Computing Arbitrage-Free Yields in Multi-Factor Gaussian Shadow-Rate Term Structure Models

Marcel A. Priebsch

Figure 1 Data

maturity	TOP-LEFT:PDE	TOP-LEFT:Krippner	TOP-LEFT:First-order	TOP-LEFT:Second-order	TOP-RIGHT:PDE	TOP-RIGHT:Krippner	TOP-RIGHT:First-order	TOP-RIGHT:Second-order	BOTTOM-LEFT:PDE	BOTTOM-LEFT:Krippner	BOTTOM-LEFT:First-order	BOTTOM-LEFT:Second-order	BOTTOM-RIGHT:PDE	BOTTOM-RIGHT:Krippner	BOTTOM-RIGHT:First-order	BOTTOM-RIGHT:Second-order
0.1	6.25E-11	4.65E-20	4.66E-20	5.35E-20	6.24E-05	4.27E-05	4.28E-05	4.28E-05	0.00169211556950609	0.00170176525257394	0.0017019638280498	0.00170175048070477	0.0100567072411376	0.0100392315696318	0.0100398705395442	0.0100392392763998
0.2	1.29E-09	1.42E-12	1.37E-12	1.37E-12	0.000222860265721148	0.000213159970887328	0.000213425284470133	0.000213368812932253	0.00240929758992803	0.00241333304374696	0.00241459954762842	0.00241374750885935	0.0102021138546071	0.0101942807396823	0.0101966592095832	0.0101943751417028
0.3	1.30E-08	6.37E-10	6.42E-10	6.42E-10	0.000438750747087585	0.000435872501672401	0.000436750144385484	0.00043651766870769	0.00296142017575862	0.0029593908549065	0.00296233343765716	0.00296042207389466	0.0103953481563591	0.0103937724299153	0.0103988229886888	0.0103940959124127
0.4	6.99E-08	1.60E-08	1.61E-08	1.61E-08	0.000676557965897074	0.000674373972707236	0.000676297358373968	0.0006757166951457	0.0034235807140937	0.00341867283511492	0.00342392414675442	0.00342053880566312	0.0106052602710059	0.0106042811759033	0.0106128532950857	0.0106049994969167
0.5	2.54E-07	1.21E-07	1.23E-07	1.22E-07	0.000919183456756331	0.000915442142546587	0.000918875558369081	0.000917742251407421	0.00382763936068114	0.00382178824049094	0.00382997598754021	0.003824708537937	0.0108164625239595	0.0108141652157131	0.0108270553777678	0.0108154537042832
0.599999999999999	7.22E-07	4.96E-07	5.03E-07	5.03E-07	0.00115902400450824	0.0011537294303047	0.00115915384177742	0.00115724142502807	0.00419105404743447	0.00418449431318803	0.00419623644757752	0.00418868557075918	0.0110224327344757	0.0110189828557361	0.0110369477429037	0.0110210205351789
0.699999999999999	1.72E-06	1.41E-06	1.44E-06	1.44E-06	0.00139360218791944	0.00138695545861337	0.00139486078251783	0.00139192729010703	0.00452390367698519	0.00451618834439415	0.00453209162487949	0.00452186298194989	0.0112213498780307	0.0112170250292959	0.0112407886924926	0.0112199917113001
0.8	3.55E-06	3.19E-06	3.25E-06	3.25E-06	0.00162232203823238	0.00161417538363921	0.00162505575378632	0.0016208481192774	0.00483227756309499	0.0048230185000899	0.00484367794151667	0.00483038426774973	0.0114130218333971	0.0114077335955294	0.0114379918983687	0.0114118082654689
0.9	6.57E-06	6.14E-06	6.28E-06	6.27E-06	0.00184503058240568	0.00183507003101191	0.00184942066049198	0.00184367784051999	0.00512036168696583	0.00510927390827457	0.00513527255553948	0.0051185337075098	0.0115975762850742	0.0115910654114407	0.0116284890438176	0.0115964252536064
1	1.11E-05	1.06E-05	1.08E-05	1.08E-05	0.00206168917928136	0.00204962579655101	0.00206794078158399	0.00206039606029912	0.00539118477019384	0.00537809176762437	0.00541000061730297	0.00538944358746447	0.0117751782304144	0.0117672121580933	0.0118124488189808	0.0117740319319808
1.25	3.04E-05	2.94E-05	3.02E-05	3.02E-05	0.00257766525174708	0.00255935086146235	0.00258971771304335	0.00257647890514499	0.00600710772310024	0.00598821828325151	0.00603732180896082	0.00600563411989183	0.0121905518697658	0.0121781678852867	0.0122456340233149	0.0121893827570255
1.5	6.30E-05	6.08E-05	6.30E-05	6.28E-05	0.00305982444311524	0.00303391743104337	0.00307933411303387	0.00305868423369345	0.00655440828280137	0.00652844461414369	0.00659804997708421	0.00655305519235659	0.0125691980668374	0.0125512919848144	0.0126446044125886	0.0125679251442508
1.75	0.00010968220227731	0.000105477613077875	0.000109989196872045	0.000109507614030926	0.00351186550868481	0.00347710313053235	0.00354047164308306	0.00351069671595839	0.00704841907721977	0.00701422750226035	0.00710745949105455	0.00704708951461953	0.0129159119535586	0.0128914162689915	0.0130139243500721	0.0129144354916329
2	0.000170159591276984	0.000162987399695918	0.000170960397670234	0.000169989301543063	0.00393708150400883	0.00389229404010562	0.0039764061580442	0.00393581505112346	0.00749928253431377	0.00745579345241994	0.00757559966830666	0.00749789206677148	0.0132347233575513	0.0132026294843014	0.0133574395313638	0.0132329454965994
2.25	0.000243587767617499	0.000232361944985051	0.000245157496174404	0.000243415234932386	0.00433829129291996	0.00428238277160464	0.00438991225367459	0.00433684948609658	0.0079141591307228	0.00786036353716674	0.00800952016526377	0.0079126151333167	0.013528977226097	0.0134883205129402	0.013678314864508	0.0135267869851492
