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[]
[]
[]
[]
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[]
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[]
[null,"Menu"]
[null,"Binomial model (multi period)"]
[null,"Binomial model (one period)"]
[null,"Black 76"]
[null,"Black-Scholes (excl. dividends)"]
[null,"Black-Scholes (incl. dividends)"]
[null,"Black-Scholes (incl. Greeks)"]
[null,"Certificate Builder"]
[null,"Change in option price"]
[null,"Commodity futures"]
[null,"Currency futures"]
[null,"Futures on indiv. securities"]
[null,"Garman-Kohlhagen model"]
[null,"Historical volatility"]
[null,"Implied volatility"]
[null,"Index Futures"]
[null,"Interest rate futures"]
[null,"International month codes"]
[null,"Long Call"]
[null,"Long Put"]
[null,"Moneyness"]
[null,"Monthly volatility"]
[null,"Put-call parity"]
[null,"Replication method"]
[null,"Short Call"]
[null,"Short Put"]
[null,"Swap Valuation"]
[null,"Zero Rates"]

{"sheet":"Certificate Builder","index":1,"n_rows":115,"n_cols":11,"rows_kept":115,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"Certificate Builder"]
[]
[]
[]
[null,"bonus certificate"]
[]
[]
[null,null,"zero strike call","down and out put",null,null,"Underlying","zero","down and out put","Profit/Loss"]
[null,null,"long","long",null,null,null,"long","long"]
[]
[null,"Underlying",100,100,null,null,50,{"$f":"Payoff_EoT($G13,C$14,C$19,C$21,11,\"long\")","v":-50},{"$f":"Payoff_EoT($G13,D$14,D$19,D$21,6,\"long\")","v":-0.23972064225735679},{"$f":"H13+I13","v":-50.239720642257353}]
[null,"Strike",null,90,null,null,60,{"$f":"Payoff_EoT($G14,C$14,C$19,C$21,11,\"long\")","v":-40},{"$f":"Payoff_EoT($G14,D$14,D$19,D$21,6,\"long\")","v":-0.23972064225735679},{"$f":"H14+I14","v":-40.239720642257353}]
[null,"Interest",null,0.01,null,null,70,-30,-0.23972064225735679,-30.239720642257357]
[null,"Dividend",null,0,null,null,80,-20,9.7602793577426432,-10.239720642257357]
[null,"Vola",null,0.2,null,null,90,-10,-0.23972064225735679,-10.239720642257357]
[null,"Maturity",null,1.2,null,null,100,0,-0.23972064225735679,-0.23972064225735679]
[null,"Barrier",null,80,null,null,110,10,-0.23972064225735679,9.7602793577426432]
[null,null,null,null,null,null,120,20,-0.23972064225735679,19.760279357742643]
[null,"Theoretical Price",{"$f":"C13","v":100},{"$f":"Barrier_Option(D13,D14,D15,D16,D17,D18,D19,6)","v":0.23972064225735679},null,null,130,30,-0.23972064225735679,29.760279357742643]
[null,"Price of Certificate",{"$f":"C21+D21","v":100.23972064225735},null,null,null,140,40,-0.23972064225735679,39.760279357742647]
[null,null,null,null,null,null,150,50,-0.23972064225735679,49.760279357742647]
[]
[]
[null,"capped bonus certificate"]
[]
[]
[null,null,"zero strinke call","down and out put","call",null,"Underlying","zero","down and out put","call","Profit/Loss"]
[null,null,"long","long","short",null,null,"long","long","short"]
[]
[null,"Underlying",100,100,100,null,50,{"$f":"Payoff_EoT($G32,C$33,C$38,C$40,11,\"long\")","v":-50},{"$f":"Payoff_EoT($G32,D$33,D$38,D$40,6,\"long\")","v":-0.23972064225735679},{"$f":"Payoff_EoT($G32,E$33,E$38,-E$40,9,\"short\")","v":5.4050774999645625},{"$f":"H32+I32+J32","v":-44.834643142292791}]
[null,"Strike",null,90,110,null,60,{"$f":"Payoff_EoT($G33,C$33,C$38,C$40,11,\"long\")","v":-40},{"$f":"Payoff_EoT($G33,D$33,D$38,D$40,6,\"long\")","v":-0.23972064225735679},{"$f":"Payoff_EoT($G33,E$33,E$38,-E$40,9,\"short\")","v":5.4050774999645625},{"$f":"H33+I33+J33","v":-34.834643142292791}]
[null,"Interest",null,0.01,0.01,null,70,-30,-0.23972064225735679,5.4050774999645625,-24.834643142292794]
[null,"Dividend",null,0,0,null,80,-20,9.7602793577426432,5.4050774999645625,-4.8346431422927942]
[null,"Vola",null,0.2,0.2,null,90,-10,-0.23972064225735679,5.4050774999645625,-4.8346431422927942]
[null,"Maturity",null,1.2,1.2,null,100,0,-0.23972064225735679,5.4050774999645625,5.1653568577072058]
[null,"Barrier",null,80,null,null,110,10,-0.23972064225735679,5.4050774999645625,15.165356857707206]
[null,null,null,null,null,null,120,20,-0.23972064225735679,-4.5949225000354375,15.165356857707206]
[null,"Theoretical Price",{"$f":"C32","v":100},{"$f":"Barrier_Option(D32,D33,D34,D35,D36,D37,D38,6)","v":0.23972064225735679},{"$f":"-Black_Scholes_Call(E32,E33,E34,E35,E36,E37)","v":-5.4050774999645625},null,130,30,-0.23972064225735679,-14.594922500035437,15.165356857707206]
[null,"Price of Certificate",{"$f":"C40+D40+E40","v":94.834643142292791},null,null,null,140,40,-0.23972064225735679,-24.594922500035437,15.165356857707209]
[null,null,null,null,null,null,150,50,-0.23972064225735679,-34.594922500035437,15.165356857707209]
[]
[]
[null,"discount certificate/reverse convertible"]
[]
[]
[null,null,"zero strike call","call",null,null,"Underlying","zero","call","Profit/Loss"]
[null,null,"long","short",null,null,null,"long","short"]
[]
[null,"Underlying",100,100,null,null,50,{"$f":"Payoff_EoT($G51,C$52,C$57,C$58,11,\"long\")","v":-50},{"$f":"Payoff_EoT($G51,D$52,D$57,-D$58,9,\"short\")","v":0.19817304457824836},{"$f":"H51+I51","v":-49.801826955421753}]
[null,"Strike",null,110,null,null,60,{"$f":"Payoff_EoT($G52,C$52,C$57,C$58,11,\"long\")","v":-40},{"$f":"Payoff_EoT($G52,D$52,D$57,-D$58,9,\"short\")","v":0.19817304457824836},{"$f":"H52+I52","v":-39.801826955421753}]
[null,"Interest",null,0.01,null,null,70,-30,0.19817304457824836,-29.801826955421753]
[null,"Dividend",null,0,null,null,80,-20,0.19817304457824836,-19.801826955421753]
[null,"Vola",null,0.2,null,null,90,-10,0.19817304457824836,-9.8018269554217525]
[null,"Maturity",null,0.1,null,null,100,0,0.19817304457824836,0.19817304457824836]
[null,null,null,null,null,null,110,10,0.19817304457825458,10.198173044578255]
[null,"Theoretical Price",{"$f":"C51","v":100},{"$f":"-Black_Scholes_Call(D51,D52,D53,D54,D55,D56)","v":-0.19817304457824836},null,null,120,20,-9.8018269554217454,10.198173044578255]
[null,"Price of Certificate",{"$f":"C58+D58","v":99.801826955421745},null,null,null,130,30,-19.801826955421745,10.198173044578255]
[null,null,null,null,null,null,140,40,-29.801826955421745,10.198173044578255]
[null,null,null,null,null,null,150,50,-39.801826955421745,10.198173044578255]
[]
[null,"outperformance certificate"]
[]
[]
[null,null,"zero strike call","call",null,null,"Underlying","zero","call","Profit/Loss"]
[null,null,"long","long",null,null,null,"long","long"]
[]
[null,"Underlying",100,100,null,null,50,{"$f":"Payoff_EoT($G69,C$70,C$75,C$76,11,\"long\")","v":-50},{"$f":"Payoff_EoT($G69,D$70,D$75,D$76,9,\"long\")","v":-5.4050774999645625},{"$f":"H69+I69","v":-55.405077499964563}]
[null,"Strike",null,110,null,null,60,{"$f":"Payoff_EoT($G70,C$70,C$75,C$76,11,\"long\")","v":-40},{"$f":"Payoff_EoT($G70,D$70,D$75,D$76,9,\"long\")","v":-5.4050774999645625},{"$f":"H70+I70","v":-45.405077499964563}]
[null,"Interest",null,0.01,null,null,70,-30,-5.4050774999645625,-35.405077499964563]
[null,"Dividend",null,0,null,null,80,-20,-5.4050774999645625,-25.405077499964563]
[null,"Vola",null,0.2,null,null,90,-10,-5.4050774999645625,-15.405077499964563]
[null,"Maturity",null,1.2,null,null,100,0,-5.4050774999645625,-5.4050774999645625]
[null,null,null,null,null,null,110,10,-5.4050774999645625,4.5949225000354375]
[null,"Theoretical Price",{"$f":"C69","v":100},{"$f":"Black_Scholes_Call(D69,D70,D71,D72,D73,D74)","v":5.4050774999645625},null,null,120,20,4.5949225000354375,24.594922500035437]
[null,"Price of Certificate",{"$f":"C76+D76","v":105.40507749996456},null,null,null,130,30,14.594922500035437,44.594922500035437]
[null,null,null,null,null,null,140,40,24.594922500035437,64.594922500035437]
[null,null,null,null,null,null,150,50,34.594922500035437,84.594922500035437]
[]
[null,"sprint certificate"]
[]
[]
[null,null,"zero strike call","call","call",null,"Underlying","zero","call","call","Profit/Loss"]
[null,null,"long","long","short",null,null,"long","long","short"]
[]
[null,"Underlying",100,100,100,null,50,{"$f":"Payoff_EoT($G87,C$88,C$93,C$94,11,\"long\")","v":-50},{"$f":"Payoff_EoT($G87,D$88,D$93,D$94,9,\"long\")","v":-14.925228379415238},{"$f":"Payoff_EoT($G87,E$88,E$93,-E$94,9,\"short\")","v":5.4050774999645625},{"$f":"H87+I87+J87","v":-59.520150879450682}]
[null,"Strike",null,90,110,null,60,{"$f":"Payoff_EoT($G88,C$88,C$93,C$94,11,\"long\")","v":-40},{"$f":"Payoff_EoT($G88,D$88,D$93,D$94,9,\"long\")","v":-14.925228379415238},{"$f":"Payoff_EoT($G88,E$88,E$93,-E$94,9,\"short\")","v":5.4050774999645625},{"$f":"H88+I88+J88","v":-49.520150879450675}]
[null,"Interest",null,0.01,0.01,null,70,-30,-14.925228379415238,5.4050774999645625,-39.520150879450675]
[null,"Dividend",null,0,0,null,80,-20,-14.925228379415238,5.4050774999645625,-29.520150879450675]
[null,"Vola",null,0.2,0.2,null,90,-10,-14.925228379415238,5.4050774999645625,-19.520150879450675]
[null,"Maturity",null,1.2,1.2,null,100,0,-4.9252283794152376,5.4050774999645625,0.47984912054932494]
[null,null,null,null,null,null,110,10,5.0747716205847624,5.4050774999645625,20.479849120549325]
[null,"Theoretical Price",{"$f":"C87","v":100},{"$f":"Black_Scholes_Call(D87,D88,D89,D90,D91,D92)","v":14.925228379415238},{"$f":"-Black_Scholes_Call(E87,E88,E89,E90,E91,E92)","v":-5.4050774999645625},null,120,20,15.074771620584762,-4.5949225000354375,30.479849120549325]
[null,"Price of Certificate",{"$f":"C94+D94+E94","v":109.52015087945068},null,null,null,130,30,25.074771620584762,-14.594922500035437,40.479849120549325]
[null,null,null,null,null,null,140,40,35.074771620584762,-24.594922500035437,50.479849120549318]
[null,null,null,null,null,null,150,50,45.074771620584762,-34.594922500035437,{"$f":"H97+I97+J97","v":60.479849120549318}]
[]
[null,"turbo certificate with down and our call"]
[]
[]
[null,null,"down and out call",null,null,null,"Underlying","down and out call","Profit/Loss"]
[null,null,"long",null,null,null,null,"long"]
[]
[null,"Underlying",100,null,null,null,50,{"$f":"Payoff_EoT($G105,C$106,C$112,C$113,2,\"long\")","v":-14.387651795438954},{"$f":"H105","v":-14.387651795438954}]
[null,"Strike",90,null,null,null,60,{"$f":"Payoff_EoT($G106,C$106,C$112,C$113,2,\"long\")","v":-14.387651795438954},{"$f":"H106","v":-14.387651795438954}]
[null,"Interest",0.01,null,null,null,70,-14.387651795438954,-14.387651795438954]
[null,"Dividend",0,null,null,null,80,-14.387651795438954,-14.387651795438954]
[null,"Vola",0.2,null,null,null,90,-14.387651795438954,-14.387651795438954]
[null,"Maturity",1.2,null,null,null,100,-4.3876517954389538,-4.3876517954389538]
[null,"Barrier",80,null,null,null,110,5.6123482045610462,5.6123482045610462]
[null,null,null,null,null,null,120,15.612348204561046,15.612348204561046]
[null,"Theoretical Price",{"$f":"Barrier_Option(C105,C106,C107,C108,C109,C110,C111,2)","v":14.387651795438954},null,null,null,130,25.612348204561044,25.612348204561044]
[null,"Price of Certificate",{"$f":"C113","v":14.387651795438954},null,null,null,140,35.612348204561044,35.612348204561044]
[null,null,null,null,null,null,150,45.612348204561044,45.612348204561044]

