The art of probability-of-default curve calibration. Journal of Credit Risk, 9:63-103.

See Also

QMMRecalibrate VDBCalibratePD PTOnePeriodPD PTMultiPeriodPD somers2

Examples

# PD calibration using Multi-period Pluto and Tasche approach
portfolio <- c(10,20,30,40,10)
defaults <- c(1,2,0,0,0)
PTMultiPeriodPD(portfolio, defaults, 0.3, cor.St = 0.3, kT = 5, kNS = 1000, conf.interval = 0.5)

# PD Calibration using M. van der Burgt algorithm, 
# portfolio distribution is given by rating classes.
portf.rating <- c(20,50,60,70,10,5)
VDBCalibratePD(portf.rating, 0.1, 0.15, 0.5, rating.type = 'RATING')
# PD Calibration using M. van der Burgt algorithm, 
# portfolio distribution is given by scores.
portf.scores <- seq_len(1000)
VDBCalibratePD(portf.scores, 0.1, 0.15, 0.5, rating.type = 'SCORE')

# PD calibration using QMM algorithm, 
# portfolio distribution is given by rating classes.
pd <- c(0.2, 0.1, 0.005, 0.001, 0.001)
porfolio <- c(100, 200, 200, 200, 100)
qmm <- QMMRecalibrate(0.05, pd, porfolio, rating.type = 'RATING')
# Plot results of PD calibration.
QMMPlot(qmm)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(LDPD)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/LDPD/LDPD-package.Rd_%03d_medium.png", width=480, height=480)
> ### Name: LDPD-package
> ### Title: Probability of Default Calibration
> ### Aliases: LDPD-package LDPD
> ### Keywords: credit risk probability of default PD calibration low default
> ###   porfolios PD calibration
> 
> ### ** Examples
> 
> # PD calibration using Multi-period Pluto and Tasche approach
> portfolio <- c(10,20,30,40,10)
> defaults <- c(1,2,0,0,0)
> PTMultiPeriodPD(portfolio, defaults, 0.3, cor.St = 0.3, kT = 5, kNS = 1000, conf.interval = 0.5)
[1] 0.04188033 0.03218299 0.01733311 0.01109746 0.01018159
> 
> # PD Calibration using M. van der Burgt algorithm, 
> # portfolio distribution is given by rating classes.
> portf.rating <- c(20,50,60,70,10,5)
> VDBCalibratePD(portf.rating, 0.1, 0.15, 0.5, rating.type = 'RATING')
$lambda
[1] 3.107439

$condPD
[1] 0.42227136 0.25462348 0.11499166 0.04494328 0.02521081 0.02262089

$portf.cumdist
[1] 0.04651163 0.20930233 0.46511628 0.76744186 0.95348837 0.98837209

$portf.uncond
[1] 0.1469179

$rating.type
[1] "RATING"

> # PD Calibration using M. van der Burgt algorithm, 
> # portfolio distribution is given by scores.
> portf.scores <- seq_len(1000)
> VDBCalibratePD(portf.scores, 0.1, 0.15, 0.5, rating.type = 'SCORE')
$lambda
[1] 3.107439

