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{"sheet":"FonctionsExcel","index":0,"n_rows":21,"n_cols":5,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["CALCUL MATRICIEL AVEC EXCEL"]
[null,null,null,null,"Auteur: Ph Duchemin"]
[]
[null,"Fonction ","Objet","Entrée","Sortie"]
[null,"TRANSPOSE(M)","Transpose un vecteur ligne","Vecteur ligne n","Vecteur colonne n"]
[null,"(uk: TRANSPOSE)","Transpose un vecteur colonne","Vecteur colonne n","Vecteur ligne n"]
[null,null,"Transpose une matrice mxn","Matrice nxp","Matrice pxn"]
[]
[null,"PRODUITMAT(A,B)","Retourne le produit matriciel de 2 matrices","Matrice mxn et matrice nxp","Matrice Carrée mxp"]
[null,"(uk: MMLT)"]
[]
[null,"INVERSEMAT(M)","Retourne la matrice inverse","Matrice Carrée nxn","Matrice Carrée nxn"]
[null,"(uk: MATINVERSE)"]
[]
[null,"DETERMAT(M)","Retourne le déterminant de la matrice","Matrice Carrée nxn","Scalaire"]
[null,"(uk: DET)"]
[]
[null,"PRINCIPE DE SAISIE","SI L'ARGUMENT DE SORTIE EST UNE TABLE"]
[null,null,"1 - IL FAUT SELECTIONNER LA ZONE DE SORTIE"]
[null,null,"2 - ENSUITE SAISIR LA FORMULE, PAR DEFINITION COMMENCANT PAR LE SIGNE \"=\""]
[null,null,"3 - PUIS SAISIR LA SEQUENCE SUIVANTE : \"CTRL +  MAJ\"  et \"ENTER\""]

{"sheet":"Exemples","index":1,"n_rows":80,"n_cols":13,"rows_kept":80,"cut":false,"hidden":false,"merged":[]}
["MATRICES - Exemples"]
[]
[null,"PRINCIPE DE SAISIE",null,"SI L'ARGUMENT DE SORTIE EST UNE TABLE",null,null,null,"SELECTIONNER LA ZONE DE SORTIE EN PREMIER"]
[null,null,null,null,null,null,null,"SAISIR LA FORMULE"]
[null,null,null,null,null,null,null,"PUIS SAISIR LA SEQUENCE SUIVANTE : CTRL +  MAJ  et ENTER"]
[]
[]
["ADDITION DE DEUX MATRICES",null,null,"Somme des cellules en référence relative",null,null,null,null,null,null,null,null,"Fonction"]
["FONCTION ALGEBRIQUE: PLUS (+)"]
[null,null,"A",null,"+",null,"B",null,"=",null,"S"]
[]
[null,3,-2,6,null,4,0,4,null,{"$f":"B12:D13+F12:H13","v":7},-2,10,{"$f":"form(J12)","v":"=B12:D13+F12:H13"}]
[null,2,-7,-6,null,-6,1,0,null,-4,-6,-6]
[]
["MULTIPLICATION PAR UN NOMBRE",null,null,"Multiplication des cellules en référence absolue"]
["FONCTION ALGEBRIQUE: MULTIPLICATION (*)"]
[null,null,null,"a","x",null,"A",null,"=",null,"aA"]
[]
[null,null,null,5,null,3,-2,6,null,{"$f":"D19*F19:H20","v":15},-10,30,{"$f":"form(J19)","v":"=D19*F19:H20"}]
[null,null,null,null,null,2,-7,-6,null,10,-35,-30]
[]
["DETERMINANT D'UNE MATRICE",null,null,"Fonction DETERMAT avec un argument table en entrée et un argument cellule en sortie"]
["FONCTION: DETERMAT"]
[null,null,"A",null,null,null,null,null,null,"DET(A)"]
[]