{"sheet":"Historical volatility","index":2,"n_rows":19,"n_cols":4,"rows_kept":19,"cut":false,"hidden":false,"merged":[[1,1,1,3]]}
[]
[null,"Historical volatility (annualized)"]
[]
[null,"Date","Closing price","Change"]
[null,"2000-12-31",100.5]
[null,"2001-12-31",76.5,{"$f":"LN(C6/C5)","v":-0.27286698666664033}]
[null,"2002-12-31",40.799999999999997,-0.62860865942237421]
[null,"2003-12-31",65.099999999999994,0.46724246780440748]
[null,"2004-12-31",64.400000000000006,-1.0810916104215506E-2]
[null,"2005-12-31",70.8,9.4745367589366108E-2]
[null,"2006-12-31",75.5,6.4273655555304912E-2]
[null,"2007-12-31",100.05,0.2815374047747633]
[null,"2008-12-31",48.8,-0.71793974817064099]
[null,"2009-12-31",60.95,0.22232354306817914]
[]
[null,"Result"]
[null,"Average return",null,{"$f":"AVERAGE(D5:D14)","v":-5.5567096841316693E-2}]
[null,"Variance",null,{"$f":"VARP(D5:D14)","v":0.14638718400544984}]
[null,"Standard deviation",null,{"$f":"STDEVP(D5:D14)","v":0.38260578145847435}]

{"sheet":"Monthly volatility","index":3,"n_rows":22,"n_cols":8,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Monthly volatility"]
[]
[null,"Date","Closing price","Change"]
[null,"2022-12-30",50.81]
[null,"2023-01-31",43.57,{"$f":"LN(C6/C5)","v":-0.1537243454762898}]
[null,"2023-02-28",39.07,{"$f":"LN(C7/C6)","v":-0.10901393106237159}]
[null,"2023-03-30",41.45,5.9132972514324908E-2]
[null,"2023-04-30",50.2,0.19152714511637944]
[null,"2023-05-31",51.38,2.3233964984054029E-2]
[null,"2023-06-29",48.97,-4.8041125967511568E-2]
[null,"2023-07-31",55.13,0.11848616688736624]
[null,"2023-08-31",60.16,8.7313647039992046E-2]
[null,"2023-09-28",62.97,4.5650742859067034E-2]
[null,"2023-10-31",61.1,-3.014655632310163E-2]
[null,"2023-11-30",64.989999999999995,6.1721545728707722E-2]
[null,"2023-12-30",64.209999999999994,-1.2074450100300563E-2]
[]
[null,"Monthly perspective",null,null,null,"Annual values"]
[null,"Average return",null,{"$f":"AVERAGE(D6:D17)","v":1.9505481350026357E-2},null,"Average return",null,{"$f":"12*D20","v":0.23406577620031627}]
[null,"Variance",null,{"$f":"VARP(D6:D17)","v":8.5489633358770793E-3},null,"Variance",null,{"$f":"12*D21","v":0.10258756003052495}]
[null,"Standard deviation",null,{"$f":"STDEVP(D6:D17)","v":9.2460604237032104E-2},null,"Standard deviation",null,{"$f":"SQRT(H21)","v":0.32029292847411561}]

