{"text_format":"1","workbook":"xlsx","n_sheets":2,"sheets":["Aufgabe 1","Aufgabe 2"],"not_rendered":{"charts":2,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Aufgabe 1","index":0,"n_rows":1020,"n_cols":3,"rows_kept":1020,"cut":false,"hidden":false,"merged":[]}
["Simulation von Ornstein-Uhlenbeck Pfaden:"]
[]
["Zeithorizont  T",10]
["Schrittweite  dt",0.01]
[]
["mean reversion speed   kappa",2]
["mean reversion level   mu",2]
["volatility   sigma",0.5]
[]
["Startwert   X0",5]
[]
[]
[]
[]
[]
[]
[]
[]
["tk","X(tk) mit Rekursion","X(tk) mit expliziter Formel"]
[0,5,5]
[0.01,4.9863774263858796,4.9863774263858796]
[0.02,4.8657057080984112,4.8657057080984112]
[0.03,4.8028280069861404,4.8028280069861413]
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[0.05,4.7131039931206322,4.7131039931206331]
[0.06,4.6298860781542306,4.6298860781542324]
[7.0000000000000007E-2,4.5600638123044179,4.5600638123044197]
[0.08,4.3916940141772258,4.3916940141772276]
[0.09,4.2854703331067094,4.2854703331067112]
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[0.11,4.1297617726501432,4.1297617726501441]
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[0.13,4.088911617760532,4.0889116177605329]
[0.14000000000000001,4.0817025594566063,4.0817025594566072]
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[1.1200000000000001,2.3335081235445023,2.3335081235445023]
[1.1300000000000001,2.36443319141457,2.36443319141457]
[1.1400000000000001,2.3490270485003562,2.3490270485003562]
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[8.86,1.9544649637954015,1.954464963795401]
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[8.89,2.015854520036549,2.0158545200365485]
[8.9,2.016684705798919,2.0166847057989186]
[8.91,1.9743376108898651,1.9743376108898649]
[8.92,2.1281479968861792,2.1281479968861787]
[8.93,2.1807181472332609,2.1807181472332604]
[8.94,2.1322852935449585,2.1322852935449581]
[8.9500000000000011,2.0702767529820578,2.0702767529820578]
[8.9600000000000009,2.1349489330808793,2.1349489330808793]
[8.9700000000000006,2.1075885624457662,2.1075885624457662]
[8.98,2.0788248968277254,2.0788248968277254]
[8.99,2.0254506810814936,2.0254506810814936]
[9,2.1175816918834629,2.1175816918834629]
[9.01,2.0915480895952472,2.0915480895952476]
[9.02,2.0572029430899788,2.0572029430899788]
[9.0299999999999994,2.0609595840820765,2.0609595840820765]
[9.0400000000000009,2.0794432143704209,2.0794432143704209]
[9.0500000000000007,2.0851444809366653,2.0851444809366653]
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[9.08,2.1956196370821033,2.1956196370821033]
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[9.1,2.136226856715882,2.136226856715882]
[9.11,2.1960747571063597,2.1960747571063597]
[9.120000000000001,2.164358143870742,2.164358143870742]
[9.1300000000000008,2.2171583377991286,2.2171583377991286]
[9.14,2.1851282949845676,2.1851282949845676]
[9.15,2.1434089866169961,2.1434089866169956]
[9.16,2.1616224511813025,2.161622451181302]
[9.17,2.1807399856114271,2.1807399856114267]
[9.18,2.2142879726213818,2.2142879726213813]
[9.19,2.1674045914896483,2.1674045914896478]
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[9.24,2.2420802197766627,2.2420802197766618]
[9.25,2.2219356294745287,2.2219356294745278]
[9.26,2.2495323690124946,2.2495323690124938]
[9.27,2.2276822438738373,2.2276822438738364]