2.5	0.000328840943295099	0.000312400385292133	0.000331524704204441	0.000328658830023036	0.00471787035971107	0.00464981823187138	0.00478331691725599	0.00471617114931034	0.00829833402202396	0.00823328763065224	0.00841440551371737	0.00829654263895193	0.0138014383339478	0.0137513034756863	0.0139791563237356	0.0137987179150023
2.75	0.000424696410946956	0.000401836515451247	0.000428905898049807	0.000424496017110513	0.00507783289000835	0.00499668074311211	0.00515857713340526	0.00507578683958557	0.00865586393974756	0.00857867860046784	0.00879420945243508	0.0086537243757072	0.0140544187645188	0.013993935648835	0.0142621267005944	0.0140510408226906
3	0.000529937505025072	0.000499433753586024	0.000536144287323553	0.000529706577201836	0.00541989633866649	0.00532475102803112	0.00551735052663009	0.00541740774556076	0.00898995032624469	0.00889979245364412	0.00915203511016612	0.00898735614379542	0.0142898684521323	0.014218212492086	0.0145290390843106	0.014285698172992
3.25	0.000643405671791821	0.000604033010052756	0.000652134860576604	0.000643127564913591	0.00574553887596779	0.005635566872582	0.00586105316029264	0.00574250588601025	0.00930318131282876	0.00919926896434482	0.00949037560168241	0.00930002034737597	0.0145094501523491	0.0144258410456005	0.0147814290891296	0.0145043459507352
3.5	0.000764024044265329	0.000714573634420815	0.000775849461460014	0.000763678872991733	0.00605604553490507	0.00593046806197978	0.00619090526427627	0.00605235885223508	0.00959769259657011	0.00947929083207361	0.00981127310690832	0.00959384510225313	0.0147145975141171	0.014618296104721	0.0150206101034152	0.0147084099487132
3.75	0.000890809361010212	0.000830099374527692	0.000906346343101273	0.000890372940091846	0.00635254106390133	0.00621063168591971	0.00650796709515912	0.00634808493938338	0.00987527340665752	0.00974169284218478	0.0101164279189998	0.00987061333269667	0.0149065556900038	0.0147968633543034	0.0152477156636798	0.0148991289604895
4	0.00102287212522753	0.000949756281271205	0.00104277114789933	0.00102231566128852	0.00663601811949418	0.00647709991052219	0.00681316709548215	0.00663067075851481	0.0101374444381305	0.00998803905314405	0.0104072754955715	0.0101318398856112	0.0150864155339931	0.0149626727650448	0.0154637322072794	0.0150775881973249
4.25	0.00115941256729875	0.00107278654486715	0.00118435335019643	0.00115870261839309	0.00690735926286184	0.00673080195294763	0.00710732413405922	0.00690099306175455	0.0103855139983967	0.0102196788150239	0.0106850423245438	0.0103788274693024	0.0152551399738258	0.0151167247159961	0.015669524636698	0.0152447454044847
4.5	0.0012997151414836	0.0011985205284521	0.00133040048977734	0.00129881301350533	0.00716735362151115	0.0069725716073063	0.00739116520762165	0.00715983612687513	0.010620618631085	0.010437788350444	0.0109507873409612	0.0106127081501313	0.0154135838815096	0.0152599106493723	0.0158658564807457	0.0154014514905983
4.75	0.00144314098419426	0.0013263682649442	0.00148029152254481	0.0014420026702858	0.00741671128797499	0.00720316134532431	0.00766533964967279	0.00740790572330409	0.0108437550612597	0.0106434022325116	0.0112054332331853	0.0108344747432119	0.0155625110847036	0.0153930295782319	0.0160534059590046	0.015548466995972
5	0.00158912048825223	0.00145581110270915	0.00163347002812304	0.00158769686859591	0.00765607495152001	0.00742325376307513	0.00793043063410693	0.00764584042992234	0.0110558047121998	0.0108374376322471	0.0114497905138791	0.0110450049708825	0.0157026080067181	0.0155168014169619	0.0162327789094432	0.0156864753736475
5.25	0.00173714668633464	0.00158639384993106	0.00178943767102622	0.00173538342647838	0.00788602873751331	0.00763347095550916	0.00818696456734101	0.00787422088577029	0.0112575521003403	0.0110207132875543	0.0116845763100932	0.0112450803419911	0.015834494050191	0.0156318778525145	0.0164045192899228	0.0158160938039977
5.5	0.00188676803123168	0.00171771757505238	0.00194774811224502	0.00188460623771918	0.00810710707871721	0.00783438225957297	0.00843541881879325	0.00809357741404685	0.0114497011969572	0.0111939645501186	0.0119104292305841	0.0114354011091563	0.0159587317851067	0.0157388512927294	0.0165691177846093	0.0159378820813407
5.75	0.00203758434255141	0.00184943311200594	0.00210800145299336	0.00203495935400847	0.00831979775040474	0.00802651070212301	0.00867622813282176	0.00830439635533115	0.0116328837319711	0.0113578554715672	0.0121279212730573	0.01161659826595	0.0160758309352208	0.0158382622963308	0.0167270189158733	0.0160523499787947