{"sheet":"Implied volatility","index":4,"n_rows":10,"n_cols":6,"rows_kept":10,"cut":false,"hidden":false,"merged":[[3,1,3,2],[3,4,3,5]]}
[]
[null,"Implied volatility"]
[]
[null,"Implied volatility from the price of the call",null,null,"Derivation of call volatility from the price of the put"]
[null,"Price of the underlying",23,null,"Price of the underlying",35]
[null,"Strike price",24,null,"Strike price",35]
[null,"Period in years",0.5,null,"Period in years",1]
[null,"Risk-free rate of interest",0.03,null,"Risk-free rate of interest",0.06]
[null,"Option price call",5.25,null,"Option price put",3.44]
[null,"Implied volatility",{"$f":"Callvolatility(C5,C6,C7,C8,C9)","v":0.85904169082641602},null,"Implied volatility",{"$f":"PutVolatility(F5,F6,F7,F8,F9)","v":0.32490396499633789}]

{"sheet":"Change in option price","index":5,"n_rows":10,"n_cols":5,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Effect of term to maturity on option price"]
[]
[null,"Strike price of the option ","Expiry","Price of call option","Price of put option"]
[null,50,"2023-08-01",0.65,1.45]
[null,50,"2023-09-01",1.35,2]
[null,50,"2023-10-01",1.8,2.5499999999999998]
[null,50,"2023-01-01",2.9,3.4]
[null,50,"2024-01-01",5.4,5.2]
[null,50,"2024-01-01",6.8,5.8]

{"sheet":"Moneyness","index":6,"n_rows":37,"n_cols":5,"rows_kept":37,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Moneyness"]
[]
[null,"Underlying",null,null,60]
[]
[null,"Period considered","Strike price","Call price","In-the-Money or Out-of-the-money"]
[null," Aug01",7.5,11.9]
[null," Aug01",10,9.6]
[null," Aug01",12.5,6.5]
[null," Aug01",15,4.2]
[null," Aug01",17.5,2.1]
[null," Aug01",20,0.65]
[null," Aug01",22.5,0.15]
[null," Aug01",25,0.05]
[null," Aug01",27.5,0.1]
[null," Aug01",30,0.1]
[null," Aug01",32.5,0.05]
[null," Aug01",35,0.05]
[null,"2009-01-15",50,6.9,{"$f":"IF($E$4>C19,\"IN-THE-MONEY\",\"OUT-OF-THE-MONEY\")","v":"IN-THE-MONEY"}]
[null,"2009-01-16",55,5,{"$f":"IF($E$4>C20,\"IN-THE-MONEY\",\"OUT-OF-THE-MONEY\")","v":"IN-THE-MONEY"}]
[null,"2009-01-17",57,3.2,"IN-THE-MONEY"]
[null,"2009-01-18",60,1.8,"OUT-OF-THE-MONEY"]
[null,"2009-01-19",62.5,0.95,"OUT-OF-THE-MONEY"]
[null,"2009-01-20",65,0.45,"OUT-OF-THE-MONEY"]
[null,"2009-01-21",67,0.2,"OUT-OF-THE-MONEY"]
[null,"2009-01-22",70,0.15,"OUT-OF-THE-MONEY"]
[]
[null,"Period considered","Strike price","Put price","In-the-Money or Out-of-the-money"]
[null,"2009-01-22",50,0.1,{"$f":"IF(C29>$E$4,\"IN-THE-MONEY\",\"OUT-OF-THE-MONEY\")","v":"OUT-OF-THE-MONEY"}]
[null,"2009-01-23",55,0.25,{"$f":"IF(C30>$E$4,\"IN-THE-MONEY\",\"OUT-OF-THE-MONEY\")","v":"OUT-OF-THE-MONEY"}]
[null,"2009-01-24",57,0.65,"OUT-OF-THE-MONEY"]
[null,"2009-01-25",60,1.4,"OUT-OF-THE-MONEY"]
[null,"2009-01-26",62.5,2.5499999999999998,"IN-THE-MONEY"]
[null,"2009-01-27",65,4.0999999999999996,"IN-THE-MONEY"]
[null,"2009-01-28",67,6,"IN-THE-MONEY"]
[null,"2009-01-29",70,7.5,"IN-THE-MONEY"]
[null,"2009-01-30",72.5,10.7,"IN-THE-MONEY"]

{"sheet":"Replication method","index":7,"n_rows":38,"n_cols":4,"rows_kept":38,"cut":false,"hidden":false,"merged":[[1,1,1,4]]}
[]
[null,"Replication method"]
[]
[null,"Securities"]
[null,"Share:","Siemens (x)"]
[null,"Bond:","One year zero bond (y)"]
[]
[null,"Call"]
[null,"Share price in t0",61.73]
[null,"Increase in %",0.40494999999999998]
[null,"Decline in %",0.28822967723739035]
[null,"Share price t1 è Price increase",{"$f":"C9*(1+C10)","v":86.727563499999988}]
[null,"Share price t1 è Price decline",{"$f":"C9*(1-C11)","v":43.937582024135892}]
[null,"Call price at expiry",{"$f":"IF(C12>C9,(C12-C9),0)+IF(C13>C9,(C13-C9),0)","v":24.997563499999991}]
[]
[null,"Replication model"]
[null,"Share price in t0",61.73]
[null,"Increase in %",0.40494999999999998]
[null,"Decline in %",0.28822967723739035]
[null,"Share price t1 è Price increase",{"$f":"C17*(1+C18)","v":86.727563499999988}]
[null,"Share price t1 è Price decline",{"$f":"C17*(1-C19)","v":43.937582024135892}]
[null,"Zero bond t0",61.73]
[null,"Interest rate on zero bond (risk-free) in %",0.01]
[null,"Zero bond t1 ",{"$f":"C22*(1+C23)","v":62.347299999999997}]
[]
[null,"Calculations"]
[null,"Price increase","86,73x + 62,35y = 25,00"]
[null,"Price decline","43,94x + 62,35y = 0"]
[]
[null,"Solving scenario price increase for  x","x = (25,00 - 62,35y)/86,73"]
[]
[null,"x = (25,00 - 62,35y)/86,73 into scenario Price decline"]
[]
[null,null,"y =",{"$f":"(C21*(C20-C17)/C20)/((C21*C24)/C20-C24)","v":-0.41169357009952229}]
[null,null,"x =",{"$f":"((C20-C17)-C24*D34)/C20","v":0.58419196825546638}]
[]
[null,"Value of the portfolio"]
[null,"Price of the call",{"$f":"D35*C17+D34*C22","v":10.648326118166427}]

{"sheet":"Binomial model (one period)","index":8,"n_rows":29,"n_cols":4,"rows_kept":29,"cut":false,"hidden":false,"merged":[[1,1,1,4]]}
[]
[null,"Binomial model for one period"]
[]
[null,"Assumptions"]
[null,"Price of underlying",null,100]
[null,"Volatility",null,0.34]
[null,"Strike price",null,100]
[null,"Risk-free rate of interest ",null,0.01]
[null,"Time to maturity of option in years",null,1]
[]
[null,"Calculations"]
[null,"Up-factor",null,{"$f":"EXP(D6*SQRT(D9))","v":1.4049475905635938}]
[null,"Down-factor",null,{"$f":"EXP(-D6*SQRT(D9))","v":0.71177032276260965}]
[null,"Pseudo probability q",null,{"$f":"(1+D8-D13)/(D12-D13)","v":0.43023580127416139}]
[]
[]
[null,"Value development"]
[null,"Time"]
[null,0,null,1]
[null,null,null,{"$f":"B21*D12","v":140.49475905635938}]
[null,{"$f":"D5","v":100}]
[null,null,null,{"$f":"B21*D13","v":71.17703227626096}]
[]
[null,"Option tree"]
[null,"Time"]
[null,0,null,1]
[null,null,null,{"$f":"IF(D20>D7,(D20-D7),0)","v":40.494759056359385}]
[null,{"$f":"D27*D14/(1+D8)+D29*(1-D14)/(1+D8)","v":17.249797138630576}]
[null,null,null,{"$f":"IF(D22>D7,(D22-D7),0)","v":0}]