[null,3,-2,null,null,null,null,null,null,{"$f":"MDETERM(B26:C27)","v":-17},null,null,{"$f":"form(J26)","v":"=DETERMAT(B26:C27)"}]
[null,2,-7]
[]
["TRANSPOSEE D'UNE MATRICE",null,null,"Fonction TRANSPOSE avec un argument table en entrée et en sortie"]
["FONCTION MATRICIELLE: TRANSPOSE"]
[null,null,"A",null,null,null,null,null,null,"TA"]
[]
[null,null,null,null,null,null,null,null,null,{"$f":"TRANSPOSE(B34:D35)","v":3},2,null,{"$f":"form(J33)","v":"=TRANSPOSE(B34:D35)"}]
[null,3,-2,6,null,null,null,null,null,-2,-7]
[null,2,-7,-6,null,null,null,null,null,6,-6]
[]
["PRODUIT DE DEUX MATRICES",null,null,"Fonction PRODUITMAT avec deux arguments Table en entrée, et un argument Table en sortie"]
["FONCTION MATRICIELLE: PRODUITMAT"]
[null,null,"A",null,null,null,"B",null,null,null,"AB"]
[]
[null,null,null,null,null,1,2,3]
[null,1,-2,3,null,-1,-2,-3,null,{"$f":"MMULT(B42:D43,F41:H43)","v":15},21,21,{"$f":"form(J42)","v":"=PRODUITMAT(B42:D43;F41:H43)"}]
[null,4,5,-6,null,4,5,4,null,-25,-32,-27]
[]
[]
["INVERSE D'UNE MATRICE",null,null,"Fonction INVERSEMAT avec un argument table en entrée et en sortie"]
["FONCTION MATRICIELLE: INVERSEMAT"]
[null,null,"A",null,null,null,null,null,null,"A-1"]
[]
[null,null,null,null,null,null,null,null,null,{"$f":"+MINVERSE(B51:D53)","v":-2.0761245674740483E-2},-6.9204152249134954E-2,0.16955017301038061,{"$f":"form(J50)","v":"=+INVERSEMAT(B51:D53)"}]
[null,3,7,6,null,null,null,null,null,9.6885813148788927E-2,-1.038062283737024E-2,-0.1245674740484429]
[null,-8,-7,8,null,null,null,null,null,6.4013840830449822E-2,4.6712802768166091E-2,6.0553633217993084E-2]
[null,3,-2,4]
[]
["PRODUIT SCALAIRE",null,null,"Fonction PRODUITMAT avec un argument table en entrée et en sortie"]
["FONCTION MATRICIELLE: PRODUITMAT"]
[null,null,"A",null,null,"B",null,null,null,"AB"]
[]
[null,null,null,null,null,null,null,null,null,{"$f":"MMULT(B60:D60,F60:F62)","v":-4},null,null,{"$f":"form(J59)","v":"=PRODUITMAT(B60:D60;F60:F62)"}]
[null,3,7,6,null,1]
[null,null,null,null,null,-1]
[null,null,null,null,null,0]
[]
["PRODUIT EXTERNE",null,null,"Fonction PRODUITMAT avec 2 arguments Table en entrée et une Table en sortie"]
["FONCTION MATRICIELLE: PRODUITMAT"]
[null,null,"B",null,null,"A",null,null,null,"BA"]
[]
[null,null,null,null,null,null,null,null,null,{"$f":"MMULT(C69:C71,E69:G69)","v":3},7,6,{"$f":"form(J68)","v":"=PRODUITMAT(C69:C71;E69:G69)"}]
[null,null,1,null,3,7,6,null,null,-3,-7,-6]
[null,null,-1,null,null,null,null,null,null,0,0,0]
[null,null,0]
[]
["PRODUIT D'UNE MATRICE",null,null,"Fonction PRODUITMAT avec deux arguments Table en entrée, et un argument Table en sortie"]
