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{"sheet":"Black Scholes Option Pricing","index":0,"n_rows":12,"n_cols":6,"rows_kept":12,"cut":false,"hidden":false,"merged":[]}
["The Black-Scholes Options Pricing Model"]
[]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Stock Price","S =",40,null,"d1 =",{"$f":"((LN(C4/C5))+(C6+0.5*C7^2)*C8)/(C7*C8^0.5)","v":1.4757282898071233}]
["Exercise Price","X =",30,null,"d2 =",{"$f":"F4-C7*C8^0.5","v":1.2257282898071233}]
["Riskless Rate","r =",0.05,null,"N(d1) =",{"$f":"NORMDIST(F4,0,1,1)","v":0.92999157585964298}]
["Standard Deviation","sigma =",0.25,null,"N(d2) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.88984952969063391}]
["Time to Expiry","T =",1,null,"c0 =",{"$f":"C4*F6-C5*2.7182818^(-C6*C8)*F7","v":11.806131340497263}]
[null,null,null,null,"p0 =",{"$f":"F8+C5*EXP(-C6*C8)-C4","v":0.34301407551868124}]
[]
[]
["The Black Scholes Options Pricing Formulas:"]

{"sheet":"Greeks","index":1,"n_rows":17,"n_cols":8,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
["        Option Greeks"]
[]
[]
[null,"The Black-Scholes Options Pricing Model"]
[null,"Option 1"]
[null,"Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
[null,"Stock Price","S =",75,null,"d1 =",{"$f":"((LN(D7/D8))+(D9+0.5*D10^2)*D11)/(D10*D11^0.5)","v":9.0019921813306827E-2}]
[null,"Exercise Price","X =",80,null,"d2 =",{"$f":"G7-D10*D11^0.5","v":-0.19282279066131225}]
[null,"Riskless Rate","r =",0.1,null,"N(d1) =",{"$f":"NORMDIST(G7,0,1,1)","v":0.53586430810880148}]
[null,"Standard Deviation","sigma =",0.4,null,"N(d2) =",{"$f":"NORMDIST(G8,0,1,1)","v":0.4235488770307978}]
[null,"Time to Expiry","T =",0.5,null,"c0 =",{"$f":"D7*G9-D8*2.7182818^(-D9*D11)*G10","v":7.9584507276134389}]
[null,null,null,null,null,"p0 = ",{"$f":"-D7+G11+D8*2.7182818^(-D9*D11)","v":9.0568047275061332},"Puts"]
[null,null,null,null,null,"Delta =",{"$f":"G9","v":0.53586430810880148},{"$f":"G13-1","v":-0.46413569189119852}]
[null,null,null,null,null,"Gamma =",{"$f":"((2.7182818^(-($G$7^2)/2))/(2*3.141)^0.5)/($D$7*$D$10*$D$11^0.5)","v":1.8732041259171394E-2},{"$f":"((2.7182818^(-($G$7^2)/2))/(2*3.141)^0.5)/($D$7*$D$10*$D$11^0.5)","v":1.8732041259171394E-2}]
[null,null,null,null,null,"Theta =",{"$f":"(-$D$9*$D$8*2.7182818^(-$D$9*$D$11))*$G$10-($D$10*$D$7)*((2.7182818^(-($G$7^2)/2))/(2*(2*3.14128)^0.5*$D$11^0.5))","v":-11.652180115504722},{"$f":"($D$9*$D$8*2.7182818^(-$D$9*$D$11))*NORMDIST(-G8,0,1,1)-($D$10*$D$7)*((2.7182818^(($G$7^2)/2))/(2*(2*3.14128)^0.5*$D$11^0.5))","v":-4.1109277001363322}]
[null,null,null,null,null,"Vega =",{"$f":"($D$7*$D$11^0.5)*((2.7182818^(-($G$7^2)/2))/(2*3.14128)^0.5)","v":21.072607193625139},{"$f":"($D$7*$D$11^0.5)*((2.7182818^(-($G$7^2)/2))/(2*3.14128)^0.5)","v":21.072607193625139}]
[null,null,null,null,null,"Rho = ",{"$f":"$D$11*$D$8*2.7182818^(-$D$9*$D$11)*$G$10","v":16.115686190273337},{"$f":"-$D$11*$D$8*2.7182818^(-$D$9*$D$11)*NORMDIST(-G8,0,1,1)","v":-21.93349080967301}]

{"sheet":"Black-Scholes Variance Estimate","index":2,"n_rows":12,"n_cols":7,"rows_kept":12,"cut":false,"hidden":false,"merged":[]}
["The Black-Scholes Options Pricing Model"]
[]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Stock Price","S =",30,null,"d1 =",{"$f":"((LN(C4/C5))+(C6+0.5*C7^2)*C8)/(C7*C8^0.5)","v":-0.35055059032555297}]
["Exercise Price","X =",35,null,"d2 =",{"$f":"F4-C7*C8^0.5","v":-0.63339330280017203}]
["Riskless Rate","r =",0.03,null,"N(d1) =",{"$f":"NORMDIST(F4,0,1,1)","v":0.36296276503571989}]
["Standard Deviation","sigma =",0.4,null,"N(d2) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.26323841868434872}]
["Time to Expiry","T =",0.5,null,"c0 =",{"$f":"C4*F6-C5*2.7182818^(-C6*C8)*F7","v":1.8127071273598876},"Substitute values for sigma until c0 equals market price."]