6	0.00218923930241729	0.00198123525952761	0.00226983922738095	0.00218608163290935	0.00852455078062048	0.00821033841100339	0.00890978998583747	0.00850712536820467	0.0118076729856518	0.0115129886224408	0.0123375674659436	0.0117892432780407	0.0161862582704574	0.0159306057928053	0.0168786269668069	0.0161599634008437
6.25	0.00234141677280312	0.00211285763317803	0.00243293992546947	0.0023376519355976	0.00872178069872563	0.00838631118941697	0.00913646909290139	0.00870217789726144	0.0119745893089987	0.0116599131524142	0.0125398337539745	0.0119538560571212	0.0162904405569556	0.0160163363292149	0.0170243109490021	0.0162611495616482
6.5	0.00249383489691193	0.00224406811472465	0.00259701501034181	0.00248938483918894	0.00891187479607398	0.00855484240984615	0.00935660122336298	0.00888993696465171	0.0121341115099016	0.0117991314699617	0.01273514350639	0.0121109115561159	0.0163887732558048	0.0160958725279645	0.0171644087976889	0.0163563013738909
6.75	0.00264624568070128	0.00237466483906785	0.00276180538517185	0.00264102681994413	0.00909518694431767	0.00871631635048578	0.00957049645112773	0.00907075840802747	0.0122866722510585	0.0119311048265278	0.0129238829333345	0.0122608452709648	0.0164816151953584	0.0161696008996509	0.0172992309367996	0.0164457811928862
7	0.00279842846898603	0.00250447265967924	0.00292707826445556	0.00279235286123039	0.00927204832403059	0.00887109107169212	0.00977844193915958	0.00924497366230845	0.012432671257332	0.0120562580226951	0.0131064056283047	0.0124040578666524	0.0165692995324287	0.0162378791248298	0.0174290633265104	0.0165299240302665
7.25	0.00295018745710615	0.00263334003703916	0.0030926244049366	0.00294316344111453	0.00944276879161838	0.00901950091033512	0.00998070433779679	0.00941289216307402	0.0125724780923724	0.0121749834041424	0.0132830364047221	0.012540919095408	0.0166521354923054	0.016301038895342	0.0175541700828167	0.0166090403282541
7.5	0.00310134934696095	0.00276113629934086	0.00325825565477179	0.00309328185724386	0.00960763917770635	0.00916185865471269	0.0101775318609055	0.00957480343415824	0.0127064356352483	0.0122876442781899	0.0134540745576242	0.0126717711379678	0.0167304108443849	0.0163593883879149	0.0176747957409424	0.01668341836753
7.75	0.00325176137530011	0.00288774922992305	0.00342380278321615	0.00324255185027337	0.00976693009172169	0.00929845745077637	0.0103691560917268	0.0097309789101147	0.0128348598643028	0.0123945778538624	0.0136197966535436	0.0127969314708923	0.0168043913361719	0.0164132144288074	0.0177911672205515	0.016753326367686
8	0.0034012889097858	0.00301308294102796	0.00358911355703489	0.00339083549096208	0.00992089687996497	0.00942957248103908	0.0105557935606833	0.00988167353483661	0.0129580457304691	0.0124960977871946	0.013780458930381	0.0129166953417003	0.0168743254512131	0.0164627843973103	0.017903495539881	0.0168190143282485
8.25	0.00354981364787439	0.00313705599831187	0.00375405103367545	0.00353801129986984	0.0100697740545975	0.00955546245009849	0.0107376471298074	0.0100271271701782	0.0130762623635626	0.0125924963972037	0.0139362993727405	0.0130313379172581	0.01694044016989	0.0165083479072631	0.0180119773173371	0.0168807156495574
8.5	0.00369723122643585	0.00325959976494289	0.00391849204480452	0.00368397257217107	0.0102137864934946	0.00967637090477431	0.0109149072123764	0.0101675658424858	0.0131897649903883	0.0126840466053127	0.0140875395155152	0.0131411161582056	0.0170029510112266	0.0165501382988539	0.0181167960922704	0.0169386485658606
8.75	0.00384345036764951	0.00338065693806895	0.00408232584706368	0.00382862588338429	0.0103531468382249	0.00979252741209121	0.0110877528514626	0.010303202850177	0.013298792754888	0.0127710036411162	0.014234386018595	0.0132462704622925	0.0170620599694554	0.0165883739674503	0.0182181234911769	0.0169930174174344
9	0.00398839162845265	0.00350018025393082	0.00424545291980196	0.00397188975476662	0.0104880552935619	0.00990414861448767	0.0112563526771595	0.0104342397516554	0.0134035689679897	0.0128536065495835	0.0143770320477451	0.013347026111689	0.0171179556257822	0.0166232595517544	0.0183161202611652	0.0170440137840607
9.25	0.00413198742673069	0.00361813134095876	0.00440778389211315	0.0041136934597453	0.0106187065561403	0.0100114391785019	0.0114208657590398	0.0105608672497152	0.0135043081105413	0.0129320795285973	0.0145156584904901	0.0134435945531296	0.0171708187358734	0.0166549869999649	0.0184109371889534	0.0170918174985625
9.5	0.00427417641414016	0.00373447970286377	0.00456923858376051	0.00425397595506931	0.0107452690495375	0.01011459265063	0.0115814423677808	0.0106832659860348	0.0136011966152242	0.0130066331207676	0.0146504350308647	0.0135361745347818	0.017220806928146	0.0166837365296815	0.018502715920743	0.0171365975561363
