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{"sheet":"Dislcaimer","index":0,"n_rows":31,"n_cols":11,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["Interest Rate Derivatives Explained II (Illustrations)"]
[]
[]
[]
["This sheet does only serve for illustration purposes! It illustrates pricing using MC for Hull-White covering method of Andersen& Piterbarg and C. Fries",null,null,null,null,null,null,null,null,null,"The code comes with BSD License"]
[null,null,null,null,null,null,null,null,null,null,"'Copyright 2017 Dr. Joerg Kienitz"]
["This illustration and any accompanying material are being provided solely for information and general illustrative"]
["purposes. The author will not be responsible for the consequences of reliance upon any information contained in or",null,null,null,null,null,null,null,null,null,"'Redistribution and use in source and binary forms, with or without modification,"]
["derived from the presentation or for any omission of information therefrom and hereby excludes all liability for loss",null,null,null,null,null,null,null,null,null,"'are permitted provided that the following conditions are met:"]
["or damage (including, without limitation, direct, indirect, foreseeable, or consequential loss or damage and"]
["including loss or profit and even if advised of the possibility of such damages or if such damages were foreseeable)",null,null,null,null,null,null,null,null,null,"'1. Redistributions of source code must retain the above copyright notice,"]
["that may be incurred or su\u000bered by any person in connection with the presentation, including (without limitation)",null,null,null,null,null,null,null,null,null,"'this list of conditions and the following disclaimer."]
["for the consequences of reliance upon any results derived therefrom or any error or omission whether negligent or"]
["not. No representation or warranty is made or given by the author that the presentation or any content thereof will",null,null,null,null,null,null,null,null,null,"'2. Redistributions in binary form must reproduce the above copyright notice,"]
["be error free, updated, complete or that inaccuracies, errors or defects will be corrected.",null,null,null,null,null,null,null,null,null,"'this list of conditions and the following disclaimer in the documentation"]
["The views are solely that of the author.",null,null,null,null,null,null,null,null,null,"'and/or other materials provided with the distribution."]
["The presentation may not be reproduced in whole or part or delivered to any other person without prior permission"]
["of the author. It is accompanying material for the book Interest Rate Derivatives Explained II!",null,null,null,null,null,null,null,null,null,"'3. Neither the name of the copyright holder nor the names of its contributors"]
[null,null,null,null,null,null,null,null,null,null,"'may be used to endorse or promote products derived from this software without"]
["For comments, hints, bugs or suggestions, please,",null,null,null,null,null,null,null,null,null,"'specific prior written permission."]
["Contact:"]
["joerg.kienitz@gmx.de",null,null,null,null,null,null,null,null,null,"'THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS"]
[null,null,null,null,null,null,null,null,null,null,"'\"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,"]
[null,null,null,null,null,null,null,null,null,null,"'THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE"]
[null,null,null,null,null,null,null,null,null,null,"'ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE"]
[null,null,null,null,null,null,null,null,null,null,"'FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES"]
[null,null,null,null,null,null,null,null,null,null,"'(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;"]
[null,null,null,null,null,null,null,null,null,null,"'LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON"]
[null,null,null,null,null,null,null,null,null,null,"'ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,"]
[null,null,null,null,null,null,null,null,null,null,"'OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF"]
[null,null,null,null,null,null,null,null,null,null,"'THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE."]