[]
[]
[]
["The Black Scholes Options Pricing Formulas:"]

{"sheet":"Method of Bisection","index":3,"n_rows":27,"n_cols":10,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
["Using the Bisection Method to Estimate Implied Volatility"]
["     a1 =",0.5,"      b1=",0.2,null,null,"Enter values in the unhighlighted cells."]
["     rf  =",0.1,"      S0=",75,"X  =",80,{"$f":"\"The Implied volatility is \" & D27","v":"The Implied volatility is 0.411465644836426"}]
["     C0=",8.1999999999999993,"      T =",0.5]
[null,null,"sn","  d1(sn)","  d2(sn)","  N[d1(sn)]","  N[d2(sn)]","c(sn)","f(sn)"]
["   f(a1)=",{"$f":"I6","v":1.86046505816946},{"$f":"B2","v":0.5},{"$f":"(LN($D$3/$F$3)+($B$3+0.5*C6^2)*$D$4)/(C6*$D$4^0.5)","v":0.13565554775743471},{"$f":"D6-C6*$D$4^0.5","v":-0.21789784283583907},{"$f":"NORMDIST(D6,0,1,TRUE)","v":0.55395320473825749},{"$f":"NORMDIST(E6,0,1,TRUE)","v":0.41375435396729149},{"$f":"$D$3*F6-$F$3*2.7182818^(-$B$3*$D$4)*G6","v":10.060465058169459},{"$f":"H6-$B$4","v":1.86046505816946}]
["   f(b1)=",{"$f":"I7","v":-4.4678734997760294},{"$f":"D2","v":0.2},{"$f":"(LN($D$3/$F$3)+($B$3+0.5*C7^2)*$D$4)/(C7*$D$4^0.5)","v":-3.20921907293506E-2},{"$f":"D7-C7*$D$4^0.5","v":-0.17351354696666013},{"$f":"NORMDIST(D7,0,1,TRUE)","v":0.48719926554970322},{"$f":"NORMDIST(E7,0,1,TRUE)","v":0.43112389022303993},{"$f":"$D$3*F7-$F$3*2.7182818^(-$B$3*$D$4)*G7","v":3.7321265002239699},{"$f":"H7-$B$4","v":-4.4678734997760294}]
["n","an","bn","sn","  d1(sn)","  d2(sn)","  N[d1(sn)]","  N[d2(sn)]","c(sn)","f(sn)"]
[1,{"$f":"C6","v":0.5},{"$f":"C7","v":0.2},{"$f":"(B9+C9)/2","v":0.35},{"$f":"(LN($D$3/$F$3)+($B$3+0.5*D9^2)*$D$4)/(D9*$D$4^0.5)","v":6.499919022307131E-2},{"$f":"E9-D9*$D$4^0.5","v":-0.18248818319222032},{"$f":"NORMDIST(E9,0,1,TRUE)","v":0.52591267749934256},0.42759981355176535,{"$f":"$D$3*G9-$F$3*2.7182818^(-$B$3*$D$4)*H9","v":6.9038088305003384},{"$f":"I9-$B$4","v":-1.2961911694996608}]
[2,{"$f":"IF(J9>0,D9,B9)","v":0.5},{"$f":"IF(J9>0,C9,D9)","v":0.35},0.42499999999999999,0.10188237036778586,-0.19863801163649686,0.54057497822656431,0.42127295854051672,8.4849446373939656,0.28494463739396636]
[3,0.42499999999999999,0.35,0.38749999999999996,8.394239364301978E-2,-0.1900614840667674,0.53344888338454211,0.42463047558143546,7.6949860039017892,-0.50501399609821007]
[4,0.42499999999999999,0.38749999999999996,0.40625,9.3020421803345577E-2,-0.1942417080536894,0.53705633134512842,0.42299331321613398,8.0901299621757801,-0.10987003782421922]
[5,0.42499999999999999,0.40625,0.41562500000000002,9.7476578294108801E-2,-0.19641467763655004,0.53882603327225786,0.42214280445878005,8.2875799232076162,8.7579923207616872E-2]
[6,0.41562500000000002,0.40625,0.41093750000000001,9.5255011038008278E-2,-0.19532168185583865,0.53794386195281452,0.42257056214214767,8.1888654186342791,-1.1134581365720209E-2]