{"sheet":"Binomial (multi period)","index":9,"n_rows":79,"n_cols":14,"rows_kept":79,"cut":false,"hidden":false,"merged":[[1,1,1,4],[2,1,2,2]]}
[]
[null,"Binomial model in the multi period case "]
[]
[]
[null,"Assumptions"]
[null,"Price of underlying",null,100]
[null,"Volatility",null,0.34]
[null,"Strike price",null,100]
[null,"Risk-free rate of interest (annualized)",null,0.01]
[null,"Time to maturity of option in years",null,1]
[null,"Time to maturity of option in months",null,12]
[]
[null,"Calculations"]
[null,"Monthly up-factor",null,{"$f":"EXP(D7*SQRT(1/D11))","v":1.1031277408528339}]
[null,"Monthly down-factor",null,{"$f":"EXP(-D7*SQRT(1/D11))","v":0.90651332839014154}]
[null,"Riskfree rate of interest (monthly)",null,{"$f":"(1+D9)^(1/12)-1","v":8.295381143461622E-4}]
[null,"Pseudo probability q",null,{"$f":"(1+D16-D15)/(D14-D15)","v":0.47970140409773437}]
[]
[]
[null,"Value development"]
[null,"Time"]
[null,0,1,2,3,4,5,6,7,8,9,10,11,12]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"M24*$D$14","v":324.72047493721067}]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"L25*$D$14","v":294.36343853175839}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"K26*$D$14","v":266.84438041979115},null,{"$f":"M26*$D$14","v":266.84438041979115}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"J27*$D$14","v":241.89798745655},null,{"$f":"L27*$D$14","v":241.89798745655}]
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[null,null,null,null,null,null,null,null,{"$f":"H29*$D$14","v":198.78364183878145},null,{"$f":"J29*$D$14","v":198.78364183878145},null,{"$f":"L29*$D$14","v":198.78364183878145}]
[null,null,null,null,null,null,null,{"$f":"G30*$D$14","v":180.20002079278757},null,{"$f":"I30*$D$14","v":180.20002079278757},null,{"$f":"K30*$D$14","v":180.20002079278757},null,{"$f":"M30*$D$14","v":180.20002079278757}]
[null,null,null,null,null,null,{"$f":"F31*$D$14","v":163.35372062484257},null,{"$f":"H31*$D$14","v":163.35372062484257},null,{"$f":"J31*$D$14","v":163.35372062484257},null,{"$f":"L31*$D$14","v":163.35372062484257}]
[null,null,null,null,null,{"$f":"E32*$D$14","v":148.08232498853934},null,{"$f":"G32*$D$14","v":148.08232498853934},null,{"$f":"I32*$D$14","v":148.08232498853934},null,{"$f":"K32*$D$14","v":148.08232498853934},null,{"$f":"M32*$D$14","v":148.08232498853934}]
[null,null,null,null,{"$f":"D33*$D$14","v":134.23860130111143},null,{"$f":"F33*$D$14","v":134.23860130111143},null,{"$f":"H33*$D$14","v":134.23860130111143},null,{"$f":"J33*$D$14","v":134.23860130111143},null,{"$f":"L33*$D$14","v":134.23860130111143}]
[null,null,null,{"$f":"C34*$D$14","v":121.68908126390771},null,{"$f":"E34*$D$14","v":121.68908126390771},null,{"$f":"G34*$D$14","v":121.68908126390771},null,{"$f":"I34*$D$14","v":121.68908126390771},null,{"$f":"K34*$D$14","v":121.68908126390771},null,{"$f":"M34*$D$14","v":121.68908126390771}]
[null,null,{"$f":"B35*$D$14","v":110.31277408528339},null,{"$f":"D35*$D$14","v":110.31277408528339},null,{"$f":"F35*$D$14","v":110.31277408528339},null,{"$f":"H35*$D$14","v":110.31277408528339},null,{"$f":"J35*$D$14","v":110.31277408528339},null,{"$f":"L35*$D$14","v":110.31277408528339}]
[null,{"$f":"D6","v":100},null,{"$f":"C36*$D$14","v":100},null,{"$f":"E36*$D$14","v":100},null,{"$f":"G36*$D$14","v":100},null,{"$f":"I36*$D$14","v":100},null,{"$f":"K36*$D$14","v":100},null,{"$f":"M36*$D$14","v":100}]
[null,null,{"$f":"B35*$D$15","v":90.65133283901416},null,{"$f":"D37*$D$14","v":90.65133283901416},null,{"$f":"F37*$D$14","v":90.65133283901416},null,{"$f":"H37*$D$14","v":90.65133283901416},null,{"$f":"J37*$D$14","v":90.65133283901416},null,{"$f":"L37*$D$14","v":90.65133283901416}]
[null,null,null,{"$f":"C36*$D$15","v":82.176641454897265},null,{"$f":"E38*$D$14","v":82.176641454897265},null,{"$f":"G38*$D$14","v":82.176641454897265},null,{"$f":"I38*$D$14","v":82.176641454897265},null,{"$f":"K38*$D$14","v":82.176641454897265},null,{"$f":"M38*$D$14","v":82.176641454897265}]
[null,null,null,null,{"$f":"D37*$D$15","v":74.4942207612022},null,{"$f":"F39*$D$14","v":74.4942207612022},null,{"$f":"H39*$D$14","v":74.4942207612022},null,{"$f":"J39*$D$14","v":74.4942207612022},null,{"$f":"L39*$D$14","v":74.4942207612022}]
[null,null,null,null,null,{"$f":"E38*$D$15","v":67.530004008067394},null,{"$f":"G40*$D$14","v":67.530004008067394},null,{"$f":"I40*$D$14","v":67.530004008067394},null,{"$f":"K40*$D$14","v":67.530004008067394},null,{"$f":"M40*$D$14","v":67.530004008067394}]
[null,null,null,null,null,null,{"$f":"F39*$D$15","v":61.21684869955277},null,{"$f":"H41*$D$14","v":61.21684869955277},null,{"$f":"J41*$D$14","v":61.21684869955277},null,{"$f":"L41*$D$14","v":61.21684869955277}]
[null,null,null,null,null,null,null,{"$f":"G40*$D$15","v":55.493889268187289},null,{"$f":"I42*$D$14","v":55.493889268187289},null,{"$f":"K42*$D$14","v":55.493889268187289},null,{"$f":"M42*$D$14","v":55.493889268187289}]
[null,null,null,null,null,null,null,null,{"$f":"H41*$D$15","v":50.305950265818417},null,{"$f":"J43*$D$14","v":50.305950265818417},null,{"$f":"L43*$D$14","v":50.305950265818417}]
[null,null,null,null,null,null,null,null,null,{"$f":"I42*$D$15","v":45.60301441329598},null,{"$f":"K44*$D$14","v":45.60301441329598},null,{"$f":"M44*$D$14","v":45.60301441329598}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"J43*$D$15","v":41.339740380420537},null,{"$f":"L45*$D$14","v":41.339740380420537}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"K44*$D$15","v":37.475025647039359},null,{"$f":"M46*D14","v":37.475025647039359}]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"L45*$D$15","v":33.97161023080357}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"M46*$D$15","v":30.795717461098327}]
[]
[]
[]
[]
[null,"Option tree"]
[null,"Time"]
[null,0,1,2,3,4,5,6,7,8,9,10,11,12]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(N23>$D$8,(N23-$D$8),0)","v":224.72047493721067}]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"N55*$D$17/(1+$D$16)+N57*(1-$D$17)/(1+$D$16)","v":194.44632358688068}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"M56*$D$17/(1+$D$16)+M58*(1-$D$17)/(1+$D$16)","v":167.0100818307121},null,{"$f":"IF(N25>$D$8,(N25-$D$8),0)","v":166.84438041979115}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"L57*$D$17/(1+$D$16)+L59*(1-$D$17)/(1+$D$16)","v":142.14643658088744},null,{"$f":"N57*$D$17/(1+$D$16)+N59*(1-$D$17)/(1+$D$16)","v":141.98087251167229}]
[null,null,null,null,null,null,null,null,null,{"$f":"K58*$D$17/(1+$D$16)+K60*(1-$D$17)/(1+$D$16)","v":119.61487799237992},null,{"$f":"M58*$D$17/(1+$D$16)+M60*(1-$D$17)/(1+$D$16)","v":119.44945115103479},null,{"$f":"IF(N27>$D$8,(N27-$D$8),0)","v":119.28374974011385}]
[null,null,null,null,null,null,null,null,{"$f":"J59*$D$17/(1+$D$16)+J61*(1-$D$17)/(1+$D$16)","v":99.197380690335393},null,{"$f":"L59*$D$17/(1+$D$16)+L61*(1-$D$17)/(1+$D$16)","v":99.03209096311889},null,{"$f":"N59*$D$17/(1+$D$16)+N61*(1-$D$17)/(1+$D$16)","v":98.866526893903739}]
[null,null,null,null,null,null,null,{"$f":"I60*$D$17/(1+$D$16)+I62*(1-$D$17)/(1+$D$16)","v":80.696301771788626},null,{"$f":"K60*$D$17/(1+$D$16)+K62*(1-$D$17)/(1+$D$16)","v":80.531149045053638},null,{"$f":"M60*$D$17/(1+$D$16)+M62*(1-$D$17)/(1+$D$16)","v":80.365722203708515},null,{"$f":"IF(N29>$D$8,(N29-$D$8),0)","v":80.200020792787569}]
[null,null,null,null,null,null,{"$f":"H61*$D$17/(1+$D$16)+H63*(1-$D$17)/(1+$D$16)","v":64.115385261387488},null,{"$f":"J61*$D$17/(1+$D$16)+J63*(1-$D$17)/(1+$D$16)","v":63.76745947639651},null,{"$f":"L61*$D$17/(1+$D$16)+L63*(1-$D$17)/(1+$D$16)","v":63.602169749180021},null,{"$f":"N61*$D$17/(1+$D$16)+N63*(1-$D$17)/(1+$D$16)","v":63.436605679964856}]
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[null,null,null,null,null,{"$f":"G70*$D$17/(1+$D$16)+G72*(1-$D$17)/(1+$D$16)","v":0.65813170227311912},null,{"$f":"I70*$D$17/(1+$D$16)+I72*(1-$D$17)/(1+$D$16)","v":0.26297012149376453},null,{"$f":"K70*$D$17/(1+$D$16)+K72*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"M70*$D$17/(1+$D$16)+M72*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"IF(N39>$D$8,(N39-$D$8),0)","v":0}]
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[null,null,null,null,null,null,null,{"$f":"I72*$D$17/(1+$D$16)+I74*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"K72*$D$17/(1+$D$16)+K74*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"M72*$D$17/(1+$D$16)+M74*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"IF(N41>$D$8,(N41-$D$8),0)","v":0}]
[null,null,null,null,null,null,null,null,{"$f":"J73*$D$17/(1+$D$16)+J75*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"L73*$D$17/(1+$D$16)+L75*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"N73*$D$17/(1+$D$16)+N75*(1-$D$17)/(1+$D$16)","v":0}]
[null,null,null,null,null,null,null,null,null,{"$f":"K74*$D$17/(1+$D$16)+K76*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"M74*$D$17/(1+$D$16)+M76*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"IF(N43>$D$8,(N43-$D$8),0)","v":0}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"L75*$D$17/(1+$D$16)+L77*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"N75*$D$17/(1+$D$16)+N77*(1-$D$17)/(1+$D$16)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"M76*$D$17/(1+$D$16)+M78*(1-$D$17)/(1+$D$16)","v":0},null,{"$f":"IF(N45>$D$8,(N45-$D$8),0)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"N77*$D$17/(1+$D$16)+N79*(1-$D$17)/(1+$D$16)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(N47>$D$8,(N47-$D$8),0)","v":0}]