9.75	0.00441490829485333	0.00384920181605823	0.00472974514654053	0.00439268492239117	0.0108679156235664	0.0102137922319495	0.0117382246577381	0.0108016072572561	0.0136944223238662	0.0130774652794692	0.0147815211028877	0.0136249531197324	0.0172680783147731	0.0167096774948676	0.0185915896959318	0.0171785129327855
10	0.00455413774684125	0.00396228032775545	0.00488923929435151	0.0045297759077653	0.0109867997383058	0.0103092114813721	0.0118913472804722	0.0109160536623804	0.0137841523061604	0.0131447623258128	0.0149090667393694	0.0137101065927045	0.0173127738556855	0.0167329691711964	0.0186776840056496	0.0172177133241194

Return to Figure 1

Figure 2 Data

	Krippner (left scale)	First-order (right scale)	Second-order (left scale)
1990-01-31	1.52E-01	-23.1612433085184	1.02E-01
1990-02-28	5.96E-01	-22.7432790750885	5.56E-01
1990-03-30	-3.04E-02	-23.3452212170429	-7.92E-02
1990-04-30	1.41E-01	-23.2177843834177	1.00E-01
1990-05-31	2.85E-01	-23.0586232261957	2.49E-01
1990-06-29	-1.20E-01	-23.4634137786449	-1.53E-01
1990-07-31	1.74E-01	-23.1813992171804	1.47E-01
1990-08-31	1.91E-01	-23.2297353643247	1.79E-01
1990-09-28	3.33E-01	-23.0949560718153	3.23E-01
1990-10-31	6.32E-02	-23.3411067439989	4.70E-02
1990-11-30	1.67E-01	-23.1906191831696	1.35E-01
1990-12-31	2.67E-01	-23.0775849794408	2.28E-01
1991-01-31	-8.26E-02	-23.42526924117	-1.24E-01
1991-02-28	3.84E-01	-22.9800880101285	3.48E-01
1991-03-28	2.45E-03	-23.3630180152014	-3.49E-02
1991-04-30	1.57E-01	-23.2235090284967	1.27E-01
1991-05-31	-1.38E-01	-23.5265380218634	-1.67E-01
1991-06-28	-1.15E-01	-23.5270696907795	-1.38E-01
1991-07-31	-9.55E-02	-23.5090217084864	-1.13E-01
1991-08-30	-1.90E-01	-23.5875943257191	-2.10E-01
1991-09-30	2.41E-01	-23.125218956911	2.12E-01
1991-10-31	3.37E-01	-23.041850122467	3.14E-01
1991-11-29	-2.24E-01	-23.6068879779477	-2.48E-01
1991-12-31	2.23E-01	-23.0992866730174	1.69E-01
1992-01-31	-2.85E-01	-23.6625707168938	-3.19E-01
1992-02-28	4.05E-01	-22.9790539795499	3.72E-01
1992-03-31	1.77E-01	-23.2106890991709	1.42E-01
1992-04-30	-9.28E-02	-23.5021898537059	-1.20E-01
1992-05-29	2.58E-01	-23.1297722956032	2.27E-01
1992-06-30	2.71E-02	-23.3482963877267	-4.56E-03
1992-07-31	-8.20E-02	-23.4153483180749	-1.35E-01
1992-08-31	4.11E-01	-22.9220888006186	3.57E-01
1992-09-30	3.54E-01	-22.9388821864026	2.75E-01
1992-10-30	2.82E-01	-23.0392527172991	2.21E-01
1992-11-30	-3.97E-02	-23.3711862299786	-9.69E-02
1992-12-31	1.06E-01	-23.2149785263113	4.76E-02
1993-01-29	4.70E-01	-22.7874014546525	3.82E-01
1993-02-26	-5.67E-02	-23.2346502527808	-1.88E-01
1993-03-31	3.76E-01	-22.80404197599	2.47E-01
1993-04-30	1.67E-01	-23.0247433245284	3.77E-02
1993-05-28	3.68E-01	-22.7700705654483	2.26E-01
1993-06-30	4.82E-01	-22.5255925418688	2.73E-01
1993-07-30	2.30E-01	-22.7602187312699	1.96E-02
1993-08-31	4.05E-01	-22.4356061145294	1.08E-01
1993-09-30	7.34E-01	-22.0440878112335	4.13E-01
1993-10-29	6.58E-01	-22.1383562718973	3.53E-01
1993-11-30	5.61E-04	-22.9500085620364	-2.23E-01
1993-12-31	3.84E-01	-22.577460486207	1.64E-01
1994-01-31	4.89E-01	-22.3920529642348	2.28E-01
1994-02-28	1.35E-01	-22.8792483253853	-4.59E-02
1994-03-31	1.04E-01	-23.0484767384439	-1.46E-02
1994-04-29	4.04E-01	-22.7564106913916	2.91E-01
1994-05-31	1.32E-01	-23.0311318265186	2.29E-02
1994-06-30	3.43E-01	-22.870656814708	2.51E-01
1994-07-29	3.27E-01	-22.8400749608849	2.22E-01
1994-08-31	2.47E-01	-22.9184958680125	1.42E-01
1994-09-30	3.34E-01	-22.8990502358072	2.51E-01
1994-10-31	4.25E-01	-22.8365054550166	3.53E-01
1994-11-30	3.92E-01	-22.8146495686974	3.04E-01
1994-12-30	-1.42E-02	-23.1705064598722	-1.15E-01
1995-01-31	2.10E-03	-23.1687824825078	-9.15E-02
1995-02-28	4.00E-01	-22.732683724283	2.94E-01
1995-03-31	3.96E-01	-22.7286571533355	2.86E-01
1995-04-28	9.52E-02	-22.9791320939497	-3.37E-02
1995-05-31	6.66E-01	-22.1950245190744	4.41E-01
1995-06-30	4.61E-01	-22.3546035195385	2.20E-01
1995-07-31	2.11E-02	-22.8660221566137	-1.87E-01
1995-08-31	6.56E-01	-22.1690541569401	4.22E-01
1995-09-29	6.10E-01	-22.1440060354707	3.50E-01
1995-10-31	4.22E-01	-22.2695008049977	1.30E-01
1995-11-30	5.40E-01	-22.0698800253552	2.00E-01
1995-12-29	1.71E-01	-22.3774997202661	-2.03E-01
1996-01-31	7.30E-01	-21.8790264802741	3.71E-01
1996-02-29	4.08E-01	-22.3705787394309	1.47E-01
1996-03-29	4.46E-01	-22.4226355519627	2.30E-01
1996-04-30	4.48E-01	-22.5140620229749	2.72E-01
1996-05-31	3.79E-01	-22.6242743665699	2.20E-01
1996-06-28	-5.66E-02	-23.0246877648919	-2.29E-01
1996-07-31	5.09E-02	-22.9396007055504	-1.13E-01
1996-08-30	4.64E-01	-22.5792009397431	3.20E-01
1996-09-30	-6.37E-03	-22.9960836634884	-1.72E-01
1996-10-31	6.18E-01	-22.2743841484712	4.08E-01