[7,0.41562500000000002,0.41093750000000001,0.41328125000000004,9.6367394720135183E-2,-0.19586657969211774,0.53838560659194323,0.42235729805497357,8.2382253125701723,3.8225312570173031E-2]
[8,0.41328125000000004,0.41093750000000001,0.412109375,9.5811606305028482E-2,-0.19559372734802138,0.53816490036410292,0.42246408515170042,8.2135460231928121,1.3546023192812839E-2]
[9,0.412109375,0.41093750000000001,0.41152343749999998,9.5533409958813653E-2,-0.19545760331463474,0.53805442285144012,0.42251736258245276,8.2012058849575027,1.2058849575034003E-3]
[10,0.41152343749999998,0.41093750000000001,0.41123046875000002,9.5394235874354083E-2,-0.1953896172092936,0.53799915284673583,0.42254397211781897,8.1950356927626089,-4.9643072373903863E-3]
[11,0.41152343749999998,0.41123046875000002,0.411376953125,9.5463829253792681E-2,-0.19542360392475536,0.53802679045756496,0.42253066978630627,8.1981207991072793,-1.8792008927199788E-3]
[12,0.41152343749999998,0.411376953125,0.41145019531249999,9.5498621189759297E-2,-0.19544060203623889,0.53804060730628778,0.42252401679308388,8.1996633445948817,-3.3665540511762515E-4]
[13,0.41152343749999998,0.41145019531249999,0.41148681640624996,9.5516015970044804E-2,-0.19544910227967846,0.53804751524176853,0.42252068983990215,8.2004346154169028,4.3461541690348326E-4]
[14,0.41148681640624996,0.41145019531249999,0.411468505859375,9.5507318678854855E-2,-0.19544485205900586,0.53804406131475957,0.42252235335453175,8.2000489801660592,4.8980166059919839E-5]
[15,0.411468505859375,0.41145019531249999,0.41145935058593752,9.5502969959046932E-2,-0.19544272702288257,0.53804233432070725,0.42252318508331815,8.1998561624205166,-1.4383757948266407E-4]
[16,0.411468505859375,0.41145935058593752,0.41146392822265626,9.5505144325135641E-2,-0.19544378953475949,0.5380431978202791,0.42252276922130244,8.1999525713032995,-4.7428696699824968E-5]
[17,0.411468505859375,0.41146392822265626,0.4114662170410156,9.5506231503541442E-2,-0.19544432079533647,0.53804362956815588,0.42252256128851146,8.2000007757371876,7.7573718826329241E-7]
[18,0.4114662170410156,0.41146392822265626,0.41146507263183596,9.5505687914725079E-2,-0.19544405516466146,0.53804341369437658,0.42252266525505555,8.1999766735208652,-2.3326479134055944E-5]
[19,0.4114662170410156,0.41146507263183596,0.41146564483642578,9.5505959709229871E-2,-0.19544418797990237,0.53804352163130598,0.42252261327182061,8.1999887246291863,-1.127537081302421E-5]

{"sheet":"Newton Raphson","index":4,"n_rows":12,"n_cols":8,"rows_kept":12,"cut":false,"hidden":false,"merged":[]}
["Using the Newton Raphson Method to Estimate Implied Volatility"]
["  s0 =",0.6,null,"   S0=",75]
["   rf  =",0.1,null,"   T =",0.5]