$condPD
   [1] 0.48642015 0.48491098 0.48340649 0.48190666 0.48041149 0.47892096
   [7] 0.47743505 0.47595375 0.47447705 0.47300493 0.47153738 0.47007438
  [13] 0.46861592 0.46716198 0.46571256 0.46426763 0.46282719 0.46139121
  [19] 0.45995969 0.45853261 0.45710996 0.45569173 0.45427789 0.45286844
  [25] 0.45146336 0.45006264 0.44866627 0.44727423 0.44588651 0.44450310
  [31] 0.44312398 0.44174913 0.44037855 0.43901223 0.43765014 0.43629228
  [37] 0.43493863 0.43358919 0.43224392 0.43090284 0.42956591 0.42823313
  [43] 0.42690449 0.42557997 0.42425956 0.42294324 0.42163101 0.42032285
  [49] 0.41901875 0.41771870 0.41642268 0.41513068 0.41384269 0.41255869
  [55] 0.41127868 0.41000264 0.40873056 0.40746243 0.40619823 0.40493795
  [61] 0.40368158 0.40242911 0.40118053 0.39993582 0.39869497 0.39745798
  [67] 0.39622482 0.39499548 0.39376996 0.39254825 0.39133032 0.39011617
  [73] 0.38890579 0.38769917 0.38649628 0.38529713 0.38410170 0.38290998
  [79] 0.38172196 0.38053763 0.37935696 0.37817996 0.37700662 0.37583691
  [85] 0.37467083 0.37350837 0.37234952 0.37119426 0.37004259 0.36889449
  [91] 0.36774995 0.36660896 0.36547152 0.36433760 0.36320720 0.36208031
  [97] 0.36095691 0.35983700 0.35872056 0.35760759 0.35649807 0.35539199
 [103] 0.35428935 0.35319013 0.35209431 0.35100190 0.34991287 0.34882723
 [109] 0.34774495 0.34666603 0.34559046 0.34451823 0.34344932 0.34238373
 [115] 0.34132144 0.34026245 0.33920675 0.33815432 0.33710516 0.33605925
 [121] 0.33501659 0.33397716 0.33294096 0.33190797 0.33087818 0.32985160
 [127] 0.32882819 0.32780797 0.32679090 0.32577700 0.32476624 0.32375861
 [133] 0.32275411 0.32175273 0.32075445 0.31975928 0.31876719 0.31777817
 [139] 0.31679223 0.31580934 0.31482951 0.31385271 0.31287895 0.31190821
 [145] 0.31094048 0.30997575 0.30901401 0.30805526 0.30709948 0.30614667
 [151] 0.30519681 0.30424991 0.30330593 0.30236489 0.30142677 0.30049156
 [157] 0.29955925 0.29862983 0.29770330 0.29677964 0.29585885 0.29494091
 [163] 0.29402582 0.29311357 0.29220415 0.29129755 0.29039377 0.28949279
 [169] 0.28859460 0.28769921 0.28680659 0.28591674 0.28502965 0.28414531
 [175] 0.28326371 0.28238486 0.28150872 0.28063531 0.27976461 0.27889660
 [181] 0.27803129 0.27716867 0.27630872 0.27545144 0.27459682 0.27374485
 [187] 0.27289553 0.27204884 0.27120478 0.27036333 0.26952450 0.26868827
 [193] 0.26785463 0.26702358 0.26619511 0.26536921 0.26454587 0.26372508
 [199] 0.26290685 0.26209115 0.26127798 0.26046733 0.25965920 0.25885358
 [205] 0.25805046 0.25724982 0.25645168 0.25565601 0.25486280 0.25407206
 [211] 0.25328377 0.25249793 0.25171453 0.25093355 0.25015500 0.24937887
 [217] 0.24860514 0.24783382 0.24706488 0.24629833 0.24553417 0.24477237
 [223] 0.24401293 0.24325585 0.24250112 0.24174874 0.24099868 0.24025096
 [229] 0.23950555 0.23876246 0.23802167 0.23728318 0.23654698 0.23581306
 [235] 0.23508143 0.23435206 0.23362496 0.23290011 0.23217751 0.23145715
 [241] 0.23073903 0.23002313 0.22930946 0.22859800 0.22788875 0.22718170
 [247] 0.22647684 0.22577417 0.22507368 0.22437536 0.22367921 0.22298522
