Stats

Premises:1 Initialize repricing consistently with bidask and clock.2 Expected base hits must not depend on outsized target overshoots.3 Conditional Gaussian simulations cannot supply empiricaloptionp/W/L. Seed2026090808,N30000 per2contracts x3physicalsigmas x2IVstates=360000paths per experiment; original and quoteconsistent diagnostic total720000. Four sessionsSep8 13:50 throughSep11 20UTC,25 firstday and26 later15minchecks=103, 3 untradeable overnightgaps. Physical price drift0 (logdrift-.5variance), dailyvariance sigma²/252 split by TRAIN-only overnight/intraday squaredmoments, independentnormals,firstgap omitted; firstpartialday receives full intradayvariance, slightly optimistic, tails/crosscovariance/volclustering omitted. BSmid minus halffrozenFriday spread; r.04,qTLT.0474 trailingyieldproxy/ETHA0, earlyexercise/discretecash absent. NonsynchronousFriday entry is counterfactualTuesday. Quoteconsistent pricingIV solves BSmid=(bid+ask)/2 atTuesdayclock:TLT9.309567% vsfeed9.96%;ETHA58.261514% vsfeed58.62%. StopTLT.02/ETHA.03 bothbelowactualbid.05/.07; targets floorFridaymodelbid at S-2ATR to cents .31/.21 (originalfeedIVtarget .33/.21), not optimized. Fullpremium+assumedroundtripfees6.20/8.20<=8.5099. Terminal liquidation atbid; stop/targetfills atfirstcheckmodelbid, targetovershootcap stress. TLTquoteconsistentbase p.190333,W23.173718,L4.648795,mean+.646757,capped-.016197;calibratedmean+1.067221,capped+.258835;lowphysicalmean-1.089843,capped-1.361400. ETHAbasep.304633,W10.765094,L5.159938,mean-.308642,capped-.773303;calibrated+.162641,capped-.478444;low-1.432313,capped-1.615284. All80%quoteconsistentIVstates startbelowstop: initialinvalidstates, not certainfutureloss. Original TLTbase+1.876271 partly artificial initialmodelbid.064030>entryask.06 vsobservedbid.05; do not use. OriginalETHAcalibrated+.355611 also failscapped-.309546. QuarterKelly .25*(p-(1-p)/(W/L)) clipped0 yields positive diagnostic fractions onlyselectfavorableassumptions; no empiricaloptionedge, approvedsize0. Exactall24p/W/L,stops,targets,probabilities,inputs recordedobservations. Fee0 shiftsmeans+.20;fee1.30 shifts-1.10; quoteconsistentTLTcalibrated capped becomes-.841165 under1.30fee. No robustcost/forecast/IVsurvival. Sources https://runway.adityaperswal.workers.dev/data/option-chain/TLT?feed=indicative ; /data/option-chain/ETHA?feed=indicative ; /data/stock-bars?feed=sip&adjustment=all ; https://www.ishares.com/us/products/239454/ishares-20-year-treasury-bond-etf ; research/sim.py and sim_quote.py.