["  C0=",8.1999999999999993,null,"  X  =",80]
[]
["n","     sn","    f'(sn)","    d1(sn)","    d2(sn)","    N(d1)","   N (d2)","    f(sn)"]
[1,{"$f":"B2","v":0.6},{"$f":"($E$2*$E$3^0.5*2.7182818^(-(D7^2)/2))/((2*3.14159)^0.5)","v":20.825090590487285},{"$f":"(LN($E$2/$E$4)+($B$3+0.5*B7^2)*$E$3)/(B7*$E$3^0.5)","v":0.17786441140662915},{"$f":"D7-B7*$E$3^0.5","v":-0.24639965730529936},{"$f":"NORMDIST(D7,0,1,TRUE)","v":0.57058526963873102},0.4026864357466956,{"$f":"$E$2*F7-$E$4*2.7182818^(-$B$3*$E$3)*G7-$B$4","v":3.9501202844977463}]
[2,{"$f":"B7-(H7/C7)","v":0.4103191788129783},21.061939915427054,9.4961004885024167E-2,-0.19517846890452833,0.53782709975230114,0.42262661711473387,-2.4157437551540539E-2]
[3,{"$f":"B8-(H8/C8)","v":0.41146614996798792},21.060846389775524,9.5506199644199499E-2,-0.19544430522688572,0.53804361691595215,0.42252256738192662,-6.3687695828207325E-7]
[4,{"$f":"B9-(H9/C9)","v":0.41146618020784376},21.060846360883627,9.5506214007975265E-2,-0.19544431224591707,0.53804362262019478,0.42252256463471222,-2.5934809855243657E-13]
[5,{"$f":"B10-(H10/C10)","v":0.41146618020785608},21.060846360883613,9.550621400798108E-2,-0.19544431224591996,0.53804362262019712,0.42252256463471111,0]
[6,{"$f":"B11-(H11/C11)","v":0.41146618020785608},21.060846360883613,9.550621400798108E-2,-0.19544431224591996,0.53804362262019712,0.42252256463471111,0]

{"sheet":"Compound Option Model","index":5,"n_rows":21,"n_cols":8,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Geske-Roll-Whaley Compound Option Formula"]
[]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Stock Price","S =",50,null,"d1 =",{"$f":"((LN((C4-IF(C11<C9,C10*EXP(-C7*C11),0))/B13))+(C7+0.5*C8^2)*C11)/(C8*C11^0.5)","v":0.82440424714142491},{"$f":"((LN((C4-IF(C11<C9,C10*EXP(-C7*C9),0))/C6))+(C7+0.5*C8^2)*C9)/(C8*C9^0.5)","v":0.5669600402811027},"=y1"]
["First Exercise Price","X1 =",3,null,"d2 =",{"$f":"F4-C8*C11^0.5","v":0.62440424714142484},{"$f":"(G4-C8*C9^0.5)","v":0.28411732780648363},"=y2"]
["Second Exercise Price","X2 =",45,null,"N(d1) =",{"$f":"NORMDIST(F4,0,1,1)","v":0.79514504878571601},{"$f":"NORMDIST(G4,0,1,1)","v":0.71462933459470079},"=N(y1)"]
["Riskless Rate","r =",0.03,null,"N(d2) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.73381893172595891},{"$f":"NORMDIST(G5,0,1,1)","v":0.61183976587433286},"=N(y2)"]
["Standard Deviation","sigma =",0.4,null,null,null,{"$f":"((C11/C9)^0.5)","v":0.70710678118654757},"=rho"]
["Second Expiry Date","T2 =",0.5,null,null,null,{"$f":"bivar(F4,G4,G8)","v":{"$error":"#NAME?"}},"=bivar(d(1),y(1);rho)"]
["Dividend Amount","        D =",0,null,null,null,{"$f":"bivar(F5,G5,G8)","v":{"$error":"#NAME?"}},"=bivar(d(2),y(2);rho)"]
["First Expiry Date","        T1 =",0.25]
[]