1996-11-29	6.31E-01	-22.1037369896043	3.56E-01
1996-12-31	4.97E-01	-22.3694924694424	2.83E-01
1997-01-31	6.50E-01	-22.2339175005986	4.42E-01
1997-02-28	2.76E-01	-22.6346790487637	8.17E-02
1997-03-31	2.12E-01	-22.798931998363	5.85E-02
1997-04-30	3.35E-01	-22.6365225830008	1.65E-01
1997-05-30	8.19E-02	-22.8321154855214	-1.09E-01
1997-06-30	4.86E-01	-22.4116764252685	2.87E-01
1997-07-31	7.18E-01	-21.9882441798609	4.35E-01
1997-08-29	3.80E-01	-22.4470776523554	1.53E-01
1997-09-30	6.25E-01	-22.1139099726528	3.59E-01
1997-10-31	5.57E-01	-22.0385991965195	2.28E-01
1997-11-28	5.71E-01	-21.9684059033658	2.31E-01
1997-12-31	4.69E-01	-21.9793378171624	8.66E-02
1998-01-30	7.57E-01	-21.6056148455216	3.19E-01
1998-02-27	9.95E-01	-21.4369283752689	6.01E-01
1998-03-31	3.13E-01	-22.1052129052669	-8.32E-02
1998-04-30	6.80E-01	-21.7501063698705	2.88E-01
1998-05-29	7.27E-01	-21.6475508904852	3.13E-01
1998-06-30	9.27E-01	-21.329358906777	4.64E-01
1998-07-31	9.33E-01	-21.3651527569248	4.87E-01
1998-08-31	8.43E-01	-21.2091613507672	2.40E-01
1998-09-30	1.42213290198534	-20.1550932506436	5.51E-01
1998-10-30	1.1380620031897	-20.5650231220538	3.60E-01
1998-11-30	1.28364613578665	-20.4871811681024	5.69E-01
1998-12-31	1.32497633048962	-20.3010179102058	5.57E-01
1999-01-29	1.2659488201077	-20.3505274170846	4.83E-01
1999-02-26	9.81E-01	-21.20545225868	4.93E-01
1999-03-31	9.76E-01	-21.2947892517949	4.99E-01
1999-04-30	5.72E-01	-21.7724235653996	1.30E-01
1999-05-28	8.36E-01	-21.7089152905896	4.94E-01
1999-06-30	5.25E-01	-22.0670536277223	1.98E-01
1999-07-30	4.89E-01	-22.2437673303835	2.20E-01
1999-08-31	4.79E-01	-22.3030870376095	2.32E-01
1999-09-30	5.56E-01	-22.1825601073025	2.88E-01
1999-10-29	5.07E-01	-22.2584621539287	2.54E-01
1999-11-30	2.13E-01	-22.5644895353539	-3.11E-02
1999-12-31	3.69E-01	-22.4917774407065	1.60E-01
2000-01-31	5.18E-01	-22.3590605047105	3.20E-01
2000-02-29	2.32E-01	-22.5982648997828	1.66E-02
2000-03-31	3.29E-01	-22.2557513532845	2.22E-02
2000-04-28	2.22E-01	-22.4530461647452	-4.69E-02
2000-05-31	5.14E-01	-22.1764009432441	2.49E-01
2000-06-30	6.88E-01	-21.9186530939326	3.83E-01
2000-07-31	1.05334661751929	-21.5210250977079	7.36E-01
2000-08-31	4.25E-01	-22.063609032701	6.52E-02
2000-09-29	6.01E-01	-21.9071748951581	2.39E-01
2000-10-31	7.60E-01	-21.7014843790217	3.77E-01
2000-11-30	4.67E-01	-21.842613978165	1.14E-03
2000-12-29	8.31E-01	-21.3493952000988	2.73E-01
2001-01-31	7.84E-01	-21.5257964185298	2.65E-01
2001-02-28	8.73E-01	-21.3470348695023	3.08E-01
2001-03-30	9.23E-01	-21.3132171244958	3.65E-01
2001-04-30	4.28E-01	-22.075205720628	2.04E-02
2001-05-31	4.41E-01	-22.1472279615157	7.07E-02
2001-06-29	7.77E-01	-21.8304640727926	4.21E-01
2001-07-31	7.99E-01	-21.6870988214216	3.51E-01
2001-08-31	7.71E-01	-21.6597995135183	2.79E-01
2001-09-28	1.0275599654623	-21.3885056781847	4.74E-01
2001-10-31	5.94E-01	-21.6857384864357	-1.11E-01
2001-11-30	7.81E-01	-21.8028674324616	3.31E-01
2001-12-31	6.07E-01	-22.0811082519842	2.41E-01
2002-01-31	6.53E-01	-22.0389158470562	2.89E-01
2002-02-28	7.83E-01	-21.8640293881006	3.77E-01
2002-03-28	2.33E-01	-22.5895671586721	-4.39E-02
2002-04-30	7.65E-02	-22.6676893438318	-2.71E-01
2002-05-31	6.31E-01	-22.0733608533885	2.49E-01
2002-06-28	5.71E-01	-22.0777822982674	1.29E-01
2002-07-31	1.01318002667681	-21.5240586755631	4.07E-01
2002-08-30	9.71E-01	-21.3411063981711	1.77E-01
2002-09-30	1.66999066327583	-20.1641828049467	4.07E-01
2002-10-31	1.76001355890249	-20.3412060726532	6.91E-01
2002-11-29	1.09398579382233	-21.2641595496995	3.67E-01
2002-12-31	1.42538875091899	-20.5919983860027	3.24E-01
2003-01-31	1.54789335946425	-20.6561318134815	6.13E-01
2003-02-28	1.69615866456862	-20.2579122686365	5.10E-01
2003-03-31	1.75693512694224	-20.3160296593107	6.56E-01
2003-04-30	1.62089504736492	-20.494476231908	5.55E-01
2003-05-30	1.80805011018463	-19.7212623876332	2.40E-01
2003-06-30	1.84926277498012	-19.8965242309915	4.24E-01
2003-07-31	6.59E-01	-21.9066980438659	-1.13E-02
2003-08-29	1.30744035208074	-21.2473541180419	6.98E-01
2003-09-30	1.5661414440906	-20.6184298012086	5.50E-01
2003-10-31	1.38903768424666	-21.0173823865118	6.44E-01
2003-11-28	1.10510712232836	-21.2847856240337	4.00E-01
2003-12-31	1.21201371509727	-21.1328711265212	4.31E-01
2004-01-30	1.16125644284398	-21.0915773065667	3.15E-01
2004-02-27	1.53910538060735	-20.5580229896756	5.32E-01
2004-03-31	1.74129120420772	-20.2128272376956	6.07E-01
2004-04-30	1.28520847405985	-21.1393537485291	6.80E-01
2004-05-28	6.69E-01	-21.8116869288806	1.20E-01
2004-06-30	6.41E-01	-21.7220627412319	2.81E-02
2004-07-30	7.94E-01	-21.4946122577253	1.25E-01
2004-08-31	9.38E-01	-21.0963293263504	3.52E-02