{"sheet":"Black-Scholes (excl. dividends)","index":10,"n_rows":30,"n_cols":4,"rows_kept":30,"cut":false,"hidden":false,"merged":[[5,1,5,2]]}
[]
[null,"Black-Scholes model (excluding dividends)"]
[]
[]
[]
[null,"Assumptions"]
[null,"strike price","K",180]
[null,"price of underlying","S0",185]
[null,"volatility","σ",0.2]
[null,"risk-free rate ","r",2.5000000000000001E-3]
[null,"time to maturity of option (days)","t",80]
[]
[]
[]
[null,"Calculation Call-Option"]
[null,"time to maturity in years",{"$f":"D11/365","v":0.21917808219178081}]
[null,"d1",{"$f":"(LN(D8/D7)+(D10+(D9^2)/2)*C16)/(D9*SQRT(C16))","v":0.34528968883964295}]
[null,"d2",{"$f":"C17-(D9*SQRT(C16))","v":0.25165677108273848}]
[null,"N(d1)",{"$f":"NORMSDIST(C17)","v":0.63506170116760252}]
[null,"N(d2)",{"$f":"NORMSDIST(C18)","v":0.59934681329259254}]
[null,"price of Call-Option",{"$f":"(D8*C19)-D7*EXP(-D10*C16)*C20","v":9.6630857890720279}]
[]
[]
[null,"Calculations Put-Optiom"]
[null,"time to maturity in years",{"$f":"D11/365","v":0.21917808219178081}]
[null,"-d1",{"$f":"-C17","v":-0.34528968883964295}]
[null,"-d2",{"$f":"-C18","v":-0.25165677108273848}]
[null,"N(-d1)",{"$f":"NORMSDIST(C26)","v":0.36493829883239748}]
[null,"N(-d2)",{"$f":"NORMSDIST(C27)","v":0.40065318670740752}]
[null,"price of Put-Option",{"$f":"(D7*EXP(-D10*C25)*C29)-(D8*C28)","v":4.5644826691062264}]

{"sheet":"Black-Scholes (incl. dividends)","index":11,"n_rows":41,"n_cols":4,"rows_kept":41,"cut":false,"hidden":false,"merged":[[4,1,4,2]]}
[]
[null,"Black-Scholes Merton model (including dividends and Greeks)"]
[]
[]
[null,"Assumptions"]
[null,"strike price","K",20]
[null,"price of underlying","S0",20]
[null,"volatility","σ",0.4]
[null,"risk-free rate","r",5.0000000000000001E-3]
[null,"dividends","q",0.01]
[null,"time to maturity in days","t",10]
[]
[]
[]
[null,"Calculation Call-Option"]
[null,"time to maturity in years",{"$f":"D11/365","v":2.7397260273972601E-2}]
[null,"e-qT",{"$f":"EXP(-D10*C16)","v":0.99972606492432659}]
[null,"d1",{"$f":"(LN(D7/D6)+(D9-D10+((D8^2)/2)*C16))/(D8*SQRT(C16))","v":-4.2414801790871356E-2}]
[null,"d2",{"$f":"C18-(D8*SQRT(C16))","v":-0.10862327287906079}]
[null,"N(d1)",{"$f":"NORMSDIST(C18)","v":0.48308401442257159}]
[null,"N(d2)",{"$f":"NORMSDIST(C19)","v":0.45675065044337426}]
[null,"price of Call-Option",{"$f":"(D7*C17*C20)-((D6*EXP(-D9*C16))*C21)","v":0.5252718924015749}]
[]
[]
[null,"Calculation Put-Option"]
[null,"time to maturity in years",{"$f":"D11/365","v":2.7397260273972601E-2}]
[null,"e-qT",{"$f":"EXP(-D10*C26)","v":0.99972606492432659}]
[null,"-d1",{"$f":"-C18","v":4.2414801790871356E-2}]
[null,"-d2",{"$f":"-C19","v":0.10862327287906079}]
[null,"N(-d1)",{"$f":"NORMSDIST(C28)","v":0.51691598557742835}]
[null,"N(-d2)",{"$f":"NORMSDIST(C29)","v":0.54324934955662574}]
[null,"price of Put-Option",{"$f":"(D6*EXP(-D9*C26)*C31)-(D7*C27*C30)","v":0.5280110555315467}]
[]
[null,"distribution function of the standard normal distribution",{"$f":"(1/(SQRT(2*PI())))*EXP(-(0.5*C18^2))","v":0.3985835900927035}]
[]
[null,"Greeks","Call","Put"]
[null,"Delta",{"$f":"$C$20*$C$17","v":0.48295168076652412},{"$f":"C20*C17-1","v":-0.51704831923347583}]
[null,"Gamma",{"$f":"($C$34*$C$17)/($D$7*$D$8*$C$16^0.5)","v":0.30092403397748219},{"$f":"($C$34*$C$17)/($D$7*$D$8*$C$16^0.5)","v":0.30092403397748219}]
[null,"Theta",{"$f":"(D10*D7*C17*C20-(D7*C17*D8)/(2*C16^0.5)*C34-D9*D6*EXP(-D9*C16)*C21)/365","v":-2.6242870026687039E-2},{"$f":"(D9*D6*EXP(-D9*C16)*C31-D10*D7*C27*C30-(D7*C27*D8)/(2*C26^0.5)*C34)/365","v":-2.6516730055938499E-2}]
[null,"Vega",{"$f":"C16^0.5*D7*C17*C34/100","v":1.3191190530519765E-2},{"$f":"C16^0.5*D7*C17*C34/100","v":1.3191190530519765E-2}]
[null,"Rho",{"$f":"C16*D6*EXP(-D9*C16)*C21/100","v":2.5024004720353172E-3},{"$f":"-C26*D6*EXP(-D9*C26)*C31/100","v":-2.976301024297971E-3}]