[9.2799999999999994,2.1719684601509166,2.1719684601509162]
[9.2900000000000009,2.1977480090329964,2.1977480090329959]
[9.3000000000000007,2.1292890036043048,2.1292890036043044]
[9.31,2.0886002689061351,2.0886002689061351]
[9.32,2.0443593401977056,2.0443593401977052]
[9.33,1.9917369012517989,1.9917369012517987]
[9.34,1.9004997338844931,1.9004997338844927]
[9.35,1.9360266084942941,1.9360266084942936]
[9.36,1.8977788567904879,1.8977788567904876]
[9.370000000000001,1.8908765330669248,1.8908765330669246]
[9.3800000000000008,1.7561180462898636,1.7561180462898633]
[9.39,1.6832744293463813,1.6832744293463811]
[9.4,1.6839926633031701,1.6839926633031699]
[9.41,1.7471159947848027,1.7471159947848025]
[9.42,1.7627728172021102,1.76277281720211]
[9.43,1.7698587803164574,1.7698587803164569]
[9.44,1.7704442576127313,1.7704442576127311]
[9.4500000000000011,1.8197686643248718,1.8197686643248716]
[9.4600000000000009,1.7863098891008897,1.7863098891008895]
[9.4700000000000006,1.6885273310741209,1.6885273310741207]
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[9.5,1.6994852391978714,1.6994852391978712]
[9.51,1.6387997071682017,1.6387997071682014]
[9.52,1.6951431914889643,1.6951431914889641]
[9.5299999999999994,1.6852493611007286,1.6852493611007282]
[9.5400000000000009,1.6704229732840028,1.6704229732840024]
[9.5500000000000007,1.5596562584319702,1.5596562584319698]
[9.56,1.5425580069300941,1.5425580069300937]
[9.57,1.535499014693485,1.5354990146934846]
[9.58,1.6107096793981657,1.6107096793981655]
[9.59,1.5886706149853884,1.5886706149853882]
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[9.61,1.5229503287832962,1.5229503287832959]
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[10,1.8208951515884197,1.82089515158842]

{"sheet":"Aufgabe 2","index":1,"n_rows":520,"n_cols":5,"rows_kept":520,"cut":false,"hidden":false,"merged":[]}
["Simulation von Ornstein-Uhlenbeck Pfaden:"]
[]
["Zeithorizont  T",5]
["Schrittweite  dt",0.01]
[]
["mean reversion speed   kappa",1]
["mean reversion level   mu",2]
["volatility   sigma",3]
[]
["Startwert   X0",4]
["Anzahl MC Simus  N",5000]
[]
[]
[]
[]
[]
[]
[]
["tk","E[ X(tk) ]  analytisch","E[ X(tk) ]  Monte Carlo","V[ X(tk) ]  analytisch","V[ X(tk) ]  Monte Carlo"]
[0,4,4,0,0]
[0.01,3.9800996674983362,3.983180638015281,8.9105970119601363E-2,8.8444193282723738E-2]
[0.02,3.9603973466135107,3.9592041553932416,0.1764475238145457,0.17340133590680298]
[0.03,3.9408910670970165,3.9329019938742333,0.26205959887088076,0.26033031953881497]
[0.04,3.9215788783046461,3.9169818515156547,0.3459764412601391,0.34737050600475999]
[0.05,3.902458849001428,3.8914357941418092,0.42823161883818217,0.43231195061436384]
[0.06,3.8835290671684977,3.8715642874386269,0.50885803477279135,0.50873732396159899]
[7.0000000000000007E-2,3.8647876398118965,3.8506099877334621,0.58788794070537365,0.58514343596643315]
[0.08,3.8462326927732713,3.8250751951099811,0.66535294965204894,0.6641483213841809]
[0.09,3.8278623705424564,3.8105761323282619,0.741284048649276,0.7419400129889685]
[0.1,3.809674836071919,3.7969086792391944,0.81571161114908186,0.819772559753006]
[0.11,3.7916682705930564,3.7790734534521078,0.88866540916884684,0.89722274523653744]
[0.12,3.773840873434315,3.7606006358759201,0.96017462520050945,0.95338827674988313]