 [253] 0.22229338 0.22160369 0.22091614 0.22023072 0.21954743 0.21886626
 [259] 0.21818720 0.21751025 0.21683540 0.21616264 0.21549197 0.21482338
 [265] 0.21415687 0.21349242 0.21283004 0.21216971 0.21151142 0.21085519
 [271] 0.21020098 0.20954881 0.20889866 0.20825053 0.20760441 0.20696029
 [277] 0.20631817 0.20567805 0.20503991 0.20440375 0.20376956 0.20313734
 [283] 0.20250708 0.20187878 0.20125243 0.20062802 0.20000555 0.19938501
 [289] 0.19876639 0.19814970 0.19753491 0.19692204 0.19631107 0.19570199
 [295] 0.19509480 0.19448949 0.19388607 0.19328451 0.19268483 0.19208700
 [301] 0.19149103 0.19089690 0.19030462 0.18971418 0.18912557 0.18853879
 [307] 0.18795382 0.18737068 0.18678934 0.18620980 0.18563206 0.18505612
 [313] 0.18448196 0.18390958 0.18333898 0.18277015 0.18220309 0.18163778
 [319] 0.18107423 0.18051242 0.17995236 0.17939404 0.17883745 0.17828258
 [325] 0.17772944 0.17717802 0.17662830 0.17608029 0.17553398 0.17498937
 [331] 0.17444644 0.17390520 0.17336564 0.17282775 0.17229154 0.17175698
 [337] 0.17122408 0.17069284 0.17016325 0.16963530 0.16910898 0.16858430
 [343] 0.16806125 0.16753982 0.16702001 0.16650181 0.16598522 0.16547023
 [349] 0.16495684 0.16444504 0.16393483 0.16342621 0.16291916 0.16241368
 [355] 0.16190977 0.16140743 0.16090664 0.16040741 0.15990973 0.15941359
 [361] 0.15891899 0.15842593 0.15793439 0.15744438 0.15695589 0.15646892
 [367] 0.15598346 0.15549950 0.15501704 0.15453609 0.15405662 0.15357864
 [373] 0.15310215 0.15262713 0.15215359 0.15168151 0.15121090 0.15074175
 [379] 0.15027406 0.14980782 0.14934302 0.14887967 0.14841775 0.14795727
 [385] 0.14749821 0.14704058 0.14658437 0.14612957 0.14567619 0.14522421
 [391] 0.14477364 0.14432446 0.14387668 0.14343028 0.14298527 0.14254165
 [397] 0.14209939 0.14165851 0.14121900 0.14078085 0.14034407 0.13990863
 [403] 0.13947455 0.13904181 0.13861042 0.13818036 0.13775164 0.13732425
 [409] 0.13689819 0.13647345 0.13605002 0.13562791 0.13520711 0.13478761
 [415] 0.13436942 0.13395252 0.13353692 0.13312261 0.13270958 0.13229783
 [421] 0.13188736 0.13147816 0.13107024 0.13066358 0.13025818 0.12985404
 [427] 0.12945115 0.12904951 0.12864912 0.12824997 0.12785206 0.12745539
 [433] 0.12705994 0.12666572 0.12627273 0.12588095 0.12549039 0.12510104
 [439] 0.12471290 0.12432597 0.12394023 0.12355569 0.12317235 0.12279019
 [445] 0.12240922 0.12202943 0.12165082 0.12127338 0.12089712 0.12052202
 [451] 0.12014809 0.11977531 0.11940370 0.11903323 0.11866392 0.11829575
 [457] 0.11792872 0.11756284 0.11719808 0.11683446 0.11647197 0.11611060
 [463] 0.11575036 0.11539123 0.11503321 0.11467631 0.11432051 0.11396582
 [469] 0.11361223 0.11325973 0.11290833 0.11255802 0.11220880 0.11186065
 [475] 0.11151359 0.11116761 0.11082270 0.11047886 0.11013609 0.10979438
 [481] 0.10945373 0.10911413 0.10877559 0.10843810 0.10810166 0.10776626
 [487] 0.10743191 0.10709859 0.10676630 0.10643505 0.10610482 0.10577562
 [493] 0.10544744 0.10512027 0.10479413 0.10446899 0.10414486 0.10382174