{"sheet":"INPUT","index":1,"n_rows":44,"n_cols":20,"rows_kept":44,"cut":false,"hidden":false,"merged":[]}
[null,"delta_t",0.5,null,null,null,null,null,"MC",null,"Analytic",null,null,"Analytic"]
["ATM","strike",0.05,{"$f":"(1-C18)/(SUM(C11:C18)*0.5)","v":5.0630241048857702E-2},null,null,"swpt/cpl",1,50.008410869747202,1.5146376989120119E-5,{"$f":"hw_cflet(IF(H4=1,\"c\",\"p\"),C4,C5,H6,H5,H5+0.5)*10000","v":50.041998091536755},"Caplet","Swaption",{"$f":"hw_coupon_opt(C4,C5,H5,H5+S2,H6,1,1,IF(S5=1,\"p\",\"r\"))*10000","v":454.20219736495989},454.12223565862053,1.2801419564885535E-4,null,"Swaptenor",5]
[null,"CapStrike^{-1}",{"$f":"1+C2*C1","v":1.0249999999999999},null,null,null,"cpltenor",0.5,null,null,null,null,null,null,null,null,null,"Swapperiod",1]
[null,"kappa",1.4999999999999999E-2,null,null,"1/-1","cpl/fl",1,50.039879410517571,1.5218295751538503E-5,null,null,null,null,454.27915074202701,1.2776704950869257E-4,null,"Strike",0.04]
[null,"sigma",8.0000000000000002E-3,null,null,null,"T",7,0.9749645065401874,null,null,null,null,null,null,null,null,"PayRec",1,"1/-1"]
[null,null,null,null,null,null,"Strike",0.04]
[]
[]
["Time","Zero Curve","NPV","Fwd","Caplet","Floorlet","Cap","Floor",null,null,null,null,"Nsim",100000]
[0,0.05,{"$f":"_xludf.pv(A10)","v":1},{"$f":"-1/$C$1*LN(C11/C10)","v":5.0000000000000107E-2},0,0,{"$f":"SUM($E$10:E10)","v":0},{"$f":"SUM($F$10:F10)","v":0},null,null,null,null,"Nt",1]
[{"$f":"A10+$C$1","v":0.5},{"$f":"-LN(C11)/A11","v":5.0000000000000107E-2},{"$f":"_xludf.pv(A11)","v":0.97530991202833262},4.9999999999999885E-2,{"$f":"$C$3*hw_zero_opt(\"p\",$C$4,$C$5,1/$C$3,A11,A12,C11,C12)*10000","v":12.485521743068443},{"$f":"$C$3*hw_zero_opt(\"c\",$C$4,$C$5,1/$C$3,A11,A12,C11,C12)*10000","v":9.488002592060603},{"$f":"SUM($E$10:E11)","v":12.485521743068443},{"$f":"SUM($F$10:F11)","v":9.488002592060603}]
[1,{"$f":"-LN(C12)/A12","v":4.9999999999999996E-2},0.95122942450071402,5.0000000000000107E-2,{"$f":"$C$3*hw_zero_opt(\"p\",$C$4,$C$5,1/$C$3,A12,A13,C12,C13)*10000","v":16.514666052379791},{"$f":"$C$3*hw_zero_opt(\"c\",$C$4,$C$5,1/$C$3,A12,A13,C12,C13)*10000","v":13.591155912905027},{"$f":"SUM($E$10:E12)","v":29.000187795448234},{"$f":"SUM($F$10:F12)","v":23.07915850496563}]
[1.5,5.0000000000000024E-2,0.92774348632855286,5.0000000000000107E-2,{"$f":"$C$3*hw_zero_opt(\"p\",$C$4,$C$5,1/$C$3,A13,A14,C13,C14)*10000","v":19.321872428062441},{"$f":"$C$3*hw_zero_opt(\"c\",$C$4,$C$5,1/$C$3,A13,A14,C13,C14)*10000","v":16.470544011118587},{"$f":"SUM($E$10:E13)","v":48.322060223510675},{"$f":"SUM($F$10:F13)","v":39.549702516084217}]
[2,5.0000000000000031E-2,0.90483741803595952,4.9999999999999656E-2,21.460297712506023,18.679368845013432,{"$f":"SUM($E$10:E14)","v":69.782357936016695},{"$f":"SUM($F$10:F14)","v":58.229071361097652}]
[2.5,4.9999999999999975E-2,0.88249690258459546,5.0000000000000107E-2,23.153402431865516,20.4411349427522,{"$f":"SUM($E$10:E15)","v":92.93576036788221},{"$f":"SUM($F$10:F15)","v":78.670206303849852}]
[3,4.9999999999999996E-2,0.86070797642505781,4.9999999999999885E-2,24.520249757551127,21.874948391348205,{"$f":"SUM($E$10:E16)","v":117.45601012543334},{"$f":"SUM($F$10:F16)","v":100.54515469519805}]
