{"text_format":"3","workbook":"xlsx","n_sheets":2,"sheets":["Bicubic Interpolation Example","Cubic Interpolation"],"not_rendered":{"charts":2,"images":2,"macros":1,"defined_names":1},"read":"whole","date_system":"1900"}

{"sheet":"Bicubic Interpolation Example","index":0,"n_rows":52,"n_cols":12,"rows_kept":52,"merged":[[17,2,17,3],[22,11,25,18],[26,1,27,8]]}
[]
[null,"Left \\ Top",1.1,2.1,2.89,4.2,5,6.1,7.2,8.999]
[null,1.05,{"v":8.418295411646993,"d":"8.42"},{"v":7.833684906169614,"d":"7.83"},{"v":7.660453979265433,"d":"7.66"},{"v":7.457840326498716,"d":"7.46"},{"v":7.404200990834663,"d":"7.40"},{"v":7.408547447541296,"d":"7.41"},{"v":7.394615258701858,"d":"7.39"},{"v":7.6805692086774116,"d":"7.68"}]
[null,2,{"v":7.609410923878322,"d":"7.61"},{"v":7.1811428588374735,"d":"7.18"},{"v":7.085500095295223,"d":"7.09"},{"v":6.951332390301457,"d":"6.95"},{"v":6.952260071646361,"d":"6.95"},{"v":7.003084981239135,"d":"7.00"},{"v":7.0230113470554345,"d":"7.02"},{"v":7.370366612812581,"d":"7.37"}]
[null,2.99,{"v":6.864075029331008,"d":"6.86"},{"v":6.59232501710661,"d":"6.59"},{"v":6.571905708539055,"d":"6.57"},{"v":6.502987077379663,"d":"6.50"},{"v":6.555675768096761,"d":"6.56"},{"v":6.649864873377327,"d":"6.65"},{"v":6.700947626425057,"d":"6.70"},{"v":7.1043399681956965,"d":"7.10"}]
[null,4,{"v":6.159257894804773,"d":"6.16"},{"v":6.048547120792021,"d":"6.05"},{"v":6.101598020301688,"d":"6.10"},{"v":6.095447062410528,"d":"6.10"},{"v":6.19757816070053,"d":"6.20"},{"v":6.3324675141340405,"d":"6.33"},{"v":6.412384116139286,"d":"6.41"},{"v":6.867060630522664,"d":"6.87"}]
[null,5.1,{"v":5.48959928906525,"d":"5.49"},{"v":5.54489447130882,"d":"5.54"},{"v":5.6682810355349815,"d":"5.67"},{"v":5.721789349742456,"d":"5.72"},{"v":5.870802129155742,"d":"5.87"},{"v":6.043726671609377,"d":"6.04"},{"v":6.150199179749393,"d":"6.15"},{"v":6.651737310184008,"d":"6.65"}]
[null,6,{"v":4.871651760764197,"d":"4.87"},{"v":5.089112370709952,"d":"5.09"},{"v":5.2755535077012095,"d":"5.28"},{"v":5.383564674993336,"d":"5.38"},{"v":5.576139775415555,"d":"5.58"},{"v":5.784260063974318,"d":"5.78"},{"v":5.914931356685732,"d":"5.91"},{"v":6.45942927281499,"d":"6.46"}]
[null,7.25,{"v":4.345947277709125,"d":"4.35"},{"v":4.691841106988583,"d":"4.69"},{"v":4.92583567975868,"d":"4.93"},{"v":5.079365321387464,"d":"5.08"},{"v":5.310660738566098,"d":"5.31"},{"v":5.550565558988632,"d":"5.55"},{"v":5.702757673582088,"d":"5.70"},{"v":6.286259519283237,"d":"6.29"}]
[null,7.9,{"v":3.9734506679018016,"d":"3.97"},{"v":4.366082394088588,"d":"4.37"},{"v":4.620903647190024,"d":"4.62"},{"v":4.8056349475391285,"d":"4.81"},{"v":5.068460896551848,"d":"5.07"},{"v":5.335696706560213,"d":"5.34"},{"v":5.506127955503809,"d":"5.51"},{"v":6.123943769291397,"d":"6.12"}]
[null,9.04,{"v":3.7817116644793964,"d":"3.78"},{"v":4.129586569979688,"d":"4.13"},{"v":4.371896673818008,"d":"4.37"},{"v":4.5693758091568775,"d":"4.57"},{"v":4.854488015288033,"d":"4.85"},{"v":5.143921774133011,"d":"5.14"},{"v":5.328960895828381,"d":"5.33"},{"v":5.976713450780171,"d":"5.98"}]
[null,10.1,{"v":3.7680188506353662,"d":"3.77"},{"v":3.9305645676595704,"d":"3.93"},{"v":4.0758992993392615,"d":"4.08"},{"v":4.247405948664899,"d":"4.25"},{"v":4.546509606847934,"d":"4.55"},{"v":4.864579919620594,"d":"4.86"},{"v":5.06813680248808,"d":"5.07"},{"v":5.7672921951426295,"d":"5.77"}]
[]
[]
[null,"Left:",7.7]
[null,"Top:",3.9]
[]
[null,"Volatility:",{"$f":"BicubicInterpolation(B2:J12,C16,C15)","v":{"v":4.840939893891426,"d":"4.84093989"}}]
[]
[]
[]
[]
[{"$nulls":11},"* These buttons run two different scenarios.  One of the buttons will generate an error depending on the current VBA Array Base setting.  See the source code for more information.  Press Alt+F11 to view the source code and look in the module called Array_Test."]
