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[null,"dS(t) = m S(t) dt + s S(t) dBH(t)",null,null,null,null,"Fractional GBM"]
[null,"S0",100,null,null,null,"t","z","dBH","SH(t)","Mean(SH)","dB","S(t)"]
[null,"m",0.05,null,null,null,0,{"$f":"NORMSINV(RAND())","v":1.9448755417663235},{"$f":"$H4*SQRT(dt^(2*H))","v":0.24484532423065736},{"$f":"S0","v":100},{"$f":"NA()","v":{"$error":"#N/A"}},{"$f":"$H4*SQRT(dt^(2*BM))","v":0.61502364775355189},{"$f":"S0","v":100}]
[null,"s",0.25,null,null,null,{"$f":"G4+dt","v":0.1},{"$f":"NORMSINV(RAND())","v":4.872155393001407E-3},6.133680234459471E-4,{"$f":"J4+(mu*J4*dt)+(sigma*J4*I5)","v":100.51533420058615},{"$f":"NA()","v":{"$error":"#N/A"}},1.5407108156157241E-3,{"$f":"M4+(mu*M4*dt)+(sigma*M4*L5)","v":100.5385177703904}]
[null,"dt",0.1,null,null,null,0.2,-1.582550838127861,-0.19923134655753225,96.011459525973294,{"$f":"NA()","v":{"$error":"#N/A"}},-0.50044651614924796,88.462672619992077]
[null,null,null,null,null,null,0.30000000000000004,-0.26507731477044633,-3.3371256765467629E-2,95.690511056536025,{"$f":"NA()","v":{"$error":"#N/A"}},-8.3824807071600407E-2,87.051144366739791]
[null,"Hurst Coefft: 0 < H < 1",null,null,null,null,0.4,-0.13039709185495174,-1.64160212560257E-2,95.776249245942694,{"$f":"NA()","v":{"$error":"#N/A"}},-4.1235181052383801E-2,86.589007663878562]
[null,"Hurst, H",0.9,{"$f":"IF(H=0.5,\"Brownian Motion\",IF(H<0.5,\"Mean Reverting\",\"Trending\"))","v":"Trending"},null,null,0.5,-1.7165101345895708,-0.21609582280370374,91.080918645708763,{"$f":"AVERAGE(J5:J9)","v":95.814894534949389},-0.54280816520652175,75.271647607927108]
[null,"GBM",0.5,null,null,null,0.6,0.40737925313484491,5.1286009400918507E-2,92.704117451414348,94.252651185115013,0.12882463114043993,78.072216405572831]
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[null,"a = 2H-1",{"$f":"2*H-1","v":0.8},null,null,null,0.79999999999999993,-1.076563951347949,-0.13553137157734729,89.957092174337163,92.430192415703019,-0.34043941330902172,71.135760343595138]
[null,"Half-Life",{"$f":"LN(2)/H","v":0.77016353395549475},null,null,null,0.89999999999999991,-1.3084845661960109,-0.16472844713246257,86.702254609601255,90.615393488434734,-0.41377915123567582,64.1328155109438]
[null,null,null,null,null,null,0.99999999999999989,0.91155947846524099,0.11475853918017301,89.623221903305577,90.323854139954094,0.28826041746653708,69.075217631620788]
[null,"H = 0.5, Brownian Motion",null,null,null,null,1.0999999999999999,1.5538120905773838,0.19561335259808893,94.454212739609133,90.673873197593053,0.49135852621323872,77.905768003111874]
[null,"H < 0.5, Negative Correlation (Rough)",null,null,null,null,1.2,0.93898473384734837,0.11821117427272099,97.717869654045828,91.690930216179794,0.29693304470846216,84.078496066506204]
[null,"H > 0.5, Positive Correlation (Smooth)",null,null,null,null,1.3,0.34319259754981174,4.3205388219510678E-2,99.261943625912693,93.551900506494903,0.10852702843669269,86.780085880219758]
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[null,"Random Walk Increments",null,null,null,null,1.5000000000000002,0.62854174277906727,7.9128717235796106E-2,105.05044060921324,99.798897113537294,0.19876235116735441,98.357209102875871]
[null,"Distributions",null,null,null,null,1.6000000000000003,0.95708898563814904,0.12049036453681689,108.74008428319864,102.6560714222552,0.30265811180767338,106.29114694582748]
[null,null,null,null,null,null,1.7000000000000004,-1.585359353239103,-0.19958491766182729,103.85806451256404,103.88411039395882,-0.50133464660870064,93.500744032626642]
[null,null,null,null,null,null,1.8000000000000005,-0.5305472024741793,-6.6791935535104971E-2,102.64313454769588,104.56034857831546,-0.16777375660489272,90.046504984863205,null,"Hurst Coefficient (H)"]
[null,null,null,null,null,null,1.9000000000000006,-0.6738717599794003,-8.4835428292852691E-2,100.97940665026569,104.2542261205875,-0.21309696124012056,85.699578364145594,null,"H controls the correlation between successive Brownian Motion (BM) increments."]
[null,null,null,null,null,null,2.0000000000000004,0.50381200299584461,6.3426173333838806E-2,103.085488020854,103.86123560291564,0.15931934419984439,89.541476411761039,null,"H has a range 0 < H < 1, where H = 0.5 indicates BM. When H < 0.5 BM increments"]
[null,"Using Central Limit Theorem,",null,null,null,null,2.1000000000000005,0.39086186978024784,4.9206594036773681E-2,104.86903690098949,103.08702612647383,0.12360137590177199,92.756046215012276,null,"are negatively correlated  giving a rough effect and when H > 0.5 BM increments"]
[null,null,null,null,null,null,2.2000000000000006,-0.56386512510858788,-7.0986413482369878E-2,103.53231288175655,103.02187580031232,-0.17830980884789357,89.084998228566036,null,"are positively correlated  giving a smooth effect."]
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[null,"This gives or BM and fBM respectively,",null,null,null,null,2.5000000000000009,-0.66152334897838816,-8.3280855452407418E-2,102.68869731172646,104.04205076944326,-0.20919205081541276,85.225963676050569]
[null,null,"and",null,null,null,2.600000000000001,0.23094887719468504,2.907474103257195E-2,103.94855261861274,103.85795391296793,7.3032447499372308E-2,87.208158673869463]
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