["ET DE SA TRANSPOSEE"]
["FONCTION MATRICIELLE: PRODUITMAT"]
[null,null,"A",null,null,null,"ATA",null,null,null,"TAA"]
[]
[null,13,-8,-3,null,{"$f":"MMULT(B78:D80,TRANSPOSE(B78:D80))","v":242},-181,-64,null,{"$f":"MMULT(TRANSPOSE(B78:D80),B78:D80)","v":242},-181,-64,{"$f":"form(J78)","v":"=PRODUITMAT(TRANSPOSE(B78:D80);B78:D80)"}]
[null,-8,10,-1,null,-181,165,3,null,-181,165,3]
[null,-3,-1,11,null,-64,3,131,null,-64,3,131]

{"sheet":"Exercice","index":2,"n_rows":90,"n_cols":18,"rows_kept":90,"cut":false,"hidden":false,"merged":[]}
["MATRICES Exercices - Application avec Autocorrection"]
[]
[]
["ADDITION DE DEUX MATRICES"]
[null,"matrice A",null,null,null,"matrice B",null,null,null,null,null,null,"A+B"]
[null,15,-85,0,null,8,78,0,"OK",null,{"$f":"AND(M6:O9=EXOMatCorr!J7:L10)","v":false},null,null,null,null,{"$f":"form(M6)","v":""}]
[null,0,55,6,null,88,0,6]
[null,-7,0,-33,null,4,1,5]
[null,2,-4,8,null,-7,-22,-77]
[]
["MULTIPLICATION PAR UN NOMBRE"]
[null,"matrice A",null,null,null,"scalaire b",null,null,null,null,null,null,"A.b"]
[null,15,-85,0,null,8,null,null,"OK",null,{"$f":"AND(M13:O16=EXOMatCorr!J14:L17)","v":false},null,null,null,null,{"$f":"form(M13)","v":""}]
[null,0,55,6]
[null,-7,0,-33]
[null,2,-4,8]
[]
["DETERMINANT D'UNE MATRICE"]
[null,"matrice A",null,null,null,null,null,null,null,null,null,null,"determinant (A)"]
[null,15,-85,0,5,null,null,null,"OK",null,{"$f":"(M20=EXOMatCorr!J21)","v":false},null,null,null,null,{"$f":"form(M20)","v":""}]
[null,0,55,6,1]
[null,-7,0,-33,8]
[null,2,-4,8,7]
[]
["TRANSPOSEE D'UNE MATRICE"]
[null,"matrice A",null,null,null,null,null,null,null,null,null,null,"AT"]
[null,15,-85,0,null,null,null,null,"OK",null,{"$f":"AND(M27:P29=EXOMatCorr!J28:M30)","v":false},null,null,null,null,null,null,{"$f":"form(O27)","v":""}]
[null,0,55,6]
[null,-7,0,-33]
[null,2,-4,8]
[]
["PRODUIT DE DEUX MATRICES"]
[null,"matrice A",null,null,null,"matrice B",null,null,null,null,null,null,"A.B"]
[null,15,-85,0,null,8,78,0,"OK",null,{"$f":"AND(M34:O37=EXOMatCorr!J35:L38)","v":false},null,null,null,null,{"$f":"form(M34)","v":""}]
[null,0,55,6,null,88,0,6]
[null,-7,0,-33,null,4,1,5]
[null,2,-4,8]
[]
["INVERSE D'UNE MATRICE"]
[null,"matrice A",null,null,null,null,null,null,null,null,null,null,"A-1"]
[null,15,-85,0,null,null,null,null,"OK",null,{"$f":"AND(M41:O43=EXOMatCorr!J42:L44)","v":false},null,null,null,null,{"$f":"form(M41)","v":""}]
[null,5,55,6]
[null,-7,0,-33]
[]
["PRODUIT SCALAIRE"]
[null,"vecteur A",null,null,null,null,"vecteur B",null,null,null,null,null,"A.B"]
[null,15,8,-7,14,null,1,null,"OK",null,{"$f":"(M47=EXOMatCorr!J48)","v":false},null,null,null,null,{"$f":"form(M47)","v":""}]