{"sheet":"Black-Scholes (incl. Greeks)","index":12,"n_rows":29,"n_cols":7,"rows_kept":29,"cut":false,"hidden":false,"merged":[[7,1,7,2]]}
[]
[]
[null,"Black-Scholes model including derivation of Greeks"]
[]
[]
[]
[]
[null,"Assumptions"]
[null,"strike price","K",74]
[null,"price of underlying","S0",73.2]
[null,"volatility","σ",0.34]
[null,"risk-free rate","r",1.4999999999999999E-2]
[null,"time to maturity of option in days","t",55]
[]
[]
[]
[null,"Calculations",null,null,"Greeks","Call","Put"]
[null,"time to maturity of option in years",{"$f":"D13/365","v":0.15068493150684931},null,"Delta",{"$f":"C23","v":0.50030284746192399},{"$f":"C23-1","v":-0.49969715253807601}]
[null,"d1",{"$f":"(LN(D10/D9)+(D12+(D11^2)/2)*C18)/(D11*SQRT(C18))","v":7.5912608386936994E-4},null,"Gamma",{"$f":"C27/(D10*D11*SQRT(C18))","v":4.1293817119942955E-2},{"$f":"C27/(D10*D11*SQRT(C18))","v":4.1293817119942955E-2}]
[null,"-d1",{"$f":"-C19","v":-7.5912608386936994E-4},null,"Theta",{"$f":"-((D10*C27*D11)/(2*SQRT(C18))-(D12*D9*(EXP(-(D12*C18)))*C25))/365","v":-3.3679503593591266E-2},{"$f":"-(((D10*C27*D11)/(2*SQRT(C18)))+(D12*D9*(EXP(-(D12*C18)))*C26))/365","v":-3.6713733536497241E-2}]
[null,"d2",{"$f":"C19-(D11*SQRT(C18))","v":-0.13122260781212011},null,"Vega",{"$f":"D10*C27*SQRT(C18)/100","v":0.1133589812453992},{"$f":"D10*C27*SQRT(C18)/100","v":0.1133589812453992}]
[null,"-d2",{"$f":"-C21","v":0.13122260781212011},null,"Rho",{"$f":"D9*C18*EXP((-D12*C18))*C25/100","v":4.9819989016178068E-2},{"$f":"-D9*C18*EXP((-D12*C18))*C26/100","v":-6.1435108890374505E-2}]
[null,"N(d1)",{"$f":"NORMSDIST(C19)","v":0.50030284746192399}]
[null,"N(-d1)",{"$f":"NORMSDIST(C20)","v":0.49969715253807606}]
[null,"N(d2)",{"$f":"NORMSDIST(C21)","v":0.44779960607309688}]
[null,"N(-d2)",{"$f":"NORMSDIST(C22)","v":0.55220039392690312}]
[null,"distribution function of the standard normal distribution",{"$f":"(1/(SQRT(2*PI())))*EXP(-(0.5*C19^2))","v":0.39894216545173433}]
[null,"price Call-Option",{"$f":"(D10*C23)-D9*EXP(-D12*C18)*C25","v":3.5598120871128458}]
[null,"price Put-Option",{"$f":"(D9*EXP(-D12*C18)*C26)-(D10*C24)","v":4.192740697825009}]

{"sheet":"Put-call parity","index":13,"n_rows":18,"n_cols":9,"rows_kept":18,"cut":false,"hidden":false,"merged":[[6,1,6,2],[6,6,6,7]]}
[]
[null,"Put Call Parity"]
[]
[null,"Price of Call given",null,null,null,null,"Price of Put given"]
[]
[]
[null,"Assumptions",null,null,null,null,"Assumptions"]
[null,"price of Call t=0","c",8.9281000000000006,null,null,"price of Put t=0","p",9.84]
[null,"strike price","K",61,null,null,"strike price","K",25]
[null,"price of underlying","S0",61.73,null,null,"price of underlying","S0",20]
[null,"risk-free rate","r",0.01,null,null,"risk-free rate","r",0.02]
[null,"time to maturity in days","t",365,null,null,"time to maturity in days","t",120]
[]
[]
[]
[null,"Calculation",null,null,null,null,"Calculation"]
[null,"time to maturity in years",{"$f":"D12/365","v":1},null,null,null,"time to maturity in years",{"$f":"I12/365","v":0.32876712328767121}]
[null,"price of the Put-Option",{"$f":"D8-D10+(D9*EXP(-D11*C17))","v":7.5911398586992576},null,null,null,"price of the Call-Option",{"$f":"I8+I10-I9*EXP(-I11*H17)","v":5.0038443051165267}]

{"sheet":"Long call","index":14,"n_rows":38,"n_cols":4,"rows_kept":38,"cut":false,"hidden":false,"merged":[[37,2,37,3],[15,2,16,3],[29,2,29,3],[30,2,30,3],[31,2,31,3],[32,2,32,3],[33,2,33,3],[34,2,34,3],[23,2,23,3],[24,2,24,3],[20,2,20,3],[21,2,21,3],[35,2,35,3],[36,2,36,3],[25,2,25,3],[26,2,26,3],[27,2,27,3],[28,2,28,3],[22,2,22,3],[17,2,17,3],[18,2,18,3],[19,2,19,3],[15,1,16,1],[3,1,3,2],[9,1,9,3],[10,1,11,1],[10,2,11,2],[10,3,11,3]]}
[]
[null,"Long call"]
[]
[null,"Assumptions"]
[null,"price of Call-Option at t=0","c",3]
[null,"strike price ","K",10]
[null,"price of underlying","S0",10]
[]
[]
[null,"Calculations"]
[null,"price of underlying","Exercise option?","profit / loss"]
[]
[null,{"$f":"D7","v":10},{"$f":"IF(D7>D6,\"yes\",\"no\")","v":"no"},{"$f":"IF(D7<D6,-D5,D7-D6-D5)","v":-3}]
[]
[]
[null,"price of underlying","profit / loss"]
[]
[null,0,{"$f":"IF(B18<$D$6,-$D$5,B18-$D$6-$D$5)","v":-3}]
[null,2,{"$f":"IF(B19<$D$6,-$D$5,B19-$D$6-$D$5)","v":-3}]
[null,4,-3]
[null,6,-3]
[null,8,-3]
[null,10,-3]
[null,12,-1]
[null,14,1]
[null,16,3]
[null,18,5]
[null,20,7]
[null,22,9]
[null,24,11]
[null,26,13]
[null,28,15]
[null,30,17]
[null,32,19]
[null,34,21]
[null,36,23]
[null,38,25]
[null,40,27]

{"sheet":"Short call","index":15,"n_rows":38,"n_cols":4,"rows_kept":38,"cut":false,"hidden":false,"merged":[[37,2,37,3],[15,2,16,3],[29,2,29,3],[30,2,30,3],[31,2,31,3],[32,2,32,3],[33,2,33,3],[34,2,34,3],[23,2,23,3],[24,2,24,3],[20,2,20,3],[21,2,21,3],[35,2,35,3],[36,2,36,3],[25,2,25,3],[26,2,26,3],[27,2,27,3],[28,2,28,3],[22,2,22,3],[17,2,17,3],[18,2,18,3],[19,2,19,3],[15,1,16,1],[3,1,3,2],[9,1,9,3],[10,1,11,1],[10,2,11,2],[10,3,11,3]]}
[]
[null,"Short call"]
[]
[null,"Assumptions"]
[null,"price of Call-Option at t=0","c",3]
[null,"strike price","K",10]
[null,"price of underlying","S0",10]
[]
[]
[null,"Calculations"]
[null,"price of underlying","Exercise option?","profit / loss"]
[]
[null,{"$f":"D7","v":10},{"$f":"IF(D7>D6,\"yes\",\"no\")","v":"no"},{"$f":"IF(D7<D6,D5,D5+D6-D7)","v":3}]
[]
[]
[null,"price of underlying","profit / loss"]
[]
[null,0,{"$f":"IF(B18<$D$6,$D$5,$D$6+$D$5-B18)","v":3}]
[null,2,{"$f":"IF(B19<$D$6,$D$5,$D$6+$D$5-B19)","v":3}]
[null,4,3]
[null,6,3]
[null,8,3]
[null,10,3]
[null,12,1]
[null,14,-1]
[null,16,-3]
[null,18,-5]
[null,20,-7]
[null,22,-9]
[null,24,-11]
[null,26,-13]
[null,28,-15]
[null,30,-17]
[null,32,-19]
[null,34,-21]
[null,36,-23]
[null,38,-25]
[null,40,-27]