["Trial S*tD =",43.581910000000001,"IF B14 < B15"]
["CtD =",{"$f":"(B13-C10)*NORMDIST((LN((B13-C10)/C6)+(C7+0.5*C8^2)*(C9-C11))/(C8*(C9-C11)^0.5),0,1,1)-C6*2.7182818^(-C7*(C9-C11))*NORMDIST((LN((B13-C10)/C6)+(C7-0.5*C8^2)*(C9-C11))/(C8*(C9-C11)^0.5),0,1,1)","v":3.0000000751937144},"RAISE B13"]
["X1 =",{"$f":"C5","v":3}]
[]
[]
[]
[]
[]
["c0,call =",{"$f":"C4*G9-C6*2.7182818^-(C7*C9)*G10-C5*2.7182818^-(C7*C11)*F7","v":{"$error":"#NAME?"}}]

{"sheet":"European Known Dividend Model","index":6,"n_rows":12,"n_cols":6,"rows_kept":12,"cut":false,"hidden":false,"merged":[]}
["Black-Scholes European Known Dividend Model"]
[]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Stock Price","S =",50,null,"d1 =",{"$f":"((LN((C4-IF(C10<C8,C9*EXP(-C6*C10),0))/C5))+(C6+0.5*C7^2)*C8)/(C7*C8^0.5)","v":0.19738840433242688}]
["Exercise Price","X =",45,null,"d2 =",{"$f":"F4-C7*C8^0.5","v":-8.5454308142192181E-2}]
["Riskless Rate","r =",0.03,null,"N(d1) =",{"$f":"NORMDIST(F4,0,1,1)","v":0.57823819844057422}]
["Standard Deviation","sigma =",0.4,null,"N(d2) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.46595010968026823}]
["Time to Expiry","T =",0.5,null,"c0 =",{"$f":"(C4-IF(C10<C8,C9*EXP(-C6*C10),0))*F6-C5*2.7182818^(-C6*C8)*F7","v":5.3867360134406788}]
["Dividend Amount","        D =",5,null,"p0 =",{"$f":"F8+C5*EXP(-C6*C8)-(C4-IF(C10<C8,C9*EXP(-C6*C10),0))","v":4.6794135696741819}]
["Ex-dividend Date","        t1 =",0.25]
[]
["The European Known Dividend Options Pricing Formulas:"]

{"sheet":"Black's Pseudo American Call","index":7,"n_rows":36,"n_cols":6,"rows_kept":36,"cut":false,"hidden":false,"merged":[]}
["Black's Pseudo-American Call Model"]
["Black-Scholes European Known Dividend Model"]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Stock Price","S =",50,null,"d1 =",{"$f":"((LN((C4-IF(C10<C8,C9*EXP(-C6*C10),0))/C5))+(C6+0.5*C7^2)*C8)/(C7*C8^0.5)","v":0.19738840433242688}]
["Exercise Price","X =",45,null,"d2 =",{"$f":"F4-C7*C8^0.5","v":-8.5454308142192181E-2}]
["Riskless Rate","r =",0.03,null,"N(d1) =",{"$f":"NORMDIST(F4,0,1,1)","v":0.57823819844057422}]
["Standard Deviation","sigma =",0.4,null,"N(d2) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.46595010968026823}]
["Time to Expiry","T =",0.5,null,"c0 =",{"$f":"(C4-IF(C10<C8,C9*EXP(-C6*C10),0))*F6-C5*2.7182818^(-C6*C8)*F7","v":5.3867360134406788}]
["Dividend Amount","        D =",5,null,"p0 =",{"$f":"F8+C5*EXP(-C6*C8)-(C4-IF(C10<C8,C9*EXP(-C6*C10),0))","v":4.6794135696741819}]
["Ex-dividend Date","        t1 =",0.25]
[]
["The European Known Dividend Options Pricing Formulas:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["X[1-e-r(T-tD)]  = ",{"$f":"C5*(1-2.7182818^(-C6*(C8-C10)))","v":0.3362375296317166},"Compare dividend to present value of exercise money."]