[0.13,3.7561908618411226,3.7424115509515627,1.0302678638839518,1.0231472953775655]
[0.14000000000000001,3.7387164707976117,3.7202816307030595,1.0989731634492355,1.0808658078213116]
[0.15,3.7214159528501156,3.6981987478176461,1.1663180069322696,1.1546304299522594]
[0.16,3.7042875779324227,3.6782779664823715,1.2323293331683907,1.2199741637322792]
[0.17,3.6873296331927676,3.6589671455263093,1.2970335475682566,1.2799857030399715]
[0.18,3.670540422822544,3.6477604858818116,1.3604565326803604,1.3288685844276844]
[0.19,3.6539182678867244,3.6314549412551518,1.4226236585443988,1.3910008812729115]
[0.2,3.6374615061559634,3.6223940668432806,1.4835597928396229,1.4511563842609294]
[0.21,3.6211684919403742,3.6107994270171386,1.5432893108322445,1.5138566642423812]
[0.22,3.6050375959249568,3.5927886906448161,1.6018361051258636,1.5675942549666033]
[0.23,3.5890672050066681,3.5840435459048807,1.6592235952188332,1.6408277585599771]
[0.24,3.5732557221331067,3.5682109341849007,1.7154747368723662,1.6890742514461541]
[0.25,3.55760156614281,3.5571502720915,1.7706120312931497,1.7512240070927514]
[0.26,3.5421031716071325,3.5435682032218292,1.8246575341341253,1.7973347418231551]
[0.27,3.5267589886737065,3.533296999770565,1.8776328643170466,1.8459422882473886]
[0.28000000000000003,3.5115674829114507,3.5193801815586956,1.9295592126803331,1.9007783133189591]
[0.28999999999999998,3.4965271351571303,3.5034872783212747,1.9804573504556908,1.9543807249612568]
[0.3,3.4816364413634355,3.4868444450445089,2.030347637576881,2.0021848009783607]
[0.31,3.4668939124485787,3.4710657703127117,2.0792500308239648,2.0711533456575251]
[0.32,3.4522980741473819,3.4552262721797886,2.1271840918062814,2.1349135733362101]
[0.33,3.4378474668638521,3.4485941640319266,2.1741689947873537,2.1835949429656694]
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[0.35000000000000003,3.4093761794374267,3.4172640546414352,2.2653661329386572,2.2591711332792528]
[0.36,3.3953526521420621,3.4054767614446537,2.3096148481801273,2.3084023990271909]
[0.37,3.3814686612747096,3.3908737089443357,2.3529873801553451,2.3580836821211464]
[0.38,3.3677228184247117,3.3855635115482428,2.3955010784554083,2.406570949823053]
[0.39,3.3541137489963293,3.3793288923891631,2.4371729491264942,2.4569198822407592]
[0.4,3.3406400920712787,3.3764068180243441,2.4780196614725032,2.4950086335907677]
[0.41000000000000003,3.3273005002726386,3.3655108304791859,2.5180575547230033,2.5348175123911196]
[0.42,3.3140936396301135,3.3443631565353673,2.5573026445691411,2.5642046344577096]
[0.43,3.3010181894466331,3.3262514961909839,2.5957706295701302,2.6034320045881825]
[0.44,3.288072842166283,3.3091102427709114,2.6334768974328839,2.6152962292855002]
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[0.51,3.2009911576245318,3.2282489251942019,2.8773227692211476,2.8992260441844802]
[0.52,3.1890410959403885,3.2158103306122632,2.9094539311854892,2.916134622781112]
[0.53,3.1772099393567101,3.2076032320068086,2.9409488535147417,2.972472332651761]
[0.54,3.1654965047479795,3.1990738962971945,2.9718201345977739,2.9965145511732381]
[0.55000000000000004,3.1538996207609733,3.1857993222664724,3.0020801233586418,3.0310646834392805]
[0.56000000000000005,3.1424181276976295,3.1739428097304656,3.0317409241963222,3.0554018283667737]
[0.57000000000000006,3.1310508773990744,3.1613549704474297,3.0608144018266326,3.0917710112398638]