[]
[]
[]
[null,"=BicubicInterpolation(Table_Array, TopPoint, LeftPoint)"]
[]
[]
[]
[]
[]
[null,"This illustrates how the bicubic interpolation function selects a 4x4 subset of the data for the cubic interpolation."]
[]
[null,"Strike\\TTM",1,2,3,4,5,6,7]
[null,{"v":0.5,"d":"50%"},{"v":0.4209147705823496,"d":"42%"},{"v":0.39168424530848067,"d":"39%"},{"v":0.3830226989632716,"d":"38%"},{"v":0.3728920163249358,"d":"37%"},{"v":0.37021004954173314,"d":"37%"},{"v":0.3704273723770648,"d":"37%"},{"v":0.3697307629350929,"d":"37%"}]
[null,{"v":0.6,"d":"60%"},{"v":0.38047054619391607,"d":"38%"},{"v":0.3590571429418737,"d":"36%"},{"v":0.35427500476476115,"d":"35%"},{"v":0.34756661951507284,"d":"35%"},{"v":0.34761300358231806,"d":"35%"},{"v":0.35015424906195675,"d":"35%"},{"v":0.3511505673527717,"d":"35%"}]
[null,{"v":0.7,"d":"70%"},{"v":0.3432037514665504,"d":"34%"},{"v":0.32961625085533053,"d":"33%"},{"v":0.32859528542695277,"d":"33%"},{"v":0.32514935386898314,"d":"33%"},{"v":0.3277837884048381,"d":"33%"},{"v":0.33249324366886635,"d":"33%"},{"v":0.33504738132125284,"d":"34%"}]
[null,{"v":0.8,"d":"80%"},{"v":0.30796289474023864,"d":"31%"},{"v":0.302427356039601,"d":"30%"},{"v":0.3050799010150844,"d":"31%"},{"v":0.3047723531205264,"d":"30%"},{"v":0.3098789080350265,"d":"31%"},{"v":0.316623375706702,"d":"32%"},{"v":0.3206192058069643,"d":"32%"}]
[null,{"v":0.9,"d":"90%"},{"v":0.2744799644532625,"d":"27%"},{"v":0.277244723565441,"d":"28%"},{"v":0.28341405177674905,"d":"28%"},{"v":0.2860894674871228,"d":"29%"},{"v":0.2935401064577871,"d":"29%"},{"v":0.30218633358046887,"d":"30%"},{"v":0.30750995898746963,"d":"31%"}]
[null,{"v":1,"d":"100%"},{"v":0.24358258803820987,"d":"24%"},{"v":0.2544556185354976,"d":"25%"},{"v":0.2637776753850605,"d":"26%"},{"v":0.26917823374966676,"d":"27%"},{"v":0.27880698877077775,"d":"28%"},{"v":0.2892130031987159,"d":"29%"},{"v":0.2957465678342866,"d":"30%"}]
[null,{"v":1.1,"d":"110%"},{"v":0.21729736388545623,"d":"22%"},{"v":0.23459205534942912,"d":"23%"},{"v":0.24629178398793397,"d":"25%"},{"v":0.2539682660693732,"d":"25%"},{"v":0.26553303692830493,"d":"27%"},{"v":0.2775282779494316,"d":"28%"},{"v":0.2851378836791044,"d":"29%"}]
[null,{"v":1.2,"d":"120%"},{"v":0.19867253339509008,"d":"20%"},{"v":0.21830411970442942,"d":"22%"},{"v":0.23104518235950122,"d":"23%"},{"v":0.24028174737695643,"d":"24%"},{"v":0.25342304482759237,"d":"25%"},{"v":0.26678483532801067,"d":"27%"},{"v":0.27530639777519045,"d":"28%"}]