 [499] 0.10349962 0.10317850 0.10285838 0.10253925 0.10222111 0.10190396
 [505] 0.10158779 0.10127260 0.10095839 0.10064515 0.10033289 0.10002160
 [511] 0.09971127 0.09940190 0.09909350 0.09878605 0.09847955 0.09817401
 [517] 0.09786941 0.09756576 0.09726305 0.09696128 0.09666045 0.09636055
 [523] 0.09606158 0.09576353 0.09546642 0.09517022 0.09487494 0.09458058
 [529] 0.09428714 0.09399460 0.09370297 0.09341225 0.09312242 0.09283350
 [535] 0.09254547 0.09225834 0.09197210 0.09168674 0.09140228 0.09111869
 [541] 0.09083598 0.09055415 0.09027320 0.08999312 0.08971390 0.08943555
 [547] 0.08915807 0.08888145 0.08860568 0.08833077 0.08805672 0.08778351
 [553] 0.08751115 0.08723964 0.08696897 0.08669914 0.08643014 0.08616198
 [559] 0.08589465 0.08562816 0.08536248 0.08509764 0.08483361 0.08457041
 [565] 0.08430802 0.08404644 0.08378568 0.08352572 0.08326657 0.08300823
 [571] 0.08275069 0.08249394 0.08223800 0.08198284 0.08172848 0.08147491
 [577] 0.08122212 0.08097012 0.08071890 0.08046846 0.08021880 0.07996991
 [583] 0.07972180 0.07947445 0.07922787 0.07898206 0.07873701 0.07849272
 [589] 0.07824918 0.07800641 0.07776438 0.07752311 0.07728259 0.07704281
 [595] 0.07680377 0.07656548 0.07632793 0.07609111 0.07585503 0.07561968
 [601] 0.07538506 0.07515117 0.07491801 0.07468556 0.07445384 0.07422284
 [607] 0.07399256 0.07376299 0.07353413 0.07330598 0.07307854 0.07285180
 [613] 0.07262577 0.07240044 0.07217581 0.07195188 0.07172864 0.07150609
 [619] 0.07128424 0.07106307 0.07084259 0.07062279 0.07040368 0.07018524
 [625] 0.06996748 0.06975040 0.06953399 0.06931825 0.06910319 0.06888879
 [631] 0.06867505 0.06846198 0.06824957 0.06803781 0.06782672 0.06761628
 [637] 0.06740649 0.06719735 0.06698887 0.06678103 0.06657383 0.06636728
 [643] 0.06616137 0.06595609 0.06575146 0.06554745 0.06534409 0.06514135
 [649] 0.06493924 0.06473776 0.06453690 0.06433667 0.06413706 0.06393806
 [655] 0.06373969 0.06354193 0.06334478 0.06314825 0.06295232 0.06275701
 [661] 0.06256229 0.06236819 0.06217468 0.06198178 0.06178947 0.06159776
 [667] 0.06140665 0.06121613 0.06102620 0.06083686 0.06064810 0.06045994
 [673] 0.06027235 0.06008535 0.05989893 0.05971309 0.05952782 0.05934313
 [679] 0.05915901 0.05897546 0.05879248 0.05861007 0.05842823 0.05824695
 [685] 0.05806623 0.05788607 0.05770647 0.05752743 0.05734895 0.05717101
 [691] 0.05699364 0.05681681 0.05664052 0.05646479 0.05628960 0.05611496
 [697] 0.05594085 0.05576729 0.05559427 0.05542178 0.05524983 0.05507841
 [703] 0.05490752 0.05473716 0.05456734 0.05439803 0.05422926 0.05406100
 [709] 0.05389327 0.05372606 0.05355937 0.05339320 0.05322754 0.05306240
 [715] 0.05289776 0.05273364 0.05257003 0.05240692 0.05224433 0.05208223
 [721] 0.05192064 0.05175955 0.05159896 0.05143887 0.05127927 0.05112017
 [727] 0.05096157 0.05080345 0.05064583 0.05048870 0.05033205 0.05017589
 [733] 0.05002021 0.04986502 0.04971031 0.04955607 0.04940232 0.04924904
 [739] 0.04909624 0.04894392 0.04879206 0.04864068 0.04848977 0.04833932
 [745] 0.04818934 0.04803983 0.04789078 0.04774219 0.04759407 0.04744640