[0.57999999999999996,3.1197967331308041,3.1513537305564476,3.089312186028276,3.1178128434710359]
[0.59,3.1086545694690142,3.1371765320975658,3.1172456762949095,3.1464647712154856]
[0.6,3.097623272188053,3.1272380129385327,3.1446260463950906,3.1859022654291453]
[0.61,3.0867017381489994,3.1248651104245062,3.1714642488419362,3.2163360969671615]
[0.62,3.0758888751893489,3.1109048122889456,3.1977710192742723,3.2183355037909713]
[0.63,3.0651836020137946,3.1027958320223847,3.2235568807510333,3.2382892723039411]
[0.64,3.0545848480860971,3.0902595654703173,3.2488321479606266,3.2540302465445343]
[0.65,3.0440915535220321,3.0775041410125437,3.2736069313469431,3.2711155614879308]
[0.66,3.0337026689833984,3.0686364253351255,3.2978911411536735,3.3212728251743284]
[0.67,3.0234171555730849,3.0585899120773168,3.3216944913885329,3.3311976692781378]
[0.68,3.0132339847311789,3.0460733299254712,3.3450265037089983,3.3463932665331972]
[0.69000000000000006,3.0031521381321111,3.0366997658347334,3.3678965112310961,3.3989819101862917]
[0.70000000000000007,2.9931706075828188,3.0222944964321474,3.3903136622627712,3.4239058928271318]
[0.71,2.9832883949219302,3.0135997404259873,3.412286923963336,3.4659966892799794]
[0.72,2.9735045119199435,3.004822364657163,3.4338250859304522,3.4990347741924248]
[0.73,2.963817980180405,2.9962261132972934,3.454936763716085,3.5011475578209161]
[0.74,2.9542278310420689,2.9802279124732527,3.4756304022728428,3.5242783200862848]
[0.75,2.9447331054820296,2.9707432147708528,3.4959142793320659,3.5170966134865251]
[0.76,2.9353328540198182,2.9593078888414817,3.5157965087150336,3.5615754940065338]
[0.77,2.9260261366224563,2.9478688896120535,3.5352850435785994,3.5646015248027965]
[0.78,2.916812022610447,2.9352570230230284,3.5543876795965588,3.5974960881901281]
[0.79,2.9076895905647118,2.9281849816171421,3.5731120580780247,3.6221584589796896]
[0.8,2.8986579282344431,2.9167054021395016,3.5914656690240507,3.6520767471516091]
[0.81,2.8897161324458822,2.9115043400085416,3.609455854123734,3.6961073772352866]
[0.82000000000000006,2.8808633090119984,2.9023718103151346,3.6270898096909865,3.6971105170359442]
[0.83000000000000007,2.872098572643071,2.8933176234619866,3.6443745895431578,3.7388192057905276]
[0.84,2.8634210468581593,2.8829460613878983,3.6613171078226552,3.7566430939072299]
[0.85,2.8548298638974536,2.8668368096978387,3.677924141762694,3.7571424500995061]
[0.86,2.8463241646354978,2.8539120764589874,3.6942023343982804,3.7752369280561378]
[0.87,2.837903098495278,2.851470043478229,3.7101581972235143,3.7938060747746718]
[0.88,2.8295658233631626,2.8389379809709685,3.7257981127962725,3.7829116113694168]
[0.89,2.8213115055046911,2.8259178315770765,3.7411283372913204,3.8059149070316183]
[0.9,2.8131393194811984,2.8222613391515008,3.7561550030028608,3.8211681048666213]
[0.91,2.8050484480672719,2.8075144252228803,3.7708841207975365,3.8296401465346714]
[0.92,2.7970380821690282,2.8058771221309411,3.7853215825188569,3.8242156519875845]
[0.93,2.7891074207432021,2.8036639076766225,3.799473163344012,3.8203407405794678]
[0.94000000000000006,2.7812556707170422,2.7903794350021913,3.8133445240940227,3.8521939537156293]
[0.95000000000000007,2.7734820469090025,2.7848335059595191,3.8269412134981424,3.888017272588602]
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