[null,{"v":1.3,"d":"130%"},{"v":0.18908558322396982,"d":"19%"},{"v":0.20647932849898443,"d":"21%"},{"v":0.2185948336909004,"d":"22%"},{"v":0.22846879045784388,"d":"23%"},{"v":0.24272440076440166,"d":"24%"},{"v":0.25719608870665056,"d":"26%"},{"v":0.26644804479141904,"d":"27%"}]
[null,{"v":1.4,"d":"140%"},{"v":0.1860893565929663,"d":"19%"},{"v":0.19892723275068275,"d":"20%"},{"v":0.20897852362208796,"d":"21%"},{"v":0.21854150575570166,"d":"22%"},{"v":0.23336254902993817,"d":"23%"},{"v":0.2486432737673491,"d":"25%"},{"v":0.2584210709446522,"d":"26%"}]
[null,{"v":1.5,"d":"150%"},{"v":0.1884009425317683,"d":"19%"},{"v":0.1965282283829785,"d":"20%"},{"v":0.2037949649669631,"d":"20%"},{"v":0.21237029743324495,"d":"21%"},{"v":0.22732548034239672,"d":"23%"},{"v":0.24322899598102968,"d":"24%"},{"v":0.253406840124404,"d":"25%"}]
[]
[]
[null,"Strike:",{"v":0.87,"d":"87%"}]
[null,"TTM:",4.55]
[]
[null,"Volatility:",{"$f":"BicubicInterpolation(B35:I46,C50,C49)","v":{"v":0.2948500189609511,"d":"29.5%"}}]

{"sheet":"Cubic Interpolation","index":1,"n_rows":38,"n_cols":8,"rows_kept":38,"merged":[[37,2,38,7]]}
[]
[null,"x","y",{"$nulls":3},"x","y"]
[null,2.57,{"$f":"CubicInterpolation($G$3:$G$14,$H$3:$H$14,B3)","v":{"v":1.1946110474733027,"d":"1.1946"}},{"$nulls":3},2.2,{"v":0.2106988058881421,"d":"0.2107"}]
[null,2.98,{"$f":"CubicInterpolation($G$3:$G$14,$H$3:$H$14,B4)","v":{"v":3.914810082147503,"d":"3.9148"}},{"$nulls":3},2.5,{"v":0.9122085048010974,"d":"0.9122"}]
[null,3.12,{"v":4.757693273089744,"d":"4.7577"},{"$nulls":3},2.6,{"v":1.3312896913700927,"d":"1.3313"}]
[null,3.15,{"v":4.801481034578676,"d":"4.8015"},{"$nulls":3},2.9,{"v":3.2771260699462217,"d":"3.2771"}]
[null,3.18,{"v":4.703559923208751,"d":"4.7036"},{"$nulls":3},3,4.0625]
[null,3.24,{"v":4.115595907967953,"d":"4.1156"},{"$nulls":3},3.1,{"v":4.671923576841081,"d":"4.6719"}]
[null,3.28,{"v":2.9598907945288633,"d":"2.9599"},{"$nulls":3},3.2,{"v":4.537402734375,"d":"4.5374"}]
[null,3.32,{"v":0.5684064826337348,"d":"0.5684"},{"$nulls":3},3.3,{"v":1.9977402476859236,"d":"1.9977"}]
[null,3.35,{"v":-2.1769377594269113,"d":"-2.1769"},{"$nulls":3},3.4,{"v":-8.40137050754457,"d":"-8.4014"}]
[null,3.39,{"v":-6.988428730294938,"d":"-6.9884"}]
{"$rows_empty":25}
[null,null,"=CubicInterpolation(X_Points, Y_Points, x)"]