 [751] 0.04729919 0.04715244 0.04700615 0.04686030 0.04671491 0.04656998
 [757] 0.04642549 0.04628145 0.04613785 0.04599470 0.04585200 0.04570974
 [763] 0.04556792 0.04542654 0.04528560 0.04514510 0.04500503 0.04486539
 [769] 0.04472619 0.04458743 0.04444909 0.04431118 0.04417370 0.04403664
 [775] 0.04390002 0.04376381 0.04362803 0.04349267 0.04335773 0.04322320
 [781] 0.04308910 0.04295541 0.04282214 0.04268928 0.04255683 0.04242479
 [787] 0.04229316 0.04216194 0.04203113 0.04190072 0.04177072 0.04164112
 [793] 0.04151193 0.04138313 0.04125474 0.04112674 0.04099914 0.04087193
 [799] 0.04074512 0.04061871 0.04049268 0.04036705 0.04024181 0.04011695
 [805] 0.03999248 0.03986840 0.03974471 0.03962139 0.03949846 0.03937591
 [811] 0.03925375 0.03913196 0.03901054 0.03888951 0.03876885 0.03864857
 [817] 0.03852865 0.03840911 0.03828995 0.03817115 0.03805272 0.03793465
 [823] 0.03781696 0.03769963 0.03758266 0.03746605 0.03734981 0.03723393
 [829] 0.03711841 0.03700324 0.03688843 0.03677398 0.03665989 0.03654615
 [835] 0.03643276 0.03631972 0.03620704 0.03609470 0.03598271 0.03587107
 [841] 0.03575978 0.03564883 0.03553822 0.03542796 0.03531804 0.03520846
 [847] 0.03509923 0.03499033 0.03488176 0.03477354 0.03466565 0.03455810
 [853] 0.03445088 0.03434399 0.03423743 0.03413121 0.03402531 0.03391974
 [859] 0.03381450 0.03370959 0.03360500 0.03350074 0.03339680 0.03329318
 [865] 0.03318988 0.03308691 0.03298425 0.03288192 0.03277990 0.03267819
 [871] 0.03257680 0.03247573 0.03237497 0.03227452 0.03217439 0.03207456
 [877] 0.03197505 0.03187584 0.03177694 0.03167835 0.03158007 0.03148209
 [883] 0.03138441 0.03128704 0.03118996 0.03109319 0.03099672 0.03090055
 [889] 0.03080468 0.03070910 0.03061383 0.03051884 0.03042415 0.03032976
 [895] 0.03023566 0.03014185 0.03004833 0.02995510 0.02986216 0.02976951
 [901] 0.02967715 0.02958507 0.02949328 0.02940177 0.02931055 0.02921961
 [907] 0.02912895 0.02903858 0.02894848 0.02885867 0.02876913 0.02867987
 [913] 0.02859089 0.02850218 0.02841375 0.02832559 0.02823771 0.02815010
 [919] 0.02806276 0.02797569 0.02788889 0.02780237 0.02771611 0.02763011
 [925] 0.02754439 0.02745893 0.02737373 0.02728880 0.02720414 0.02711973
 [931] 0.02703559 0.02695171 0.02686809 0.02678473 0.02670162 0.02661878
 [937] 0.02653619 0.02645386 0.02637178 0.02628996 0.02620839 0.02612708
 [943] 0.02604602 0.02596521 0.02588465 0.02580434 0.02572428 0.02564446
 [949] 0.02556490 0.02548558 0.02540651 0.02532768 0.02524910 0.02517076
 [955] 0.02509267 0.02501481 0.02493720 0.02485983 0.02478270 0.02470581
 [961] 0.02462916 0.02455274 0.02447656 0.02440062 0.02432492 0.02424945
 [967] 0.02417421 0.02409921 0.02402444 0.02394990 0.02387559 0.02380151
 [973] 0.02372767 0.02365405 0.02358066 0.02350750 0.02343456 0.02336185
 [979] 0.02328937 0.02321711 0.02314508 0.02307327 0.02300168 0.02293032
 [985] 0.02285917 0.02278825 0.02271755 0.02264706 0.02257680 0.02250675
 [991] 0.02243692 0.02236731 0.02229791 0.02222873 0.02215976 0.02209101
 [997] 0.02202247 0.02195414 0.02188602 0.02185205