["Black-Scholes Model for Use with Black's Pseudo-American Call Model"]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Stock Price","S =",{"$f":"C4","v":50},null,"d1 =",{"$f":"((LN(C30/C31))+(C32+0.5*C33^2)*C36)/(C33*C36^0.5)","v":0.66430257828913175}]
["Exercise Price","X =",{"$f":"C5","v":45},null,"d2 =",{"$f":"F30-C33*C36^0.5","v":0.46430257828913174}]
["Riskless Rate","r =",{"$f":"C6","v":0.03},null,"N(d1) =",{"$f":"NORMDIST(F30,0,1,1)","v":0.74675166440505347}]
["Standard Deviation","sigma =",{"$f":"C7","v":0.4},null,"N(d2) =",{"$f":"NORMDIST(F31,0,1,1)","v":0.67878451149088204}]
["Time to Expiry","T =",{"$f":"C36","v":0.25},null,"c0 =",{"$f":"(C30*F32)-C31*2.7182818^(-C32*C36)*F33","v":7.0205130304589503}]
["Dividend Amount","        D =",{"$f":"C9","v":5},null,"p0 =",{"$f":"F34+C31*EXP(-C32*C34)-(C30-IF(C36<C34,C35*EXP(-C32*C36),0))","v":1.6842754973201792}]
["Ex-dividend Date","        tD =",{"$f":"C10","v":0.25}]

{"sheet":"Geske Roll Whaley Model","index":8,"n_rows":35,"n_cols":9,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
["Geske-Roll-Whaley Compound Option Dividend Adjustment Formula"]
[]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Stock Price","S =",50,null,"d1 =",{"$f":"((LN((C4-IF(C10<C8,C9*EXP(-C6*C10),0))/C5))+(C6+0.5*C7^2)*C8)/(C7*C8^0.5)","v":0.19738840433242688},{"$f":"((LN((C4-IF(C10<C8,C9*EXP(-C6*C10),0))/B13))+(C6+0.5*C7^2)*C10)/(C7*C10^0.5)","v":0.66920730244807025},"=y1"]
["Exercise Price","X =",45,null,"d2 =",{"$f":"F4-C7*C8^0.5","v":-8.5454308142192181E-2},{"$f":"(G4-C7*C10^0.5)","v":0.46920730244807024},"=y2"]
["Riskless Rate","r =",0.03,null,"N(d1) =",{"$f":"NORMDIST(F4,0,1,1)","v":0.57823819844057422},{"$f":"NORMDIST(G4,0,1,1)","v":0.7483183756745394},"=N(y1)"]
["Standard Deviation","sigma =",0.4,null,"N(d2) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.46595010968026823},{"$f":"NORMDIST(G5,0,1,1)","v":0.68053926684943855},"=N(y2)"]
["Time to Expiry","T =",0.5,null,null,null,{"$f":"((C10/C8)^0.5)","v":0.70710678118654757},"=rho"]
["Dividend Amount","        D =",5,null,null,null,{"$f":"bivar(F4,-G4,-G8)","v":{"$error":"#NAME?"}},"=bivar(d(1),-y(1);-rho)"]
["Ex-dividend Date","        tD =",0.25,null,null,null,{"$f":"bivar(F5,-G5,-G8)","v":{"$error":"#NAME?"}},"=bivar(d(2),-y(2);-rho)"]
[]
[]
["Trial S*tD =",40.493881999999999,"IF B14 > B15"]
["CtD =",{"$f":"(B13-C9)*NORMDIST((LN((B13-C9)/C5)+(C6+0.5*C7^2)*(C8-C10))/(C7*(C8-C10)^0.5),0,1,1)-C5*2.7182818^(-C6*(C8-C10))*NORMDIST((LN((B13-C9)/C5)+(C6-0.5*C7^2)*(C8-C10))/(C7*(C8-C10)^0.5),0,1,1)","v":0.49388242027942919},"RAISE B13",null,null,null,1.5,0.3,"=y1"]
["S*tD + D - X",{"$f":"B13+C9-C5","v":0.49388199999999927},null,null,null,null,{"$f":"G14-D17*D18^0.5","v":-6.2381348313356746},{"$f":"(H14-D17*D20^0.5)","v":0.3},"=y2"]
[null,null,null,null,null,null,{"$f":"NORMDIST(G14,0,1,1)","v":0.93319279873114191},{"$f":"NORMDIST(H14,0,1,1)","v":0.61791142218895267},"=N(y1)"]