[null,null,null,null,null,null,0]
[null,null,null,null,null,null,5]
[null,null,null,null,null,null,3]
[]
["PRODUIT D'UNE MATRICE ET DE SA TRANSPOSEE"]
[]
[null,"matrice A",null,null,null,null,null,null,null,null,null,null,"A.AT"]
[null,15,-85,0,null,null,null,null,"OK",null,{"$f":"AND(M55:O57=EXOMatCorr!J56:L58)","v":false},null,null,null,null,{"$f":"form(M55)","v":""}]
[null,5,55,6]
[null,-7,0,-33]
[]
[]
["RESOLUTION D'UN SYSTEME D'EQUATIONS"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,13,"a               +",-8,"b               +",-3,"c               =",20,"OK",null,{"$f":"AND(N69:N71=EXOMatCorr!K62:K64)","v":{"$error":"#NUM!"}},null,"a=",null,null,{"$f":"form(N69)","v":""}]
[null,-8,"a               +",10,"b               +",-1,"c               =",-5,null,null,null,null,"b="]
[null,-3,"a               +",-1,"b               +",11,"c               =",0,null,null,null,null,"c="]
[]
[null,"premier membre: A",null,null,null,null,"sec membre: B"]
[]
[]
[]
[]
["CALCUL DE LA TRACE DU PRODUIT DE DEUX MATRICES CARREES"]
[]
[null,"matrice A",null,null,null,"matrice B",null,null,null,null,null,null,"trace (AB)",null,"trace (BA)"]
[null,15,-85,0,null,12,2,23,"OK",null,{"$f":"AND(M81=EXOMatCorr!L69)","v":false},null,null,null,null,{"$f":"form(M81)","v":""}]
[null,5,55,6,null,-34,0,5]
[null,-7,0,-33,null,38,-11,3]
[]
["CALCUL DE LA TRACE D'UNE MATRICE CARREE"]
[]
[null,"matrice A",null,null,null,null,null,null,null,null,null,null,"trace (A)"]
[null,15,-85,0,null,null,null,null,"OK",null,{"$f":"AND(M88=EXOMatCorr!L76)","v":false},null,null,null,null,{"$f":"form(M88)","v":""}]
[null,5,55,6]
[null,-7,0,-33]

{"sheet":"EXOMatCorr","index":3,"n_rows":90,"n_cols":14,"rows_kept":90,"cut":false,"hidden":true,"merged":[]}
["MATRICES Exercices"]
[]
[]
["ADDITION DE DEUX MATRICES"]
[]
[]
[null,15,-85,0,null,8,78,0,null,{"$f":"B7:D10+F7:H10","v":23},-7,0]
[null,0,55,6,null,88,0,6,null,88,55,12]
[null,-7,0,-33,null,4,1,5,null,-3,1,-28]
[null,2,-4,8,null,-7,-22,-77,null,-5,-26,-69]
[]
["MULTIPLICATION PAR UN NOMBRE"]
[]
[null,15,-85,0,null,8,null,null,null,{"$f":"B14:D17*F14","v":120},-680,0]
[null,0,55,6,null,null,null,null,null,0,440,48]
[null,-7,0,-33,null,null,null,null,null,-56,0,-264]
[null,2,-4,8,null,null,null,null,null,16,-32,64]
[]
["DETERMINANT D'UNE MATRICE"]
[]
[null,15,-85,0,5,null,null,null,null,{"$f":"MDETERM(B21:E24)","v":-212325}]
[null,0,55,6,1]
[null,-7,0,-33,8]
[null,2,-4,8,7]
[]
["TRANSPOSEE D'UNE MATRICE"]
[]
[null,15,-85,0,null,null,null,null,null,{"$f":"TRANSPOSE(B28:D31)","v":15},0,-7,2]