2004-09-30	1.42818919936789	-20.4817186294016	4.91E-01
2004-10-29	1.610741794053	-20.2013614850978	5.95E-01
2004-11-30	1.15279180269156	-20.8728009647994	3.56E-01
2004-12-31	1.546004735474	-20.2178507982469	6.15E-01
2005-01-31	1.40676794369604	-20.1795583826177	4.27E-01
2005-02-28	1.63708426935423	-20.1034852147423	8.01E-01
2005-03-31	1.2081637354739	-20.5363572635909	3.98E-01
2005-04-29	1.07222138785986	-20.3260694582077	5.83E-02
2005-05-31	1.55786660653453	-19.5478566667489	3.79E-01
2005-06-30	1.79608677874719	-19.1175098650103	5.40E-01
2005-07-29	9.01E-01	-20.3993205990512	-9.58E-02
2005-08-31	1.70945432619411	-19.34740793982	5.26E-01
2005-09-30	1.77616036693042	-19.6078443838778	8.16E-01
2005-10-31	1.03135904116889	-20.5997867279632	2.10E-01
2005-11-30	1.76662050147935	-19.8151742927354	9.11E-01
2005-12-30	1.17528483525829	-20.2590704935945	2.46E-01
2006-01-31	7.89E-01	-20.7718705624515	-6.59E-02
2006-02-28	1.35926763899764	-20.2504143094501	5.45E-01
2006-03-31	1.13834227816626	-20.760385780755	4.60E-01
2006-04-28	5.85E-01	-21.4830910011687	-2.03E-02
2006-05-31	8.76E-01	-21.2056841515625	2.93E-01
2006-06-30	1.02571468312689	-21.0321426811443	4.36E-01
2006-07-31	1.28838417205158	-20.6616094415951	6.26E-01
2006-08-31	1.07252690326624	-20.6984669521916	3.07E-01
2006-09-29	1.11716410557891	-20.5497200277164	3.06E-01
2006-10-31	1.43602323167506	-20.1556803725683	5.92E-01
2006-11-30	1.28721830273799	-20.1864202646823	3.73E-01
2006-12-29	1.08639507485713	-20.5892145363717	3.03E-01
2007-01-31	1.35988086542276	-20.377114274658	6.16E-01
2007-02-28	1.42332236692695	-20.1620580109882	5.65E-01
2007-03-30	1.26326517700552	-20.4396718793405	4.51E-01
2007-04-30	1.49956954189636	-20.1725167155808	6.71E-01
2007-05-31	1.17950258024711	-20.7290977077254	5.09E-01
2007-06-29	1.07935398145152	-20.9582095462824	4.64E-01
2007-07-31	1.41804106414879	-20.4729942372657	6.81E-01
2007-08-31	1.26520934348298	-20.457698389146	4.18E-01
2007-09-28	9.42E-01	-20.8905375714582	1.48E-01
2007-10-31	1.12425519255242	-20.6418455971014	2.87E-01
2007-11-30	1.55640329505296	-19.9943704777758	3.93E-01
2007-12-31	1.48257687009809	-20.1772810006397	4.02E-01
2008-01-31	1.62083355455269	-19.897285241736	2.44E-01
2008-02-29	2.08017270780749	-19.4116693247299	5.31E-01
2008-03-31	2.22435284306758	-18.9999788746277	5.82E-01
2008-04-30	1.2949212320043	-20.1405615675578	1.00E-01
2008-05-30	1.08718834707643	-20.5460537938298	1.17E-01
2008-06-30	1.45016156454673	-20.0285304577536	3.76E-01
2008-07-31	1.33822806916157	-20.1560052080741	2.31E-01
2008-08-29	1.54907306322671	-19.9673570717229	3.76E-01
2008-09-30	1.48923916862955	-20.4251580175483	4.05E-01
2008-10-31	1.23355302917987	-21.1284554256205	2.23E-01
2008-11-28	3.20923354663153	-17.604718470421	8.69E-01
2008-12-31	3.72529262246928	-15.9358346742652	5.91E-01
2009-01-30	3.21022563267294	-17.2575252395135	8.34E-01
2009-02-27	2.53564897342982	-18.4006494870513	4.97E-01
2009-03-31	3.2261408250498	-16.9971706443328	5.82E-01
2009-04-30	2.82739945875992	-18.3431893447347	8.77E-01
2009-05-29	2.02372069254837	-19.8263207406667	4.90E-01
2009-06-30	1.90407235754364	-20.0605198632144	7.33E-01
2009-07-31	1.87514976485309	-20.0139267157387	6.26E-01
2009-08-31	1.8550414148194	-19.9619909022541	4.12E-01
2009-09-30	1.8920038141168	-19.8453273289861	3.42E-01
2009-10-30	2.28491267496577	-19.5554392578298	7.00E-01
2009-11-30	2.18560787073419	-19.4188777411796	1.09E-01
2009-12-31	1.68412206175617	-20.5424890325484	6.37E-01
2010-01-29	1.87456359427219	-20.1543161831072	3.00E-01
2010-02-26	1.77309477249205	-20.2283972525329	1.43E-01
2010-03-31	1.54871097447405	-20.6267549402284	3.10E-01
2010-04-30	2.22417430576452	-19.7680232836588	7.73E-01
2010-05-28	2.23688330147943	-19.4074090740093	3.68E-01
2010-06-30	3.02712741140034	-18.1077709125785	5.90E-01
2010-07-30	3.04686893107974	-17.7663402564429	2.08E-01
2010-08-31	4.03452244934581	-16.029240805934	6.39E-01
2010-09-30	4.07354177554223	-15.8469943885789	4.70E-01
2010-10-29	4.17094040806812	-15.828661565764	3.64E-01
2010-11-30	3.36854579928869	-17.3010302662238	1.21E-01
2010-12-31	2.80654718037925	-18.830019488302	5.51E-01
2011-01-31	2.73367970755611	-18.9065264444446	3.84E-01
2011-02-28	2.22111173078513	-19.542439942063	2.34E-01
2011-03-31	2.22218349950564	-19.598296744226	5.11E-01
2011-04-29	2.7082620523447	-18.8649975090367	5.26E-01
2011-05-31	3.20365165524	-17.9801428653927	4.92E-01
2011-06-30	3.10942072139601	-18.1842190644124	4.26E-01
2011-07-29	3.69159174097362	-16.8455757967692	2.95E-01
2011-08-31	4.96221293600149	-14.2771357344778	6.73E-01
2011-09-30	4.93002156738999	-13.6808169786744	4.25E-01
2011-10-31	4.61236555219467	-14.1115168270415	1.64E-01
