{"text_format":"1","workbook":"xlsx","n_sheets":6,"sheets":["_EVSCRATCH","ro_HiddenInfo","Results","general_parameters","Performance_table","Benchmark"],"not_rendered":{"charts":2,"images":0,"macros":1,"external_links":0,"defined_names":46,"comments":1,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"_EVSCRATCH","index":0,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":true,"merged":[]}

{"sheet":"ro_HiddenInfo","index":1,"n_rows":27,"n_cols":62,"rows_kept":27,"cut":false,"hidden":true,"merged":[]}
["Optimize",{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},1,1.01E+300,null,"MACROS",null,null,"FORMAT",3,null,"RISKOPT/obj",true]
["FindThe",2,0,null,null,"Start",false,null,"L.FORMULA",null,null,"MaxIter",200]
["Stop Trials",true,10000,null,null,"BeforeCalc",false,null,null,null,null,"SmartStop",0,0]
["Stop Minutes",false,150,null,null,"AfterCalc",false,null,null,null,null,"SameSeed",true]
["Stop Change",false,100,1,true,"EndTrial",false,null,null,null,null,"SampleType",3]
["Stop Formula",false,null,null,null,"Finish",false,null,null,null,null,"MacroBeforeSim",false]
["Pop. Size",100,null,null,null,null,null,null,null,null,null,"MacroAfterSim",false]
["UNUSED","UNUSED",null,null,null,"Seed",true,1]
["Up. Display",1]
["PauseOnErr",false]
["Gen.Log",true]
["Graph",false]
[]
["#Chrom.",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"#Const.",0]
["Meth+OtherOps","Mut.+Op","Cross+Op","Descr.","TimeBlocks","Const","#Ranges","Range","Min","Max","Flags",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ROFUNCEVAL","RISKOPT","DEVEVAL","EVAL","Type","Entry M.","Form.","Description","LeftVal","LeftOp","Ref.","RightOp","RightVal","PenaltyFct","ROevaltime","ROfunc","ROparam"]
["RECIPE\u000111",0.01,0.65,null,0,null,9,{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},1,50,"True,False,False"]
["Default parent selection",null,null,null,null,null,null,{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},1,50,"True,False,False"]
["Default mutation",null,null,null,null,null,null,{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},0,50,"True,False,False"]
["Default crossover",null,null,null,null,null,null,{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},0,50,"True,False,False"]
["Default backtrack",null,null,null,null,null,null,{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},0,50,"True,False,False"]
["Arithmetic crossover",null,null,null,null,null,null,{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},0,50,"True,False,False"]
["Heuristic crossover",null,null,null,null,null,null,{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},0,50,"True,False,False"]
["Cauchy mutation",null,null,null,null,null,null,{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},0,50,"True,False,False"]
["Boundary mutation",null,null,null,null,null,null,{"$f":"general_parameters!#REF!","v":{"$error":"#REF!"}},0,50,"True,False,False"]
["Non-uniform mutation"]
["Linear"]
["Local search"]