[null,0,55,6,null,null,null,null,null,-85,55,0,-4]
[null,-7,0,-33,null,null,null,null,null,0,6,-33,8]
[null,2,-4,8]
[]
["PRODUIT DE DEUX MATRICES"]
[]
[null,15,-85,0,null,8,78,0,null,{"$f":"MMULT(B35:D38,F35:H37)","v":-7360},1170,-510]
[null,0,55,6,null,88,0,6,null,4864,6,360]
[null,-7,0,-33,null,4,1,5,null,-188,-579,-165]
[null,2,-4,8,null,null,null,null,null,-304,164,16]
[]
["INVERSE D'UNE MATRICE"]
[]
[null,15,-85,0,null,null,null,null,null,{"$f":"MINVERSE(B42:D44)","v":4.8168789808917208E-2},7.444267515923568E-2,1.353503184713376E-2]
[null,5,55,6,null,null,null,null,null,-3.2643312101910825E-3,1.3136942675159238E-2,2.3885350318471341E-3]
[null,-7,0,-33,null,null,null,null,null,-1.0217622080679408E-2,-1.5790870488322718E-2,-3.3174097664543524E-2]
[]
["PRODUIT SCALAIRE"]
[]
[null,15,8,-7,14,null,1,null,null,{"$f":"MMULT(B48:E48,G48:G51)","v":22}]
[null,null,null,null,null,null,0]
[null,null,null,null,null,null,5]
[null,null,null,null,null,null,3]
[]
["PRODUIT D'UNE MATRICE"]
["ET DE SA TRANSPOSEE"]
[]
[null,15,-85,0,null,null,null,null,null,{"$f":"MMULT((B56:D58),TRANSPOSE(B56:D58))","v":7450},-4600,-105]
[null,5,55,6,null,null,null,null,null,-4600,3086,-233]
[null,-7,0,-33,null,null,null,null,null,-105,-233,1138]
[]
["RESOLUTION DE SYSTEME"]
[]
[null,{"$f":"Exercice!D73","v":0},{"$f":"Exercice!E73","v":0},{"$f":"Exercice!F73","v":0},null,{"$f":"Exercice!H69","v":20},null,null,null,null,{"$f":"MMULT(MINVERSE(B62:D64),F62:F64)","v":{"$error":"#NUM!"}}]
[null,{"$f":"Exercice!D74","v":0},{"$f":"Exercice!E74","v":0},{"$f":"Exercice!F74","v":0},null,{"$f":"Exercice!H70","v":-5},null,null,null,null,{"$error":"#NUM!"}]
[null,{"$f":"Exercice!D75","v":0},{"$f":"Exercice!E75","v":0},{"$f":"Exercice!F75","v":0},null,{"$f":"Exercice!H71","v":0},null,null,null,null,{"$error":"#NUM!"}]
[]
["CALCUL DE LA TRACE DU PRODUIT DE DEUX MATRICES CARREES"]
[]
[null,"matrice A",null,null,null,"matrice B",null,null,null,null,null,"trace (AB)",null,"trace (BA)"]
[null,15,-85,0,null,12,2,23,null,null,null,{"$f":"SUM(B69:D71*TRANSPOSE(F69:H71))","v":2754},null,{"$f":"SUM(F69:H71*TRANSPOSE(B69:D71))","v":2754}]
[null,5,55,6,null,-34,0,5]
[null,-7,0,-33,null,38,-11,3]
[]
["CALCUL DE LA TRACE D'UNE MATRICE CARREE"]
[]
[null,"matrice A",null,null,null,null,null,null,null,null,null,"trace (A)"]
[null,15,-85,0,null,null,null,null,null,null,null,{"$f":"SUM(B76:D78*MMULT(B76:D78,MINVERSE(B76:D78)))","v":37}]
[null,5,55,6]
[null,-7,0,-33]
[]
["CALCUL DU PRIX D'UNE OPTION"]
[]
[null,"Caractéristiques de l'option"]
[null,"u",1.1000000000000001]
[null,"d",0.95]
[null,"r",0.02]
[null,"S0",100]