{"sheet":"Long put","index":16,"n_rows":38,"n_cols":4,"rows_kept":38,"cut":false,"hidden":false,"merged":[[37,2,37,3],[15,2,16,3],[29,2,29,3],[30,2,30,3],[31,2,31,3],[32,2,32,3],[33,2,33,3],[34,2,34,3],[23,2,23,3],[24,2,24,3],[20,2,20,3],[21,2,21,3],[35,2,35,3],[36,2,36,3],[25,2,25,3],[26,2,26,3],[27,2,27,3],[28,2,28,3],[22,2,22,3],[17,2,17,3],[18,2,18,3],[19,2,19,3],[15,1,16,1],[3,1,3,2],[9,1,9,3],[10,1,11,1],[10,2,11,2],[10,3,11,3]]}
[]
[null,"Long put"]
[]
[null,"Assumptions"]
[null,"price of Put-Option at t=0","p",8]
[null,"strike price","K",20]
[null,"price of underlying","S0",10]
[]
[]
[null,"Calculations"]
[null,"price of underlying","Exercise option?","profit / loss"]
[]
[null,{"$f":"D7","v":10},{"$f":"IF(D7<D6,\"yes\",\"no\")","v":"yes"},{"$f":"IF(D7>D6,-D5,D6-D7-D5)","v":2}]
[]
[]
[null,"price of underlying","profit /loss"]
[]
[null,0,{"$f":"IF(B18>$D$6,-$D$5,$D$6-B18-$D$5)","v":12}]
[null,2,{"$f":"IF(B19>$D$6,-$D$5,$D$6-B19-$D$5)","v":10}]
[null,4,8]
[null,6,6]
[null,8,4]
[null,10,2]
[null,12,0]
[null,14,-2]
[null,16,-4]
[null,18,-6]
[null,20,-8]
[null,22,-8]
[null,24,-8]
[null,26,-8]
[null,28,-8]
[null,30,-8]
[null,32,-8]
[null,34,-8]
[null,36,-8]
[null,38,-8]
[null,40,-8]

{"sheet":"Short put","index":17,"n_rows":38,"n_cols":4,"rows_kept":38,"cut":false,"hidden":false,"merged":[[37,2,37,3],[15,2,16,3],[29,2,29,3],[30,2,30,3],[31,2,31,3],[32,2,32,3],[33,2,33,3],[34,2,34,3],[23,2,23,3],[24,2,24,3],[20,2,20,3],[21,2,21,3],[35,2,35,3],[36,2,36,3],[25,2,25,3],[26,2,26,3],[27,2,27,3],[28,2,28,3],[22,2,22,3],[17,2,17,3],[18,2,18,3],[19,2,19,3],[15,1,16,1],[3,1,3,2],[9,1,9,3],[10,1,11,1],[10,2,11,2],[10,3,11,3]]}
[]
[null,"Short put"]
[]
[null,"Assumptions"]
[null,"price of Put-Option at t=0","p",8]
[null,"strike price","K",20]
[null,"price of underlying","S0",10]
[]
[]
[null,"Calculations"]
[null,"price of underlying","Exercise option?","profit / loss"]
[]
[null,{"$f":"D7","v":10},{"$f":"IF(D7<D6,\"yes\",\"no\")","v":"yes"},{"$f":"IF(D7>D6,D5,D5+D7-D6)","v":-2}]
[]
[]
[null,"price of underlying","profit / loss"]
[]
[null,0,{"$f":"IF(B18>$D$6,$D$5,B18+$D$5-$D$6)","v":-12}]
[null,2,{"$f":"IF(B19>$D$6,$D$5,B19+$D$5-$D$6)","v":-10}]
[null,4,-8]
[null,6,-6]
[null,8,-4]
[null,10,-2]
[null,12,0]
[null,14,2]
[null,16,4]
[null,18,6]
[null,20,8]
[null,22,8]
[null,24,8]
[null,26,8]
[null,28,8]
[null,30,8]
[null,32,8]
[null,34,8]
[null,36,8]
[null,38,8]
[null,40,8]

{"sheet":"Black 76","index":18,"n_rows":27,"n_cols":3,"rows_kept":27,"cut":false,"hidden":false,"merged":[[5,5,5,6],[7,1,7,2]]}
[]
[]
[null,"Black 76"]
[]
[]
[]
[]
[null,"Assumptions"]
[null,"future price",40]
[null,"strike price",38]
[null,"risk-free interest rate",2.5000000000000001E-2]
[null,"vola",0.3]
[null,"time to maturity",0.2]
[]
[]
[]
[null,"Calculations"]
[null,"d1",{"$f":"(LN(C9/C10)+(C12^2/2)*C13)/(C12*C13^0.5)","v":0.4493996827932315}]
[null,"-d1",{"$f":"-C18","v":-0.4493996827932315}]
[null,"d2",{"$f":"C18-C12*C13^0.5","v":0.31523560414324414}]
[null,"-d2",{"$f":"-C20","v":-0.31523560414324414}]
[null,"N(d1)",{"$f":"NORMSDIST(C18)","v":0.67342831994981012}]
[null,"N(-d1)",{"$f":"NORMSDIST(C19)","v":0.32657168005018983}]
[null,"N(d2)",{"$f":"NORMSDIST(C20)","v":0.62370861278824363}]
[null,"N(-d2)",{"$f":"NORMSDIST(C21)","v":0.37629138721175631}]
[null,"price Call-Option",{"$f":"EXP(-C11*C13)*(C9*C22-C10*C24)","v":3.2200648697110941}]
[null,"price Put-Option",{"$f":"EXP(-C11*C13)*(C10*C25-C9*C23)","v":1.230039911325731}]

{"sheet":"Garman-Kohlhagen","index":19,"n_rows":28,"n_cols":3,"rows_kept":28,"cut":false,"hidden":false,"merged":[[5,5,5,6],[7,1,7,2]]}
[]
[]
[null,"Garman-Kohlhagen Model"]
[]
[]
[]
[]
[null,"Assumptions"]
[null,"FX price 1",40]
[null,"FX price 2",38]
[null,"risk-free interest rate",2.5000000000000001E-2]
[null,"foeign risk-free rate",0.04]
[null,"vola",0.3]
[null,"time to maturity",0.2]
[]
[]
[]
[null,"Calculations"]
[null,"d1",{"$f":"(LN(C9/C10)+(C11-C12+C13^2/2)*C14)/(C13*C14^0.5)","v":0.42703900301823355}]
[null,"-d1",{"$f":"-C19","v":-0.42703900301823355}]
[null,"d2",{"$f":"C19-C13*C14^0.5","v":0.29287492436824619}]
[null,"-d2",{"$f":"-C21","v":-0.29287492436824619}]
[null,"N(d1)",{"$f":"NORMSDIST(C19)","v":0.66532454021081322}]
[null,"N(-d1)",{"$f":"NORMSDIST(C20)","v":0.33467545978918678}]
[null,"N(d2)",{"$f":"NORMSDIST(C21)","v":0.61519112184716673}]
[null,"N(-d2)",{"$f":"NORMSDIST(C22)","v":0.38480887815283327}]
[null,"price Call-Option",{"$f":"C9*EXP(-C12*C14)*C23-C10*EXP(-C11*C14)*C25","v":3.140259058130674}]
[null,"price Put-Option",{"$f":"C10*EXP(-C11*C14)*C26-C9*EXP(-C12*C14)*C24","v":1.2694566739701827}]

{"sheet":" Index futures","index":20,"n_rows":10,"n_cols":3,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Calculation of futures price - index future"]
[]
[null,"Assumptions"]
[null,"Spot price",10000]
[null,"Financing costs",1500]
[null,"Income lost",500]
[]
[null,"Calculations"]
[null,"Futures price",{"$f":"(C5+(C6-C7))","v":11000}]

{"sheet":"Interest rate futures","index":21,"n_rows":11,"n_cols":3,"rows_kept":11,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Calculation of futures price, fixed income futures"]
[]
[null,"Assumptions"]
[null,"Spot position",100]
[null,"Price factor",0.7]
[null,"Coupon return",6.5]
[null,"Financing cost",1]
[]
[null,"Calculations"]
[null,"Futures price",{"$f":"((C5/C6)-(C7+C8))","v":135.35714285714286}]