[3.5,4.9999999999999996E-2,0.83945702076920736,5.0000000000000107E-2,25.634188350232254,23.054199707471522,{"$f":"SUM($E$10:E17)","v":143.0901984756656},{"$f":"SUM($F$10:F17)","v":123.59935440266958}]
[4,5.000000000000001E-2,0.81873075307798182,4.9999999999999885E-2,26.5447051273391,24.028416631134561,{"$f":"SUM($E$10:E18)","v":169.63490360300472},{"$f":"SUM($F$10:F18)","v":147.62777103380415}]
[4.5,4.9999999999999996E-2,0.79851621875937706,5.0000000000000107E-2,27.287339630971076,24.833178519099736,{"$f":"SUM($E$10:E19)","v":196.92224323397579},{"$f":"SUM($F$10:F19)","v":172.46094955290388}]
[5,0.05,0.77880078307140488,5.0000000000000107E-2,27.888802042083608,25.495234383961424,{"$f":"SUM($E$10:E20)","v":224.81104527605939},{"$f":"SUM($F$10:F20)","v":197.9561839368653}]
[5.5,0.05,0.75957212322496848,4.9999999999999885E-2,28.36987022961139,26.03539996753458,{"$f":"SUM($E$10:E21)","v":253.18091550567078},{"$f":"SUM($F$10:F21)","v":223.99158390439987}]
[6,4.9999999999999996E-2,0.74081822068171788,4.9999999999999885E-2,28.74714763995788,26.470315654019029,{"$f":"SUM($E$10:E22)","v":281.92806314562864},{"$f":"SUM($F$10:F22)","v":250.46189955841891}]
[6.5,4.9999999999999996E-2,0.72252735364207221,5.0000000000000107E-2,29.034189686588785,26.813572882677956,{"$f":"SUM($E$10:E23)","v":310.96225283221742},{"$f":"SUM($F$10:F23)","v":277.27547244109684}]
[7,4.9999999999999996E-2,0.70468808971871344,4.9999999999999885E-2,29.242257935963956,27.076468356294722,{"$f":"SUM($E$10:E24)","v":340.20451076818136},{"$f":"SUM($F$10:F24)","v":304.35194079739153}]
[7.5,4.9999999999999996E-2,0.68728927879097224,5.0000000000000107E-2,29.380843736416011,27.268527691996134,{"$f":"SUM($E$10:E25)","v":369.58535450459738},{"$f":"SUM($F$10:F25)","v":331.62046848938769}]
[8,4.9999999999999996E-2,0.67032004603563933,5.0000000000000107E-2,29.45804302306486,27.397880247605713,{"$f":"SUM($E$10:E26)","v":399.04339752766225},{"$f":"SUM($F$10:F26)","v":359.0183487369934}]
[8.5,4.9999999999999996E-2,0.65376978512984729,4.9999999999999885E-2,29.480831659400138,27.471534484103632,{"$f":"SUM($E$10:E27)","v":428.52422918706236},{"$f":"SUM($F$10:F27)","v":386.48988322109705}]
[9,4.9999999999999996E-2,0.63762815162177333,5.0000000000000336E-2,29.455272297542948,27.495584846264194,{"$f":"SUM($E$10:E28)","v":457.97950148460529},{"$f":"SUM($F$10:F28)","v":413.98546806736124}]
[9.5,5.000000000000001E-2,0.62188505646502001,4.9999999999999885E-2,29.386672858073233,27.475370262364773,{"$f":"SUM($E$10:E29)","v":487.36617434267851},{"$f":"SUM($F$10:F29)","v":441.46083832972602}]
[10,0.05,0.60653065971263342]
[]
[]
[]
["Pricing Swaption"]
[]
[]
["T (Option)",7]
["T (Bond)",10]
["Strike",{"$f":"atm(B37,B38,1)","v":5.127109637602404E-2}]
["delta_t",1]
[null,"swaption",null,"bond"]
[null,"Payers","Receivers"]
[null,{"$f":"hw_coupon_opt(C4,C5,B37,B38,B39,B40,1,\"p\")*10000","v":157.88176312580654},{"$f":"hw_coupon_opt(C4,C5,B37,B38,B39,B40,1,\"c\")*10000","v":157.88176310553516}]
[null,{"$f":"hw_coupon_opt(C4,C5,B37,B37+B38,B39,+B40,1,\"p\")*10000","v":425.38438420551171},{"$f":"hw_coupon_opt(C4,C5,B37,B37+B38,B39,+B40,1,\"c\")*10000","v":425.3843842055075}]

{"sheet":"MC HW","index":2,"n_rows":40,"n_cols":12,"rows_kept":40,"cut":false,"hidden":false,"merged":[]}
[null,"dt",1]
[]