[]
[null,"pay-off",null,null,null,null,null,null,null,null,null,"Prix Option"]
[null,"V1+",3,null,{"$f":"1+C85","v":1.02},{"$f":"C83","v":1.1000000000000001},null,{"$f":"C89","v":3},"OK",{"$f":"AND(L89=EXOMatCorr!L77)","v":false},null,{"$f":"SUM(MMULT(MINVERSE(E89:F90),H89:H90))","v":1.3725490196078418}]
[null,"V1-",0,null,{"$f":"E89","v":1.02},{"$f":"C84","v":0.95},null,{"$f":"C90","v":0}]

{"sheet":"ExArbitrage","index":4,"n_rows":39,"n_cols":10,"rows_kept":39,"cut":false,"hidden":false,"merged":[]}
["THEORIE DE L'ARBITRAGE"]
[]
["METHODE",1,"Inverser la matrice carrée de marché M, contenant en ligne i et colonne j, le prix de l'actif j dans l'état i, avec la fonction inversemat(M)"]
[null,2,"Multiplication matricielle, entre vecteur ligne des prix actuels et la matrice M inverse pour obtenir le vecteur ligne des prix des portefeuilles AD"]
[null,3,"Faire la somme S des valeurs des portefeuills AD"]
[null,4,"A partir de S, calculer le TSR"]
[null,5,"Diviser le vecteur ligne des prix des PTF AD par (1+TSF), pour obtenir les probabilités RN"]
[]
["FINANCE A 2 ACTIFS",null,null,null,null,"FINANCE A 3 ACTIFS"]
[]
["Cas 1",null,"actif 1","actif 2",null,"Cas 1",null,"actif 1","actif 2","actif 3"]
[null,"état 1",60,110,null,null,"état 1",60,90,110]
[null,"état 2",50,90,null,null,"état 2",60,110,110]
[null,"PRIX",60,105,null,null,"état 3",80,130,110]
[null,null,null,null,null,null,"PRIX",60,105,100]
[null,null,"actif 1","actif 2"]
["Cas 2","état 1",60,110]
[null,"état 2",50,85]
[null,"PRIX",60,105]
[]
[null,null,"actif 1","actif 2"]
["Cas 3","état 1",60,110]
[null,"état 2",50,85]
[null,"PRIX",52.171304478254349,95.645652499983697]
[]
[null,null,"actif 1","actif 2"]
["Cas 4","état 1",108,115]
[null,"état 2",115,108]
[null,"PRIX",92,113]
[]
[null,null,"actif 1","actif 2"]
["Cas 5","état 1",90,150]
[null,"état 2",55,60]
[null,"PRIX",60,85]
[]
[null,null,"actif 1","actif 2"]
["Cas 6","état 1",1.25,8]
[null,"état 2",1.25,2]
[null,"PRIX",1,4]

{"sheet":"2actifs","index":5,"n_rows":43,"n_cols":6,"rows_kept":43,"cut":false,"hidden":false,"merged":[]}
["FINANCE A 2 ACTIFS"]
[]
["Cas 1",null,"actif 1","actif 2","pente","CONDITION AOA"]
[null,"état 1",60,110,{"$f":"-D4/C4","v":-1.8333333333333333},{"$f":"MIN(E4:E5)<E6","v":true}]
[null,"état 2",50,90,{"$f":"-D5/C5","v":-1.8},{"$f":"MAX(E4:E5)>E6","v":false}]
[null,"PRIX",60,105,{"$f":"-D6/C6","v":-1.75},{"$f":"IF(AND(F4,F5),\"NOARB\",\"ARB\")","v":"ARB"}]
[null,"prix TSR",{"$f":"MMULT(C6:D6,MINVERSE(C4:D5))","v":-1.5},2.9999999999999929,{"$f":"SUM(C7:D7)","v":1.4999999999999929},{"$f":"1/E7-1","v":-0.33333333333333015}]