$portf.cumdist
   [1] 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 0.0070 0.0080 0.0090 0.0100
  [11] 0.0110 0.0120 0.0130 0.0140 0.0150 0.0160 0.0170 0.0180 0.0190 0.0200
  [21] 0.0210 0.0220 0.0230 0.0240 0.0250 0.0260 0.0270 0.0280 0.0290 0.0300
  [31] 0.0310 0.0320 0.0330 0.0340 0.0350 0.0360 0.0370 0.0380 0.0390 0.0400
  [41] 0.0410 0.0420 0.0430 0.0440 0.0450 0.0460 0.0470 0.0480 0.0490 0.0500
  [51] 0.0510 0.0520 0.0530 0.0540 0.0550 0.0560 0.0570 0.0580 0.0590 0.0600
  [61] 0.0610 0.0620 0.0630 0.0640 0.0650 0.0660 0.0670 0.0680 0.0690 0.0700
  [71] 0.0710 0.0720 0.0730 0.0740 0.0750 0.0760 0.0770 0.0780 0.0790 0.0800
  [81] 0.0810 0.0820 0.0830 0.0840 0.0850 0.0860 0.0870 0.0880 0.0890 0.0900
  [91] 0.0910 0.0920 0.0930 0.0940 0.0950 0.0960 0.0970 0.0980 0.0990 0.1000
 [101] 0.1010 0.1020 0.1030 0.1040 0.1050 0.1060 0.1070 0.1080 0.1090 0.1100
 [111] 0.1110 0.1120 0.1130 0.1140 0.1150 0.1160 0.1170 0.1180 0.1190 0.1200
 [121] 0.1210 0.1220 0.1230 0.1240 0.1250 0.1260 0.1270 0.1280 0.1290 0.1300
 [131] 0.1310 0.1320 0.1330 0.1340 0.1350 0.1360 0.1370 0.1380 0.1390 0.1400
 [141] 0.1410 0.1420 0.1430 0.1440 0.1450 0.1460 0.1470 0.1480 0.1490 0.1500
 [151] 0.1510 0.1520 0.1530 0.1540 0.1550 0.1560 0.1570 0.1580 0.1590 0.1600
 [161] 0.1610 0.1620 0.1630 0.1640 0.1650 0.1660 0.1670 0.1680 0.1690 0.1700
 [171] 0.1710 0.1720 0.1730 0.1740 0.1750 0.1760 0.1770 0.1780 0.1790 0.1800
 [181] 0.1810 0.1820 0.1830 0.1840 0.1850 0.1860 0.1870 0.1880 0.1890 0.1900
 [191] 0.1910 0.1920 0.1930 0.1940 0.1950 0.1960 0.1970 0.1980 0.1990 0.2000
 [201] 0.2010 0.2020 0.2030 0.2040 0.2050 0.2060 0.2070 0.2080 0.2090 0.2100
 [211] 0.2110 0.2120 0.2130 0.2140 0.2150 0.2160 0.2170 0.2180 0.2190 0.2200
 [221] 0.2210 0.2220 0.2230 0.2240 0.2250 0.2260 0.2270 0.2280 0.2290 0.2300
 [231] 0.2310 0.2320 0.2330 0.2340 0.2350 0.2360 0.2370 0.2380 0.2390 0.2400
 [241] 0.2410 0.2420 0.2430 0.2440 0.2450 0.2460 0.2470 0.2480 0.2490 0.2500
 [251] 0.2510 0.2520 0.2530 0.2540 0.2550 0.2560 0.2570 0.2580 0.2590 0.2600
 [261] 0.2610 0.2620 0.2630 0.2640 0.2650 0.2660 0.2670 0.2680 0.2690 0.2700
 [271] 0.2710 0.2720 0.2730 0.2740 0.2750 0.2760 0.2770 0.2780 0.2790 0.2800
 [281] 0.2810 0.2820 0.2830 0.2840 0.2850 0.2860 0.2870 0.2880 0.2890 0.2900
 [291] 0.2910 0.2920 0.2930 0.2940 0.2950 0.2960 0.2970 0.2980 0.2990 0.3000
 [301] 0.3010 0.3020 0.3030 0.3040 0.3050 0.3060 0.3070 0.3080 0.3090 0.3100
 [311] 0.3110 0.3120 0.3130 0.3140 0.3150 0.3160 0.3170 0.3180 0.3190 0.3200
 [321] 0.3210 0.3220 0.3230 0.3240 0.3250 0.3260 0.3270 0.3280 0.3290 0.3300
 [331] 0.3310 0.3320 0.3330 0.3340 0.3350 0.3360 0.3370 0.3380 0.3390 0.3400
 [341] 0.3410 0.3420 0.3430 0.3440 0.3450 0.3460 0.3470 0.3480 0.3490 0.3500