[null,"x(t)","I(t)",null,null,"f(0,t)","r(t) = x(t) + f(0,t)","DF","Sum  x(t)","Trapz x(t)","DF Sum","DF Trapz"]
[0,0,0,null,null,{"$f":"forward(A4)","v":5.0000000000033351E-2},{"$f":"B4+F4","v":5.0000000000033351E-2},{"$f":"EXP(C4)","v":1},0,{"$f":"SUM($I$18:I18)","v":4.064077466494914E-3},{"$f":"EXP(I4)","v":1},{"$f":"EXP(J4)","v":1.0040723470282398}]
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[3,{"$f":"HW_MC(B6,C6,INPUT!$C$4,INPUT!$C$5,A7,A6,D7,E7)","v":-2.7903793854434631E-3},1.5891824602987568E-2,0.66668546598196032,1.2147445039855973,5.0000000000036127E-2,4.7209620614592662E-2,1.0160187712272475,{"$f":"-SUM($B$4:B7)*$C$1","v":1.9280130015087882E-2},{"$f":"SUM($I$18:I21)","v":2.6560621065293527E-2},1.0194671919807785,1.0269164981468908]
[4,{"$f":"HW_MC(B7,C7,INPUT!$C$4,INPUT!$C$5,A8,A7,D8,E8)","v":-1.4560982100411294E-2},7.2372044928549718E-3,-1.5141857599492343,-2.3000591844603475,5.0000000000063882E-2,3.5439017899652592E-2,1.0072634563490952,{"$f":"-SUM($B$4:B8)*$C$1","v":3.3841112115499172E-2},{"$f":"SUM($I$18:I22)","v":3.7662940251899382E-2},1.0344202368271564,1.0383811773889211]
[5,{"$f":"HW_MC(B8,C8,INPUT!$C$4,INPUT!$C$5,A9,A8,D9,E9)","v":-7.6436562728004224E-3},2.5411201397017566E-2,0.8101817401251673,0.27476606487305993,5.0000000000022249E-2,4.2356343727221829E-2,1.0257368182297726,{"$f":"-SUM($B$4:B9)*$C$1","v":4.1484768388299592E-2},{"$f":"SUM($I$18:I23)","v":4.4463767625958793E-2},1.0423572849491409,1.0454670962693307]
[6,{"$f":"HW_MC(B9,C9,INPUT!$C$4,INPUT!$C$5,A10,A9,D10,E10)","v":-5.957998475318394E-3},3.0269963376670487E-2,0.1573964696151981,-1.3838452332535045,5.0000000000050004E-2,4.404200152473161E-2,1.0307327564922666,{"$f":"-SUM($B$4:B10)*$C$1","v":4.7442766863617987E-2},{"$f":"SUM($I$18:I24)","v":5.2275856774179029E-2},1.0485861855276966,1.0536663634307244]
[7,{"$f":"HW_MC(B10,C10,INPUT!$C$4,INPUT!$C$5,A11,A10,D11,E11)","v":-9.6661798211220788E-3},3.3453306757517669E-2,-0.52541819182688543,-0.19943793352081146,5.0000000000050004E-2,4.0333820178927927E-2,1.0340191608916354,{"$f":"-SUM($B$4:B11)*$C$1","v":5.7108946684740064E-2},{"$f":"SUM($I$18:I25)","v":6.5460485758282366E-2},1.0587711537193458,1.0676505490781192]
[8,{"$f":"HW_MC(B11,C11,INPUT!$C$4,INPUT!$C$5,A12,A11,D12,E12)","v":-1.6703078147084594E-2},3.7793589136032257E-2,-0.95806998925957887,-0.53717136779511976,5.0000000000022249E-2,3.3296921852937658E-2,1.0385168495935697,{"$f":"-SUM($B$4:B12)*$C$1","v":7.3812024831824655E-2},{"$f":"SUM($I$18:I26)","v":8.0865922084539757E-2},1.0766044115789757,1.0842255161237342]
[9,{"$f":"HW_MC(B12,C12,INPUT!$C$4,INPUT!$C$5,A13,A12,D13,E13)","v":-1.4107794505430187E-2},5.3854361528350533E-2,0.23550686969963616,-0.52736570076228662,4.9999999999994493E-2,3.5892205494564303E-2,1.0553308941839412,{"$f":"-SUM($B$4:B13)*$C$1","v":8.7919819337254845E-2},{"$f":"SUM($I$18:I27)","v":9.8940349799436389E-2},1.0919005692069319,1.1040004437468534]
[10,{"$f":"HW_MC(B13,C13,INPUT!$C$4,INPUT!$C$5,A14,A13,D14,E14)","v":-2.2041060924363063E-2},6.1620657031532508E-2,-1.0916857455694651,-0.71141019776476766,4.9999999999994493E-2,2.795893907563143E-2,1.0635588146368373,{"$f":"-SUM($B$4:B14)*$C$1","v":0.1099608802616179},{"$f":"SUM($I$18:I28)","v":0.10996088026161792},1.1162344028069324,1.1162344028069324]