{"sheet":"Results","index":2,"n_rows":30,"n_cols":9,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
[null,"Quasi-Random and Traditional Monte Carlo Simulation of Black-Scholes (European Call Option)",null,null,null,null,null,null,"This workbook is downloaded from: http://marcoagd.usuarios.rdc.puc-rio.br/spreads_list.html"]
[null,null,"Do you have comments or suggestions? Email to marcoagd@pobox.com "]
[null,"Set the number of simulations and click the button below to get the results",null,null,"Input: yellow cells"]
[null,"Number of Simulations = ",1000000,null,"Simulation Output: blue cells"]
[null," RESULTS"]
[null,"Intrisic Value: (V - K) = ",{"$f":"general_parameters!P0_-D0_","v":0},"$",null,"Exact Value"]
[null,"Quasi-Monte Carlo Option Value =  ",2.3912717238476491,"$","Analytical Result = ",{"$f":"BlackScholesMerton(P0_,D0_,r_,delta,sigma,T_)","v":2.3913916482553494},"(compare this number with the simulated option value: they need be close)"]
[null,"QMC simulation error = ",{"$f":"($C$7-$F$7)/$F$7","v":-5.0148376067073053E-5}]
[null,"Probability of Option Exercise"]
[null,"Expected Exercise Time Given that Occurred Exercise"]
[]
[null,"Traditional Monte Carlo with Moro Inversion = ",2.3954555991671391]
[null,"Monte Carlo + Moro simulation error = ",{"$f":"($C$12-$F$7)/$F$7","v":1.6994083402250551E-3}]
[]
[null,"Traditional Monte Carlo with Excel Inversion = ",2.3876971932998186]
[null,"Monte Carlo Excel error = ",{"$f":"($C$15-$F$7)/$F$7","v":-1.5448974902234004E-3}]
[]
[]
[]
[]
[]
[null,null,null,null,"Computational Time: Look the sheet \"Performance_table\" in order to have an idea on the computational time with the number of simulations."]
[null,null,null,null,"   5,000 simulations take one second or less for one simulation and ~ 2 seconds for the three simulations in parallel"]
[]
[]
[]
[null,"Start time = ","2020-02-09T16:48:00"]
[null,"Finish time = ","2020-02-09T16:48:08"]
[null,"Computational Time = ",{"$f":"Finish_time-start_time","v":"00:00:08"},"min:sec"]
[null,"Precise Calculation Time=",8.4974106999579817,"sec"]

{"sheet":"general_parameters","index":3,"n_rows":8,"n_cols":104,"rows_kept":8,"cut":false,"hidden":false,"merged":[]}
["General Parameters: "]
["Volatility, Asset Current Price, Exercise Price, Interest Rate, Dividend Yield and Time to Expiration",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Não Exercício","Exercício"]
["Risk-Free Interest Rate (r)",0.08,"per annum",null,"Input: yellow cells"]
["Volatility (s)",0.25,"p.a.",null,"Output: blue cells (see the sheet \"results\")"]
["Dividend Yield (d) ",0.08,"p.a."]
["Current Price (V0)",20,"$"]
["Exercise Price ",20,"$"]
["Time to Expiration  (T)",2,"years"]

{"sheet":"Performance_table","index":4,"n_rows":14,"n_cols":6,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Results for the Default Parameters ",null,null,"Correto = ",2.3913915150146572]
[null,null,"One simulation (QMC) only"]
[null,"Pentium III, 1 GHz"]
[null,"Num Simul","Time (seconds)","Simulated Black Scholes","Error Sim."]
[null,1000000,"00:00:28",2.3912717238476491,-5.0092662057210467E-5]
[null,400000,"00:00:11",2.3911105651379354,-1.1748384777557392E-4]
[null,100000,"00:00:02",2.3904289367797538,-4.025180439337312E-4]
[null,50000,"00:00:01",2.3896228050770945,-7.3961537726368004E-4]
[null,20000,"00:00:01",2.3876971944070084,-1.5448413965063745E-3]
[null,10000,"00:00:00",2.3846294795696887,-2.8276572039802545E-3]
[null,5000,"00:00:00",2.3791348166762551,-5.1253415684745854E-3]
[null,1000,"00:00:00",2.3470268032829118,-1.8551839568383459E-2]
[null,500,"00:00:00",2.3107674303778687,-3.371429735807787E-2]

{"sheet":"Benchmark","index":5,"n_rows":35,"n_cols":2,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
["Original VBA code","Compiled VBA code"]
[8.4974106999579817,3]
[]
["Performance Rank:",{"$f":"IF(AND(ISNUMBER(A2), ISNUMBER(B2), B2>0), A2/B2, \"Not enough data\")","v":2.8324702333193272}]
[]
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["Original VBA code","Compiled VBA code"]
[1.7018390001030639,0.55000000000000004]
[]
["Performance Rank:",{"$f":"IF(AND(ISNUMBER(A33), ISNUMBER(B33), B33>0), A33/B33, \"Not enough data\")","v":3.0942527274601157}]