2011-11-30	4.97564739772297	-13.5537613068443	4.82E-01
2011-12-30	5.04800669497956	-12.8298397575767	3.03E-01
2012-01-31	5.45109339585649	-11.7844174128756	4.22E-01
2012-02-29	5.38489028188007	-12.2821945148289	6.88E-01
2012-03-30	4.92435682668809	-13.3676349126289	6.80E-01
2012-04-30	5.25093775501132	-12.0161325096341	5.45E-01
2012-05-31	5.73637144134251	-10.2746239340971	6.55E-01
2012-06-29	5.63234063254623	-10.3434222905645	6.61E-01
2012-07-31	5.6369363360605	-9.71327363473835	3.63E-01
2012-08-31	5.77945132923864	-9.61966728172407	4.51E-01
2012-09-28	5.72759615740396	-9.97643312611797	4.63E-01
2012-10-31	5.6950521280746	-10.5421604772646	6.45E-01
2012-11-30	5.52085276632707	-10.4366418631912	2.88E-01
2012-12-31	5.81253280377346	-10.6440915240732	7.64E-01

Return to Figure 2

Figure 3 data

1990-01-31	0.0738069715247449
1990-02-28	0.0765280294340845
1990-03-30	0.0786434812357967
1990-04-30	0.078714371697528
1990-05-31	0.0798650837736512
1990-06-29	0.0790591043334355
1990-07-31	0.0781243322311513
1990-08-31	0.0741248237590162
1990-09-28	0.0729455915855921
1990-10-31	0.0713817333861006
1990-11-30	0.0686447785501436
1990-12-31	0.0634581546748158
1991-01-31	0.0592895877409378
1991-02-28	0.0577141773012084
1991-03-28	0.0571649103357749
1991-04-30	0.0572292385820607
1991-05-31	0.0552770862088216
1991-06-28	0.0567670943663421
1991-07-31	0.0578804999440993
1991-08-30	0.054855212482315
1991-09-30	0.0520540936336351
1991-10-31	0.0510964851090126
1991-11-29	0.0458202020776985
1991-12-31	0.0380474038743368
1992-01-31	0.0359354548432295
1992-02-28	0.0370195165782543
1992-03-31	0.0384931881752374
1992-04-30	0.0359944536745667
1992-05-29	0.0369013245591763
1992-06-30	0.0376566694146794
1992-07-31	0.0319197905688868
1992-08-31	0.0323250252662459
1992-09-30	0.0284900339627151
1992-10-30	0.0278531828862182
1992-11-30	0.0289778761627615
1992-12-31	0.0312155276106223
1993-01-29	0.0321096963862799
1993-02-26	0.0300399438514288
1993-03-31	0.0296509163319736
1993-04-30	0.0298952330852831
1993-05-28	0.0300167757444847
1993-06-30	0.0314377815659895
1993-07-30	0.0315168663754036
1993-08-31	0.0310602590655952
1993-09-30	0.0294273403831032
1993-10-29	0.0296287958661887
1993-11-30	0.0300188464180615
1993-12-31	0.0307135035870603
1994-01-31	0.0309906358707911
1994-02-28	0.0326331544142962
1994-03-31	0.0348318902522745
1994-04-29	0.0388311689841627
1994-05-31	0.0420825896864942
1994-06-30	0.0435928507102097
1994-07-29	0.0463711464621787
1994-08-31	0.0486711269606894
1994-09-30	0.0508463093932379
1994-10-31	0.0552172245886747
1994-11-30	0.0593465925632184
1994-12-30	0.0638438850871779
1995-01-31	0.0653545556161594
1995-02-28	0.0651647653824835
1995-03-31	0.0640162364699378
1995-04-28	0.0623643312090518
1995-05-31	0.0620954468139597
1995-06-30	0.0550156171931278
1995-07-31	0.0538544885208585
1995-08-31	0.0542183721183009
1995-09-29	0.054081617256821
1995-10-31	0.0535076964588602
1995-11-30	0.0530005158137982
1995-12-29	0.0507161142551589
1996-01-31	0.0494693153995163
1996-02-29	0.0467195335233047
1996-03-29	0.0480626546868447
1996-04-30	0.0487432575339563
1996-05-31	0.0494077451374009
1996-06-28	0.0525369321129284
1996-07-31	0.0538869006529423
1996-08-30	0.0525473705078726
1996-09-30	0.0535484817633991
1996-10-31	0.0530991280433912
1996-11-29	0.0518483819660064
1996-12-31	0.0506730990919165
1997-01-31	0.0512015537768123
1997-02-28	0.0508854828139673
1997-03-31	0.0546451995636519
1997-04-30	0.056328900786992
1997-05-30	0.0548493673581475
1997-06-30	0.0535727058855248
1997-07-31	0.0539804698706098
1997-08-29	0.0538676140594343
1997-09-30	0.0534067127481965
1997-10-31	0.0533422108680446
1997-11-28	0.0522419288643637
1997-12-31	0.0516787718001915
1998-01-30	0.0514530944727309
1998-02-27	0.0510847309968097
1998-03-31	0.0510393071844827
1998-04-30	0.0512433130829313
1998-05-29	0.051456325933984
1998-06-30	0.050914174581294
1998-07-31	0.0503363376054596
1998-08-31	0.0508802627782268
1998-09-30	0.0470835793220952
1998-10-30	0.0385838764486014
1998-11-30	0.039350437589877
1998-12-31	0.0402196346689497
1999-01-29	0.0415129227451506
1999-02-26	0.0426777472936551
1999-03-31	0.0439245931621865
1999-04-30	0.0432229344081893
1999-05-28	0.0442027803499372
1999-06-30	0.0479511984989181
1999-07-30	0.0474611394956372
1999-08-31	0.0480040449589672
1999-09-30	0.0490228001730882
1999-10-29	0.0503835964640914
1999-11-30	0.0519256926853135
1999-12-31	0.0548383702508783
2000-01-31	0.0575334291672112
2000-02-29	0.0598043992433803
2000-03-31	0.062944698642129
2000-04-28	0.063119664967956
2000-05-31	0.0662243370520409
2000-06-30	0.0638851317469902
2000-07-31	0.0638617790518821