 [351] 0.3510 0.3520 0.3530 0.3540 0.3550 0.3560 0.3570 0.3580 0.3590 0.3600
 [361] 0.3610 0.3620 0.3630 0.3640 0.3650 0.3660 0.3670 0.3680 0.3690 0.3700
 [371] 0.3710 0.3720 0.3730 0.3740 0.3750 0.3760 0.3770 0.3780 0.3790 0.3800
 [381] 0.3810 0.3820 0.3830 0.3840 0.3850 0.3860 0.3870 0.3880 0.3890 0.3900
 [391] 0.3910 0.3920 0.3930 0.3940 0.3950 0.3960 0.3970 0.3980 0.3990 0.4000
 [401] 0.4010 0.4020 0.4030 0.4040 0.4050 0.4060 0.4070 0.4080 0.4090 0.4100
 [411] 0.4110 0.4120 0.4130 0.4140 0.4150 0.4160 0.4170 0.4180 0.4190 0.4200
 [421] 0.4210 0.4220 0.4230 0.4240 0.4250 0.4260 0.4270 0.4280 0.4290 0.4300
 [431] 0.4310 0.4320 0.4330 0.4340 0.4350 0.4360 0.4370 0.4380 0.4390 0.4400
 [441] 0.4410 0.4420 0.4430 0.4440 0.4450 0.4460 0.4470 0.4480 0.4490 0.4500
 [451] 0.4510 0.4520 0.4530 0.4540 0.4550 0.4560 0.4570 0.4580 0.4590 0.4600
 [461] 0.4610 0.4620 0.4630 0.4640 0.4650 0.4660 0.4670 0.4680 0.4690 0.4700
 [471] 0.4710 0.4720 0.4730 0.4740 0.4750 0.4760 0.4770 0.4780 0.4790 0.4800
 [481] 0.4810 0.4820 0.4830 0.4840 0.4850 0.4860 0.4870 0.4880 0.4890 0.4900
 [491] 0.4910 0.4920 0.4930 0.4940 0.4950 0.4960 0.4970 0.4980 0.4990 0.5000
 [501] 0.5010 0.5020 0.5030 0.5040 0.5050 0.5060 0.5070 0.5080 0.5090 0.5100
 [511] 0.5110 0.5120 0.5130 0.5140 0.5150 0.5160 0.5170 0.5180 0.5190 0.5200
 [521] 0.5210 0.5220 0.5230 0.5240 0.5250 0.5260 0.5270 0.5280 0.5290 0.5300
 [531] 0.5310 0.5320 0.5330 0.5340 0.5350 0.5360 0.5370 0.5380 0.5390 0.5400
 [541] 0.5410 0.5420 0.5430 0.5440 0.5450 0.5460 0.5470 0.5480 0.5490 0.5500
 [551] 0.5510 0.5520 0.5530 0.5540 0.5550 0.5560 0.5570 0.5580 0.5590 0.5600
 [561] 0.5610 0.5620 0.5630 0.5640 0.5650 0.5660 0.5670 0.5680 0.5690 0.5700
 [571] 0.5710 0.5720 0.5730 0.5740 0.5750 0.5760 0.5770 0.5780 0.5790 0.5800
 [581] 0.5810 0.5820 0.5830 0.5840 0.5850 0.5860 0.5870 0.5880 0.5890 0.5900
 [591] 0.5910 0.5920 0.5930 0.5940 0.5950 0.5960 0.5970 0.5980 0.5990 0.6000
 [601] 0.6010 0.6020 0.6030 0.6040 0.6050 0.6060 0.6070 0.6080 0.6090 0.6100
 [611] 0.6110 0.6120 0.6130 0.6140 0.6150 0.6160 0.6170 0.6180 0.6190 0.6200
 [621] 0.6210 0.6220 0.6230 0.6240 0.6250 0.6260 0.6270 0.6280 0.6290 0.6300
 [631] 0.6310 0.6320 0.6330 0.6340 0.6350 0.6360 0.6370 0.6380 0.6390 0.6400
 [641] 0.6410 0.6420 0.6430 0.6440 0.6450 0.6460 0.6470 0.6480 0.6490 0.6500
 [651] 0.6510 0.6520 0.6530 0.6540 0.6550 0.6560 0.6570 0.6580 0.6590 0.6600
 [661] 0.6610 0.6620 0.6630 0.6640 0.6650 0.6660 0.6670 0.6680 0.6690 0.6700
 [671] 0.6710 0.6720 0.6730 0.6740 0.6750 0.6760 0.6770 0.6780 0.6790 0.6800
 [681] 0.6810 0.6820 0.6830 0.6840 0.6850 0.6860 0.6870 0.6880 0.6890 0.6900
 [691] 0.6910 0.6920 0.6930 0.6940 0.6950 0.6960 0.6970 0.6980 0.6990 0.7000