[null,null,null,{"$f":"G6/G7","v":1.099596176336576},null,null,{"$f":"NORMDIST(G15,0,1,1)","v":2.214094554808124E-10},{"$f":"NORMDIST(H15,0,1,1)","v":0.61791142218895267},"=N(y2)"]
[null,null,null,{"$f":"(C4-C9*2.7182818^-(C10*C6))*D17","v":49.522908546470795},null,null,null,0.5,"=rho"]
[null,null,null,{"$f":"D18-C9*2.7182818^-(C10*C6)","v":44.560268271985429},null,null,null,{"$f":"bivar(G14,H14,H18)","v":{"$error":"#NAME?"}},"=bivar(d(1),-y(1);rho)"]
[null,null,null,null,null,null,null,{"$f":"bivar(G15,-H15,H18)","v":{"$error":"#NAME?"}},"=bivar(d(2),-y(2);rho)"]
["c0 =",{"$f":"SUM(B26:B35)","v":{"$error":"#NAME?"}}]
[]
[]
[]
[]
[null,{"$f":"($C$4-$C$9*2.7182818^(-$C$6*$C$10))*G6","v":33.702283874467028}]
[]
[]
[null,{"$f":"($C$4-$C$9*2.7182818^(-$C$6*$C$10))*G9","v":{"$error":"#NAME?"}}]
[]
[]
[null,{"$f":"-($C$5*2.7182818^(-$C$6*$C$8))*G10","v":{"$error":"#NAME?"}}]
[]
[]
[null,{"$f":"-(($C$5-$C$9)*2.7182818^(-$C$6*$C$10))*G7","v":-27.018172592286131}]

{"sheet":"Merton Dividend Leakage","index":9,"n_rows":27,"n_cols":6,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
["The Merton Continuous Dividend Leakage Options Pricing Model"]
[]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Stock Price","S =",75,null,"d1 =",{"$f":"((LN(C4/C5))+(C6-C9+0.5*C7^2)*C8)/(C7*C8^0.5)","v":5.4664582753979479E-2}]
["Exercise Price","X =",80,null,"d2 =",{"$f":"F4-C7*C8^0.5","v":-0.22817812972063958}]
["Riskless Rate","r =",0.1,null,"N(d1) =",{"$f":"NORMDIST(F4,0,1,1)","v":0.52179715698974583}]
["Standard Deviation","sigma =",0.4,null,"N(d2) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.40975388147424863}]
["Time to Expiry","T =",0.5,null,"c0 =",{"$f":"C4*(2.7182818^(-C9*C8))*F6-C5*2.7182818^(-C6*C8)*F7","v":7.5637932184354817}]
["Dividend Yield","d =",0.02,null,"p0 =",{"$f":"F8+C5*EXP(-C6*C8)-C4*(2.7182818^(-C9*C8))","v":9.4084096395310155}]
[]
[]
["The Merton Continuous Leakage Formulas:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"p0 = c0  + Xe-rft - S0e-rfT"]

{"sheet":"Margrabe Exchange Options","index":10,"n_rows":10,"n_cols":6,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
["The Margrabe-Fisher Exchange Options Pricing Model"]
[]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Asset 1 Value","S1,0 =",50,null,"σ =",{"$f":"(C7^2+C8^2-2*C10*C7*C8)^0.5","v":0.72111025509279791}]
["Asset 2 Value","S2,0 =",40,null,"d1 =",{"$f":"((LN(C4/C5))+(0.5*F4^2)*C9)/(F4*C9^0.5)","v":0.79916642227513257}]
["Riskless Rate","r(f) =",0.05,null,"d2 =",{"$f":"F5-F4*C9^0.5","v":0.43861129472873361}]
["Standard Deviation 1","sigma (1) =",0.4,null,"N(d1) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.78790304048413617}]
["Standard Deviation 1","sigma (1) =",0.6,null,"N(d2) =",{"$f":"NORMDIST(F6,0,1,1)","v":0.66952839420655352}]
["Time to Expiry","T =",0.25,null,"c0 =",{"$f":"C4*F7-C5*F8","v":12.614016255944669}]