2000-08-31	0.0641490698010978
2000-09-29	0.0638679087026872
2000-10-31	0.063549811320711
2000-11-30	0.0639171214887728
2000-12-29	0.0592530323857638
2001-01-31	0.0501724400973043
2001-02-28	0.0461066267429425
2001-03-30	0.0398772124799355
2001-04-30	0.0347283926084203
2001-05-31	0.0326867564382364
2001-06-29	0.0300395203818511
2001-07-31	0.0314904695766739
2001-08-31	0.030598682184375
2001-09-28	0.0186725729478655
2001-10-31	0.0178220406547498
2001-11-30	0.0147774650230925
2001-12-31	0.0120540460417655
2002-01-31	0.0139477341662014
2002-02-28	0.0156796633433236
2002-03-28	0.0170226201904561
2002-04-30	0.0192403185307043
2002-05-31	0.0200451503306412
2002-06-28	0.0185280226493151
2002-07-31	0.0176602154543605
2002-08-30	0.0168626286727409
2002-09-30	0.0170194055683742
2002-10-31	0.0160881843200154
2002-11-29	0.0103779939708516
2002-12-31	0.0111235743265362
2003-01-31	0.0105440309853584
2003-02-28	0.0110781405548906
2003-03-31	0.00989362654151303
2003-04-30	0.0103468181690689
2003-05-30	0.0091994691563864
2003-06-30	0.00701711958218351
2003-07-31	0.00598673372169471
2003-08-29	0.00617947457392442
2003-09-30	0.00756551121055841
2003-10-31	0.0070086509907372
2003-11-28	0.00726527573772514
2003-12-31	0.00778575893388858
2004-01-30	0.00833184415543514
2004-02-27	0.00903171719349021
2004-03-31	0.00780215666365408
2004-04-30	0.0087410642538282
2004-05-28	0.0120595512174959
2004-06-30	0.0153588148498056
2004-07-30	0.0177963884175051
2004-08-31	0.0200115406029489
2004-09-30	0.0213867444913112
2004-10-29	0.022645546012571
2004-11-30	0.0246700853513854
2004-12-31	0.0268399624045644
2005-01-31	0.0289785502375864
2005-02-28	0.0302523229978613
2005-03-31	0.0325343835569062
2005-04-29	0.0345943167812289
2005-05-31	0.0359068387423246
2005-06-30	0.0365876546833658
2005-07-29	0.0381451770963736
2005-08-31	0.0414780561646691
2005-09-30	0.0412453370474357
2005-10-31	0.0435448850826117
2005-11-30	0.0451340665794149
2005-12-30	0.0463567772631362
2006-01-31	0.0469698560431526
2006-02-28	0.048236462088105
2006-03-31	0.0497025259046183
2006-04-28	0.0507761470566619
2006-05-31	0.0511886504936011
2006-06-30	0.053683710757894
2006-07-31	0.0541473691190454
2006-08-31	0.0531115835641437
2006-09-29	0.0507364569846883
2006-10-31	0.0509394475878295
2006-11-30	0.0508273259412642
2006-12-29	0.0499477510538242
2007-01-31	0.0503763449061366
2007-02-28	0.0514343021605057
2007-03-30	0.0512062570402304
2007-04-30	0.0511464007614671
2007-05-31	0.0497531755859413
2007-06-29	0.0497697974938173
2007-07-31	0.051107379454529
2007-08-31	0.0455716927185345
2007-09-28	0.0400896944426295
2007-10-31	0.0395199917276157
2007-11-30	0.035784275606176
2007-12-31	0.0324540272712363
2008-01-31	0.0211297620326556
2008-02-29	0.0192128508381156
2008-03-31	0.0116646924486993
2008-04-30	0.0108635620396666
2008-05-30	0.0129817957431173
2008-06-30	0.0158635605928618
2008-07-31	0.0156425097729302
2008-08-29	0.0165085525564446
2008-09-30	0.0139783532741435
2008-10-31	0.00702671139948689
2008-11-28	0.00334028842264234
2008-12-31	-0.00343676209437839
2009-01-30	-0.00679199699297827
2009-02-27	-0.00567066523203163
2009-03-31	-0.0058544242461725
2009-04-30	-0.00593246188140496
2009-05-29	-0.00670621470405963
2009-06-30	-0.0068955107353275
2009-07-31	-0.00617569839624845
2009-08-31	-0.0056765414393165
2009-09-30	-0.00607775766565571
2009-10-30	-0.00535164445281344
2009-11-30	-0.00506903469486351
2009-12-31	-0.00548370391592793
2010-01-29	-0.00344327570885395
2010-02-26	-0.00259131889895707
2010-03-31	-0.00392290710755419
2010-04-30	-0.00198526928625948
2010-05-28	-0.00199880461285988
2010-06-30	-0.00394970901981631
2010-07-30	-0.00399323912794501
2010-08-31	-0.0050887410578486
2010-09-30	-0.00583143136588096
2010-10-29	-0.00624530939875862
2010-11-30	-0.00685919581408959
2010-12-31	-0.00757924927198137
2011-01-31	-0.00773743146139203
2011-02-28	-0.00760285767298954
2011-03-31	-0.00750877947513123
2011-04-29	-0.00616501496446029
2011-05-31	-0.00515367825793371
2011-06-30	-0.00563452513317359
2011-07-29	-0.00646476272958949
2011-08-31	-0.0109549295627991
2011-09-30	-0.0155905885277315
2011-10-31	-0.0182339718090382
2011-11-30	-0.0193087857646867
2011-12-30	-0.0201892937228889
2012-01-31	-0.0207490777640341
2012-02-29	-0.0194106346922532
2012-03-30	-0.0180363293119332
2012-04-30	-0.0176001886211786
2012-05-31	-0.0164768779637853
2012-06-29	-0.0162202109629263
2012-07-31	-0.0166655241229755
2012-08-31	-0.0165014789100346
2012-09-28	-0.0160823988885003
2012-10-31	-0.0151316510404937
2012-11-30	-0.015065953850806
2012-12-31	-0.0151267483670475

Return to Figure 3

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