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{"sheet":"Introduction","index":0,"n_rows":11,"n_cols":8,"rows_kept":11,"cut":false,"hidden":false,"merged":[[3,3,3,5]]}
[null,null,null,null,null,null,{"$f":" RIGHT(CELL(\"filename\",A1), LEN(CELL(\"filename\",A1)) - SEARCH(\"]\", CELL(\"filename\",A1)))","v":"Introduction"}]
[null,null,null,null,null,null,"by Hugues Pirotte"]
[]
[null,null,null,"Below is a list of the worksheets\nof the file, by order of appearance:\n(CTRL+h = back to \"Introduction\")",null,null,null,{"$f":"MID(CELL(\"filename\",A1),SEARCH(\"[\",CELL(\"filename\",A1))+1,SEARCH(\".\",CELL(\"filename\",A1))-SEARCH(\"[\",CELL(\"filename\",A1))-1)","v":"INGESTriskmgt (2012) - PREPA - Matrix calculus and Monte carlo"}]
[null,null,1,"Introduction"]
[null,null,2,"Matrix"]
[null,null,3,"MC simulations"]
[null,null,4,"Examples"]
[null,null,5,"Examples2"]
[null,null,6,"Example - cumulative"]
[null,null,7,"Example - correlated randoms"]

{"sheet":"Matrix","index":1,"n_rows":45,"n_cols":12,"rows_kept":45,"cut":false,"hidden":false,"merged":[]}
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[]
[null,1,null,"Some comments"]
[null,null,"a","You need to know exactly how much space you need for the result."]
[null,null,"b","Any function in Excel that uses tables or matrices, in fact uses the notion of Range."]
[null,null,null,"Range(cells(1,1),cells(2.2))"]
[null,null,null,"Range.FormulaArray"]
[null,null,"c","Any \"array\" result must be confirmed/entered with \"CTRL+shift+ENTER\""]
[null,null,"d","The functions that need this CTRL+shift+ENTER:"]
[null,null,null,"FREQUENCY()"]
[null,null,null,"Matrix functions: MMULT(), MINVERSE(),…."]
[]
[null,2,null,"Typical examples in our course"]
[null,null,"a","Inverting a matrix for the purposes of finding the weights in a system…"]
[]
[null,null,null,null,3,5,null,"units1","units 2",null,1.05,1.05]
[null,null,null,null,null,null,null,null,null,null,2,0.5]
[]
[]
[]
[]
[null,null,null,null,null,null,null,{"$f":"MMULT(E16:F16,MINVERSE(K16:L17))","v":5.3968253968253963},-1.333333333333333]
[]
[null,null,"b","In an investment course, for the optimal asset allocation, or to"]
[null,null,null,"draw an efficent frontier, you need also to invert a matrix…."]
[null,null,null,"…the variance/covariance matrix. (Elton Gruber)"]
[]
[null,null,"c","To find the Choleski decomposition"]
[]
[null,3,"For VBA"]
[null,null,"a","With ALT+F11"]
[null,null,"b","Two ways of programming: functions or subs"]
[null,null,"c","Example of function to show contents of cells"]
[]
[null,null,null,100]
[null,null,null,200]
[null,null,null,{"$f":"D35+D36","v":300},{"$f":"[1]!GetFormula(D37)","v":"1004"}]
[null,null,null,null,{"$f":"GetFormulaNumbers(D37)","v":"=+"}]
[null,null,"d","Use \"Application.ScreenUpdating\" at the beginning and at the end"]
[null,null,null,"of your programme"]
[null,null,"e","To access the contents of a cell or a sheet in VBA:"]
[null,null,null,"Cells(line, column)"]
[null,null,null,"Sheets(\"xxx\")"]
[null,null,null,"Workbooks(\"xxx\")"]
[null,null,null,"Copy and Paste function need you to activate the Sheet where you are."]

{"sheet":"MC simulations","index":2,"n_rows":52,"n_cols":7,"rows_kept":52,"cut":false,"hidden":false,"merged":[]}
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[]
[null,1,"The idea"]
[null,null,"a","For a binomial tree"]
[]
[]
[]
[]
[]
[]
[]
[null,null,"b","With MC simulations, you just let the system"]
[null,null,null,"produce examples following a distribution of"]
[null,null,null,"probabilities…"]
[null,null,null,"And to get a good probability of seeing some"]
[null,null,null,"observations in the extremes…you have to generate"]
[null,null,null,"many simulations…"]
[]
[null,2,"Generating random numbers"]
[null,null,"a","Use the RAND() formula - generates uniform numbers [0,1]"]
[null,null,null,{"$f":"RAND()","v":0.71207726956421813}]
[null,null,null,"You always have a probability density function and"]
[null,null,null,"the cumulative density function."]
[]
[]
[]
[]
[]
[]
[]
[null,null,"b","To imagine the roll of a dice"]
[null,null,null,{"$f":"RAND()","v":0.51056730411671758},{"$f":"VLOOKUP(D32,F32:G37,2)","v":3},{"$f":"G32/6","v":0.16666666666666666},1]
[null,null,null,null,null,0.33333333333333331,2]
[null,null,null,null,null,0.5,3]
[null,null,null,null,null,0.66666666666666663,4]
[null,null,null,null,null,0.83333333333333337,5]
[null,null,null,null,null,1,6]
[null,null,null,"For a normal random observation…"]
[null,null,null,{"$f":"RAND()","v":0.71717277655380807},{"$f":"NORMSINV(D39)","v":0.57446312503030506}]
[null,null,"c","The precision…"]
[null,null,null,"is "]
[]
[]
[null,null,"d","There are small problems with MC simulations."]
[null,null,null,"In particular, the volatility of simulations is a little bit"]
[null,null,null,"overestimated by the #of trials."]
[null,null,null,"There are some ways to be quicker and increase the "]
[null,null,null,"properties that are desired…."]
[null,null,null,"…the principle of antithetic variables."]
[null,null,null,"---> produce 1'000 simulations, copy them but with the opposite sign"]
[]
[null,3,"Generate correlated random numbers"]

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[null,null,null,null,null,null,null,null,null,null,null,null,null,"(to be generated)"]
[null,null,null,"average",{"$f":"AVERAGE(E12:E260)","v":2.349479974651144E-2},"1st moment",null,null,null,null,null,null,"average",0.05]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,"(check)"]
[null,null,null,null,null,null,null,null,null,null,null,null,"average",{"$f":"AVERAGE(N12:N260)","v":5.7048439923953399E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,"sigma",{"$f":"STDEV(N12:N260)","v":0.29601828758393817}]
[]
[]
[]
[null,null,null,"Uniform random (p)","Normally dist. Z random",null,null,null,null,null,null,null,null,"Normally distributed X (yearly)"]
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{"sheet":"Examples2","index":4,"n_rows":2001,"n_cols":8,"rows_kept":2001,"cut":false,"hidden":false,"merged":[]}
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[]
[null,null,null,"S(0)",100,"Strike (K)"]
[null,null,null,"Random normally dist.","Random prices",120]
[null,null,null,"exp(r )-1","in one-year from now"]
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[null,null,null,-0.13136343080156077,86.863656919843919,0,null,"(I assumed that 5.56% was"]
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{"sheet":"Example - cumulative","index":5,"n_rows":206,"n_cols":5,"rows_kept":206,"cut":false,"hidden":false,"merged":[]}
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