[]
[]
[null,"x(t)  Approx","I(t) Approx",null,null,"f(0,t)","r(t) Approx= x(t) Approx + f(0,t)","DF Approx"]
[0,0,0,null,null,{"$f":"forward(A18)","v":5.0000000000033351E-2},{"$f":"B18+F18","v":5.0000000000033351E-2},{"$f":"EXP(C18)","v":1},{"$f":"-$C$1/2*(B4+B5)","v":4.064077466494914E-3}]
[{"$f":"A18+$C$1","v":1},{"$f":"HW_MC_Approx(B18,C18,INPUT!$C$4,INPUT!$C$5,A19,A18,D19)","v":-8.2209526220536587E-3},0,{"$f":"D5","v":-1.0276190777567074},null,4.9999999999994493E-2,4.1779047377940831E-2,1,8.2448753148222087E-3]
[{"$f":"A19+$C$1","v":2},{"$f":"HW_MC_Approx(B19,C19,INPUT!$C$4,INPUT!$C$5,A20,A19,D20)","v":-8.4869656515942308E-3},8.2209526220536587E-3,-5.6373260147775245E-2,null,4.9999999999987554E-2,4.1513034348393325E-2,1.0082548374445863,5.5759875410490269E-3]
[3,{"$f":"HW_MC_Approx(B20,C20,INPUT!$C$4,INPUT!$C$5,A21,A20,D21)","v":-2.9038189308876411E-3},1.6707918273647891E-2,0.66668546598196032,null,5.0000000000036127E-2,4.7096181069148486E-2,1.0168482761465372,8.6756807429273792E-3]
[4,{"$f":"HW_MC_Approx(B21,C21,INPUT!$C$4,INPUT!$C$5,A22,A21,D22)","v":-1.4791829548709168E-2},1.9611737204535531E-2,-1.5141857599492343,null,5.0000000000063882E-2,3.5208170451354714E-2,1.0198053106892444,1.1102319186605859E-2]
[5,{"$f":"HW_MC_Approx(B22,C22,INPUT!$C$4,INPUT!$C$5,A23,A22,D23)","v":-7.8507178348051938E-3},3.4403566753244699E-2,0.8101817401251673,null,5.0000000000022249E-2,4.2149282165217059E-2,1.0350022149395393,6.8008273740594082E-3]
[6,{"$f":"HW_MC_Approx(B23,C23,INPUT!$C$4,INPUT!$C$5,A24,A23,D24)","v":-6.1797253703177084E-3},4.225428458804989E-2,0.1573964696151981,null,5.0000000000050004E-2,4.3820274629732293E-2,1.0431597044636483,7.8120891482202359E-3]
[7,{"$f":"HW_MC_Approx(B24,C24,INPUT!$C$4,INPUT!$C$5,A25,A24,D25)","v":-9.9422657788991106E-3},4.8434009958367601E-2,-0.52541819182688543,null,5.0000000000050004E-2,4.0057734221150894E-2,1.0496261046645337,1.3184628984103337E-2]
[8,{"$f":"HW_MC_Approx(B25,C25,INPUT!$C$4,INPUT!$C$5,A26,A25,D26)","v":-1.7057733253105653E-2},5.8376275737266711E-2,-0.95806998925957887,null,5.0000000000022249E-2,3.2942266746916596E-2,1.0601138157800434,1.5405436326257391E-2]
[9,{"$f":"HW_MC_Approx(B26,C26,INPUT!$C$4,INPUT!$C$5,A27,A26,D27)","v":-1.4467924784482033E-2},7.5434008990372364E-2,0.23550686969963616,null,4.9999999999994493E-2,3.5532075215512458E-2,1.0783520638285626,1.8074427714896625E-2]
[10,{"$f":"HW_MC_Approx(B27,C27,INPUT!$C$4,INPUT!$C$5,A28,A27,D28)","v":-2.248498806817054E-2},8.9901933774854392E-2,-1.0916857455694651,null,4.9999999999994493E-2,2.7515011931823954E-2,1.0940669874247126,{"$f":"-$C$1/2*(B14+C15)","v":1.1020530462181531E-2}]
[]
[null,"Rel Error r","Rel Erro DF"]
[null,{"$f":"(B5-B19)/B5","v":-1.1416820893409858E-2},{"$f":"(H4-H18)","v":0}]
[null,-1.4993544233405022E-2,-5.3242048017914101E-3]
[null,-4.0653807161834928E-2,-6.0401352757746274E-3]
[null,-1.5853837791020512E-2,-8.2950491928968084E-4]
[null,-2.7089334555975505E-2,-1.2541854340149206E-2]
[null,-3.7214996935269515E-2,-9.2653967097666712E-3]
[null,-2.8562054802016189E-2,-1.2426947971381663E-2]
[null,-2.1232919040312423E-2,-1.5606943772898285E-2]
[null,-2.5527043147192809E-2,-2.1596966186473665E-2]
[null,-2.0140915418312835E-2,-2.302116964462142E-2]