["Asset Correlation","r1,2 =",0,null,"       p0=",{"$f":"F9+C5-C4","v":2.6140162559446694}]

{"sheet":"Currency Option Pricing","index":11,"n_rows":9,"n_cols":6,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["The Garman and Köhlagen Options Pricing Model (Currencies)"]
[]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Exchange Rate","s0 =",0.5,null,"d1 =",{"$f":"((LN((C4)/(C5)))+(C6-C9+0.5*C7^2)*C8)/(C7*C8^0.5)","v":0.13133573032668661}]
["Exercise Price","X =",0.45,null,"d2 =",{"$f":"F4-C7*C8^0.5","v":-8.0796304029277649E-2}]
["Domestic Riskless Rate","r(d) =",0.03,null,"N(d1) =",{"$f":"NORMDIST(F4,0,1,1)","v":0.55224513606692172}]
["Standard Deviation","sigma =",0.15,null,"N(d2) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.46780197370949589}]
["Time to Expiry","T =",2,null,"c0 =",{"$f":"C4*2.7182818^(-C9*C8)*F6-C5*2.7182818^(-C6*C8)*F7","v":3.7044443201585731E-2}]
["Foreign Riskless Rate","          r(f) =",0.08,null,"       p0=",{"$f":"F8+C5*2.718^(-C6*C8)-C4*2.718^(-C9*C8)","v":3.476215691492307E-2}]

{"sheet":"Chooser Options","index":12,"n_rows":12,"n_cols":13,"rows_kept":12,"cut":false,"hidden":false,"merged":[]}
["Chooser Options"]
["Call(S,X,r,s,T,d)",null,null,null,null,null,null,"Put(S,X,r,s,tc,d)"]
["Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs",null,"Input Definitions","Symbols","Inputs",null,"Formula Values","Outputs"]
["Stock Price","S =",50,null,"d1 =",{"$f":"((LN(C4/C5))+(C6-C9+0.5*C7^2)*C8)/(C7*C8^0.5)","v":0.32500000000000001},null,"Stock Price","S =",{"$f":"C4","v":50},null,"d1 =",{"$f":"(((LN(J4/J5))+(J6-J9)*C8+(0.5*J7^2)*C10))/(J7*C10^0.5)","v":0.31819805153394637}]
["Exercise Price","X =",50,null,"d2 =",{"$f":"F4-C7*C8^0.5","v":-7.5000000000000011E-2},null,"Exercise Price","X =",50,null,"d2 =",{"$f":"M4-J7*C10^0.5","v":3.5355339059327306E-2}]
["Riskless Rate","r =",0.05,null,"N(d1) =",{"$f":"NORMDIST(F4,0,1,1)","v":0.62740946415328402},null,"Riskless Rate","r =",0.05,null,"N(d1) =",{"$f":"NORMDIST(M4,0,1,1)","v":0.62483264466500554}]
["Standard Deviation","sigma =",0.4,null,"N(d2) =",{"$f":"NORMDIST(F5,0,1,1)","v":0.47010735594710523},null,"Standard Deviation","sigma =",0.4,null,"N(d2) =",{"$f":"NORMDIST(M5,0,1,1)","v":0.5141018016521639}]
["Time to Expiry","T =",1,null,"c0 =",{"$f":"C4*(2.7182818^(-C9*C8))*F6-C5*2.7182818^(-C6*C8)*F7","v":9.0114757134039678},null,"Time to Expiry","T =",1,null,"c0 =",{"$f":"J4*(2.7182818^(-J9*C8))*M6-J5*2.7182818^(-J6*C8)*M7","v":6.790194174432159}]
["Dividend Yield","d =",0,null,"p0 =",{"$f":"F8+C5*EXP(-C6*C8)-C4*(2.7182818^(-C9*C8))","v":6.5729469384396708},null,"Dividend Yield","d =",0,null,"p0 =",{"$f":"M8+J5*EXP(-J6*C8)-J4*(2.7182818^(-J9*C8))","v":4.351665399467862}]
["Chooser Date","tc =",0.5,null,null,null,null,"Chooser Date","tc =",0.5]
[]
[null,null,null,null,"Chooser Option Value:",null,null,{"$f":"F8+M9","v":13.36314111287183}]