{"sheet":"Currency futures","index":22,"n_rows":10,"n_cols":3,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Calculation of futures price, currency futures"]
[]
[null,"Assumptions"]
[null,"Spot price of currency",1.1200000000000001]
[null,"Financing cost currency",2.0999999999999999E-3]
[null,"Income currency",1E-3]
[]
[null,"Calculations"]
[null,"Futures price",{"$f":"(C5+(C6-C7))","v":1.1211000000000002}]

{"sheet":"Commodity futures","index":23,"n_rows":11,"n_cols":3,"rows_kept":11,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Calculation of futures price, commodity futures"]
[]
[null,"Assumptions"]
[null,"Spot price",100]
[null,"Financing cost",2]
[null,"Convenience Yield",0.78]
[null,"Storage cost",0.2]
[]
[null,"Calculations"]
[null,"Futures price",{"$f":"C5+((C6+C8)-C7)","v":101.42}]

{"sheet":"Futures on indiv. securities","index":24,"n_rows":10,"n_cols":3,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Single Stock Futures"]
[]
[null,"Assumptions"]
[null,"Spot price",20]
[null,"Financing cost",1.34]
[null,"Income lost",0.2]
[]
[null,"Calculations"]
[null,"Futures price",{"$f":"(C5+(C6-C7))","v":21.14}]

{"sheet":"Swap Valuation","index":25,"n_rows":34,"n_cols":7,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"Swap Valuation"]
[]
[null,"Assumptions"]
[null,"principal:",10000000]
[null,"fixed rate (p.a.):",0.05]
[null,"ESTR rate (p.a.):",3.8800000000000001E-2]
[null,"frequency of payments:","quarterly",{"$f":"IF(C9=\"annually\",12,IF(C9=\"semi-annually\",6,3))","v":3}]
[null,"valuation date:","2024-02-08"]
[null,"next payment dates:","2024-06-04",{"$f":"EDATE(C11,$D$9)","v":"2024-09-04"},{"$f":"EDATE(D11,$D$9)","v":"2024-12-04"},{"$f":"EDATE(E11,$D$9)","v":"2025-03-04"},{"$f":"EDATE(F11,$D$9)","v":"2025-06-04"}]
[]
[]
[null,"days till the next payment",{"$f":"$C$11-$C$10","v":117},{"$f":"D11-C11","v":92},{"$f":"E11-D11","v":91},{"$f":"F11-E11","v":90},{"$f":"G11-F11","v":92}]
[]
[null,"Cash Flow (basis 365)",{"$f":"$C$7*C14/365","v":1.6027397260273975E-2},{"$f":"$C$7*D14/365","v":1.2602739726027398E-2},{"$f":"$C$7*E14/365","v":1.2465753424657534E-2},{"$f":"$C$7*F14/365","v":1.2328767123287671E-2},{"$f":"$C$7*G14/365","v":1.2602739726027398E-2}]
[null,"Cash Flow (basis 360)",{"$f":"$C$7*C14/360","v":1.6250000000000001E-2},{"$f":"$C$7*D14/360","v":1.2777777777777779E-2},{"$f":"$C$7*E14/360","v":1.2638888888888889E-2},{"$f":"$C$7*F14/360","v":1.2500000000000001E-2},{"$f":"$C$7*G14/360","v":1.2777777777777779E-2}]
[]
[null,"Discount Rates",{"$f":"'Zero Rates'!E8","v":0.99019704921279328},{"$f":"'Zero Rates'!E9","v":0.97174799141496038},{"$f":"'Zero Rates'!E10","v":0.94734190626130788},{"$f":"'Zero Rates'!E11","v":0.91846880253722019},{"$f":"'Zero Rates'!E12","v":0.88684947462282149}]
[]
[null,"PV Fixed (basis 365)",{"$f":"C16*C19*$C$6","v":158702.81473684497},{"$f":"D16*D19*$C$6","v":122466.87015092652},{"$f":"E16*E19*$C$6","v":118093.30612298494},{"$f":"F16*F19*$C$6","v":113235.87976486277},{"$f":"G16*G19*$C$6+$C$6","v":10111767.331048356}]
[null,"PV Fixed (basis 360)",{"$f":"C17*C19*$C$6","v":160907.02049707892},{"$f":"D17*D19*$C$6","v":124167.79890302272},{"$f":"E17*E19*$C$6","v":119733.49093024863},{"$f":"F17*F19*$C$6","v":114808.60031715252},{"$f":"G17*G19*$C$6+$C$6","v":10113319.655090693}]
[]
[null,"Cumulative PV Fixed (basis 365)",{"$f":"C21","v":158702.81473684497},{"$f":"C24+D21","v":281169.68488777149},399262.99101075646,512498.87077561923,10624266.201823976]
[null,"Cumulative PV Fixed (basis 360)",{"$f":"C22","v":160907.02049707892},285074.81940010167,404808.3103303503,519616.91064750281,10632936.565738196]
[]
[null,"PV Variable (basis 365)",{"$f":"(1+C14/365*$C$8)*$C$6","v":10124372.602739727}]
[null,"PV Variable (basis 360)",{"$f":"(1+C14/360*$C$8)*$C$6","v":10126100}]
[]
[null,"Value Receiver Swap (basis 365)",{"$f":"G24-C27","v":499893.59908424877}]
[null,"Value Receiver Swap (basis 360)",{"$f":"G25-C28","v":506836.56573819555}]
[]
[null,"Value Payer Swap (basis 365)",{"$f":"C27-G24","v":-499893.59908424877}]
[null,"Value Payer Swap (basis 360)",{"$f":"C28-G25","v":-506836.56573819555}]

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[]
[null,"Zero Rates"]
[]
[]
[null,"SWAP Maturity ","Yield","Zero Rate","Discount Factor"]
[]
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[null,3,1.8100000000000002E-2,1.8195289830908346E-2,{"$f":"(100-C10*100*(E8+E9))/(C10*100+100)","v":0.94734190626130788}]
[null,4,2.1299999999999999E-2,2.1489478467835665E-2,{"$f":"(100-C11*100*(E9+E10+E8))/(C11*100+100)","v":0.91846880253722019}]
[null,5,2.4E-2,2.4306709276521454E-2,{"$f":"(100-C12*100*(E10+E11+E9+E8))/(C12*100+100)","v":0.88684947462282149}]
[null,6,2.6200000000000001E-2,2.6632998340627712E-2,{"$f":"(100-C13*100*(E11+E12+E10+E9+E8))/(C13*100+100)","v":0.85409992509249022}]
[null,7,2.8199999999999999E-2,2.8783975467801648E-2,{"$f":"(100-C14*100*(E12+E13+E11+E10+E9+E8))/(C14*100+100)","v":0.81984294377962175}]
[null,8,3.0200000000000001E-2,3.098316086353603E-2,{"$f":"(100-C15*100*(E13+E14+E12+E11+E10+E9+E8))/(C15*100+100)","v":0.78340695747794542}]
[null,9,3.2000000000000001E-2,3.3001481169299574E-2,{"$f":"(100-C16*100*(E14+E15+E13+E12+E11+E10+E9+E8))/(C16*100+100)","v":0.74660604494886329}]
[null,10,3.3700000000000001E-2,3.495268140325325E-2,{"$f":"(100-C17*100*(E15+E16+E14+E13+E12+E11+E10+E9+E8))/(C17*100+100)","v":0.70924300192200018}]
[]
[]
[]
[null,"Note:"]
[null,"Using bootstraping on SWAP rates might give a better approximation."]
[null,"However, using bond yields can be used as a starting point."]

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[null,"Random NO Intervall  [-5 ; 5]","Sum of 5 random NO Intervall   [-5 ; 5]","Sum of  10 random NO Intervall [-5 ; 5]",null,"F9 create a new one"]
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[]
[]
["International Month Codes"]
[]
[]
[]
[null,"Call","Options","Put",null,"Futures"]
["JAN","A",null,"M",null,"F"]
["FEB","B",null,"N",null,"G"]
["MRZ"," C ",null,"O",null,"H"]
["APR","D",null,"P ",null,"J"]
["MAI","E",null,"Q",null,"K"]
["JUN","F",null,"R",null,"M"]
["JUL","G",null,"S",null,"N"]
["AUG","H",null,"T",null,"Q"]
["SEP","I",null,"U",null,"U"]
["OCT","J",null,"V",null,"V"]
["NOV","K",null,"W",null,"X"]
["DEC","L",null,"X",null,"Z"]

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