[null,"proba RN",{"$f":"C7/E7","v":-1.0000000000000047},{"$f":"D7/E7","v":2.0000000000000049},{"$f":"SUM(C8:D8)","v":1.0000000000000002},"TSR"]
[]
[null,null,"actif 1","actif 2","pente","CONDITION AOA"]
["Cas 2","état 1",60,110,{"$f":"-D11/C11","v":-1.8333333333333333},{"$f":"MIN(E11:E12)<E13","v":true}]
[null,"état 2",50,85,{"$f":"-D12/C12","v":-1.7},{"$f":"MAX(E11:E12)>E13","v":true}]
[null,"PRIX",60,105,{"$f":"-D13/C13","v":-1.75},{"$f":"IF(AND(F11,F12),\"NOARB\",\"ARB\")","v":"NOARB"}]
[null,"prix TSR",{"$f":"MMULT(C13:D13,MINVERSE(C11:D12))","v":0.375},0.74999999999999822,{"$f":"SUM(C14:D14)","v":1.1249999999999982},{"$f":"1/E14-1","v":-0.11111111111110972}]
[null,"proba RN",{"$f":"C14/E14","v":0.33333333333333387},{"$f":"D14/E14","v":0.66666666666666619},{"$f":"SUM(C15:D15)","v":1},"TSR"]
[]
[null,null,"actif 1","actif 2","pente","CONDITION AOA"]
["Cas 3","état 1",60,110,{"$f":"-D18/C18","v":-1.8333333333333333},{"$f":"MIN(E18:E19)<E20","v":true}]
[null,"état 2",50,85,{"$f":"-D19/C19","v":-1.7},{"$f":"MAX(E18:E19)>E20","v":true}]
[null,"PRIX",52.171304478254349,95.645652499983697,{"$f":"-D20/C20","v":-1.8332999999999999},{"$f":"IF(AND(F18,F19),\"NOARB\",\"ARB\")","v":"NOARB"}]
[null,"prix TSR",{"$f":"MMULT(C20:D20,MINVERSE(C18:D19))","v":0.86930436086891305},2.6085652238982959E-4,{"$f":"SUM(C21:D21)","v":0.86956521739130288},{"$f":"1/E21-1","v":0.15000000000000191}]
[null,"proba RN",{"$f":"C21/E21","v":0.99970001499925165},{"$f":"D21/E21","v":2.9998500074830453E-4},{"$f":"SUM(C22:D22)","v":1},"TSR"]
[]
[null,null,"actif 1","actif 2","pente","CONDITION AOA"]
["Cas 4","état 1",108,115,{"$f":"-D25/C25","v":-1.0648148148148149},{"$f":"MIN(E25:E26)<E27","v":false}]
[null,"état 2",115,108,{"$f":"-D26/C26","v":-0.93913043478260871},{"$f":"MAX(E25:E26)>E27","v":true}]
[null,"PRIX",92,113,{"$f":"-D27/C27","v":-1.2282608695652173},{"$f":"IF(AND(F25,F26),\"NOARB\",\"ARB\")","v":"ARB"}]
[null,"prix TSR",{"$f":"MMULT(C27:D27,MINVERSE(C25:D26))","v":1.9596412556053817},-1.0403587443946209,{"$f":"SUM(C28:D28)","v":0.91928251121076077},{"$f":"1/E28-1","v":8.7804878048782342E-2}]
[null,"proba RN",{"$f":"C28/E28","v":2.1317073170731748},{"$f":"D28/E28","v":-1.1317073170731751},{"$f":"SUM(C29:D29)","v":0.99999999999999978},"TSR"]
[]
[null,null,"actif 1","actif 2","pente","CONDITION AOA"]
["Cas 5","état 1",90,150,{"$f":"-D32/C32","v":-1.6666666666666667},{"$f":"MIN(E32:E33)<E34","v":true}]
[null,"état 2",55,60,{"$f":"-D33/C33","v":-1.0909090909090908},{"$f":"MAX(E32:E33)>E34","v":true}]
[null,"PRIX",60,85,{"$f":"-D34/C34","v":-1.4166666666666667},{"$f":"IF(AND(F32,F33),\"NOARB\",\"ARB\")","v":"NOARB"}]