 [701] 0.7010 0.7020 0.7030 0.7040 0.7050 0.7060 0.7070 0.7080 0.7090 0.7100
 [711] 0.7110 0.7120 0.7130 0.7140 0.7150 0.7160 0.7170 0.7180 0.7190 0.7200
 [721] 0.7210 0.7220 0.7230 0.7240 0.7250 0.7260 0.7270 0.7280 0.7290 0.7300
 [731] 0.7310 0.7320 0.7330 0.7340 0.7350 0.7360 0.7370 0.7380 0.7390 0.7400
 [741] 0.7410 0.7420 0.7430 0.7440 0.7450 0.7460 0.7470 0.7480 0.7490 0.7500
 [751] 0.7510 0.7520 0.7530 0.7540 0.7550 0.7560 0.7570 0.7580 0.7590 0.7600
 [761] 0.7610 0.7620 0.7630 0.7640 0.7650 0.7660 0.7670 0.7680 0.7690 0.7700
 [771] 0.7710 0.7720 0.7730 0.7740 0.7750 0.7760 0.7770 0.7780 0.7790 0.7800
 [781] 0.7810 0.7820 0.7830 0.7840 0.7850 0.7860 0.7870 0.7880 0.7890 0.7900
 [791] 0.7910 0.7920 0.7930 0.7940 0.7950 0.7960 0.7970 0.7980 0.7990 0.8000
 [801] 0.8010 0.8020 0.8030 0.8040 0.8050 0.8060 0.8070 0.8080 0.8090 0.8100
 [811] 0.8110 0.8120 0.8130 0.8140 0.8150 0.8160 0.8170 0.8180 0.8190 0.8200
 [821] 0.8210 0.8220 0.8230 0.8240 0.8250 0.8260 0.8270 0.8280 0.8290 0.8300
 [831] 0.8310 0.8320 0.8330 0.8340 0.8350 0.8360 0.8370 0.8380 0.8390 0.8400
 [841] 0.8410 0.8420 0.8430 0.8440 0.8450 0.8460 0.8470 0.8480 0.8490 0.8500
 [851] 0.8510 0.8520 0.8530 0.8540 0.8550 0.8560 0.8570 0.8580 0.8590 0.8600
 [861] 0.8610 0.8620 0.8630 0.8640 0.8650 0.8660 0.8670 0.8680 0.8690 0.8700
 [871] 0.8710 0.8720 0.8730 0.8740 0.8750 0.8760 0.8770 0.8780 0.8790 0.8800
 [881] 0.8810 0.8820 0.8830 0.8840 0.8850 0.8860 0.8870 0.8880 0.8890 0.8900
 [891] 0.8910 0.8920 0.8930 0.8940 0.8950 0.8960 0.8970 0.8980 0.8990 0.9000
 [901] 0.9010 0.9020 0.9030 0.9040 0.9050 0.9060 0.9070 0.9080 0.9090 0.9100
 [911] 0.9110 0.9120 0.9130 0.9140 0.9150 0.9160 0.9170 0.9180 0.9190 0.9200
 [921] 0.9210 0.9220 0.9230 0.9240 0.9250 0.9260 0.9270 0.9280 0.9290 0.9300
 [931] 0.9310 0.9320 0.9330 0.9340 0.9350 0.9360 0.9370 0.9380 0.9390 0.9400
 [941] 0.9410 0.9420 0.9430 0.9440 0.9450 0.9460 0.9470 0.9480 0.9490 0.9500
 [951] 0.9510 0.9520 0.9530 0.9540 0.9550 0.9560 0.9570 0.9580 0.9590 0.9600
 [961] 0.9610 0.9620 0.9630 0.9640 0.9650 0.9660 0.9670 0.9680 0.9690 0.9700
 [971] 0.9710 0.9720 0.9730 0.9740 0.9750 0.9760 0.9770 0.9780 0.9790 0.9800
 [981] 0.9810 0.9820 0.9830 0.9840 0.9850 0.9860 0.9870 0.9880 0.9890 0.9900
 [991] 0.9910 0.9920 0.9930 0.9940 0.9950 0.9960 0.9970 0.9980 0.9990 0.9995

$portf.uncond
[1] 0.1497671

$rating.type
[1] "SCORE"

> 
> # PD calibration using QMM algorithm, 
> # portfolio distribution is given by rating classes.
> pd <- c(0.2, 0.1, 0.005, 0.001, 0.001)
> porfolio <- c(100, 200, 200, 200, 100)
> qmm <- QMMRecalibrate(0.05, pd, porfolio, rating.type = 'RATING')
> # Plot results of PD calibration.
> QMMPlot(qmm)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>