[null,"prix TSR",{"$f":"MMULT(C34:D34,MINVERSE(C32:D33))","v":0.37719298245614041},0.47368421052631549,{"$f":"SUM(C35:D35)","v":0.8508771929824559},{"$f":"1/E35-1","v":0.17525773195876315}]
[null,"proba RN",{"$f":"C35/E35","v":0.44329896907216515},{"$f":"D35/E35","v":0.55670103092783485},{"$f":"SUM(C36:D36)","v":1},"TSR"]
[]
[null,null,"actif 1","actif 2","pente","CONDITION AOA"]
["Cas 6","état 1",1.25,8,{"$f":"-D39/C39","v":-6.4},{"$f":"MIN(E39:E40)<E41","v":true}]
[null,"état 2",1.25,2,{"$f":"-D40/C40","v":-1.6},{"$f":"MAX(E39:E40)>E41","v":true}]
[null,"PRIX",1,4,{"$f":"-D41/C41","v":-4},{"$f":"IF(AND(F39,F40),\"NOARB\",\"ARB\")","v":"NOARB"}]
[null,"prix TSR",{"$f":"MMULT(C41:D41,MINVERSE(C39:D40))","v":0.4},0.4,{"$f":"SUM(C42:D42)","v":0.8},{"$f":"1/E42-1","v":0.25}]
[null,"proba RN",{"$f":"C42/E42","v":0.5},{"$f":"D42/E42","v":0.5},{"$f":"SUM(C43:D43)","v":1},"CONDITION AOA"]

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["FINANCE A 3 ACTIFS"]
[]
["Cas 1",null,"actif 1","actif 2","actif 3","actif 1","CONDITION AOA"]
[null,"état 1",60,90,110,{"$f":"+C4","v":60},{"$f":"MDETERM(D4:E5)","v":-2200},0,{"$f":"MDETERM(C4:D5)","v":1200}]
[null,"état 2",60,110,110,{"$f":"+C5","v":60},-2199.9999999999995,2200,{"$f":"MDETERM(C5:D6)","v":-1000}]
[null,"état 3",80,130,110,80,4400.0000000000009,-2200,{"$f":"MDETERM(C6:D7)","v":-600}]
[null,"état 1",{"$f":"C4","v":60},{"$f":"D4","v":90},110,60]
[null,"PRIX",60,105,100,null,{"$f":"IF(ABS(SIGN(I8)+SIGN(I9)+SIGN(I10))=3,\"NOARB\",\"ARB\")","v":"NOARB"},null,{"$f":"SUMPRODUCT($C$8:$E$8,G4:I4)","v":-12000}]
[null,"prix TSR",{"$f":"MMULT(C8:E8,MINVERSE(C4:E6))","v":2.2727272727272929E-2},0.61363636363636354,0.27272727272727293,{"$f":"SUM(C9:E9)","v":0.90909090909090939},{"$f":"1/F9-1","v":9.9999999999999645E-2},null,{"$f":"SUMPRODUCT($C$8:$E$8,G5:I5)","v":-999.9999999999709}]
[null,"proba RN",{"$f":"C9/F9","v":2.5000000000000213E-2},{"$f":"D9/F9","v":0.67499999999999971},{"$f":"E9/F9","v":0.3000000000000001},{"$f":"SUM(C10:E10)","v":1},"TSR",null,{"$f":"SUMPRODUCT($C$8:$E$8,G6:I6)","v":-26999.999999999942}]

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["CALCUL DU PRIX D'UNE OPTION"]
[]
[null,"Caractéristiques de l'option"]
[null,"u",1.1000000000000001]
[null,"d",0.95]
[null,"r",0.02]
[null,"S0",100]
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[null,"pay-off",null,null,"matrice (r,u,d)",null,null,"pay-off",null,null,null,null,"Prix Option"]
[null,"V1+",3,null,null,null,null,null,"OK",null,{"$f":"AND(M10=EXOMatCorr!#REF!)","v":{"$error":"#REF!"}}]
[null,"V1-",0]