Premises:1 Value surplus must translate to realizable exits.2 Stops cannot guarantee full-premium loss limits or overnight execution.3 Conditional simulation is not empirical option p/W/L. Numpy seed2026090805, 2puts x3physicalforecasts x2IVstates x30000=360000paths. Model five sessionsSep8–14 at FridayS15.19/ask.07 (counterfactual Tuesday quote). Physical daily variance sigma²/252 from base/clip/RV60; paired Gaussian overnight/intraday logtotals normalized to measured second moments .000665257/.001140850 with crossmoment-.0000679354; Cholesky covariance, intraday Brownian bridge26quarters, first overnight skipped, -.5dailyvariance logdrift applied intraday. Initial quote check plus26quarterhour checks/day; cannot sell overnight. EuropeanBS bid approximation with remaining calendarT,r.04,q0, frozen FridayIV or .8IV, less halfFriday spread floored0; American exercise premium and changing spread/skew omitted, so not validated execution model. Targets from Sept14bid at S-2ATR=13.272343 using originalIV: floor to cents .15/.16, not fitted for return. Diagnostic stop.03, fee$.20roundtrip assumed. Fullrisk$7.20, targets net$7.80/$8.80 -> fullrisk reward1.083/1.222; nominal stoprisk$4.20 would imply1.857/2.095 but ignores gaps and spread. Oct2 initial Fridaybid.01 is already belowstop.03; initial modelbid also fails, all6scenarios immediately stop. These p=0 outcomes diagnose an incoherent entry/stop combination, NOT forecast certainty of loss; never deploy that stop. Oct16 baseline conditional p.263733,W$9.669162,L$4.484038,mean-$0.751367; clipping mean-$1.35568,RV60-$1.489095. Capping favorable exit overshoots at target lowers means further to-1.10214/-1.56129/-1.66335. .8IV causes initial repricing stop, not proof IV will drop. Every12conditionalmeannegative; quarterKelly truncated0 (actual empiricalp/W/L remains UNKNOWN). Costs0/$1.30 would shift eachmean +.20/-1.10, stillnegative. Targets already use2ATR bearish movement within5sessions; do not increase them to meet funding need. Exactscenario p/W/L,stophits,targethits stored. Source https://runway.adityaperswal.workers.dev/data/option-chain/PATH?feed=indicative ; https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=PATH&feed=sip ; local research/sim.py .

Premises:1 Fullpremiumriskmustfit8.5099;stopdoesnotlimitgaps.2 Basehittargetsneedreachablebidexits,notfairvaluealone.3 Simulatedp/W/Ldependsontestedassumptionsandisnotempiricaledge. Numpyseed20260908,4finalistsx3scenariosx20,000paths=240,000conditionalpaths. HypotheticalTuesdaySep8entryatFridaySep4spot/ask,notforecastofTuesdayquotes. DailyGBM S*=exp(-.5sigma²/252+sigma/sqrt252*Z),expectedspotdrift0,first4or5businessdayclosingchecks throughSep11/Sep14. EuropeanBSexitatquotedIV(orfactor.8),r.04,q0,remainingactualcalendartime,bid=max(value-halfFridayquotedspread,0),fee.20USD. Entry/exitIVcanbedifferentfromphysicalvol. Stophalfaskflooreddowncent,min.01;diagnostictarget2.5*(100ask+.20)/100 givesPATHputs.18,RIOT.205,PATHcall.055. Fractionalcenttargetsnotorders; noassertionofactualtickeligibility. Calendar/IV/normaldiffusion anddividendsassumed; noovernightgapmodel or15minexecution. FourlegsfrozenmeanPnL PATHOct2P12 -3.3336USD,Oct16P11 -.0452,RIOTSep11P19 +1.3894,PATHSep11C18 +.2980. Lowerphysicalvol.8andIV.8turnallnegative(-6.8147,-5.8913,-4.7035,-1.6721). RIOTfrozenp=.1952,W36.6302,L7.1581USD,conditionalquarterKelly.009483:largeaveragewinexceedstargetnet12.3USD,showingdailyovershootdependence. ConservativecappositivePnLatplannedtargetnet changesfourfrozenmeans to-4.5044,-1.3030,-3.3628,-1.2814;all12scenario cappedmeansnegative. This stressisnotclaimtargetordersactuallycapfills,butrejectsbasingbase-hitexpectancyonrareunmodeledovershoots. Actualoptionholdout0,p/W/Lunknown,notzero;quarterKellyforcapitalnotdefensibleandallocation0. Fullriskputs7.20/7.20/8.20,call2.20fitsdollarcapbutdoesnotestablishexpectedreturn. Sources https://runway.adityaperswal.workers.dev/data/option-chain/PATH?feed=indicative ; /RIOT ; https://runway.adityaperswal.workers.dev/data/stock-bars ; code research/validate.py/cap_validate.py .

Premises:1 Simulated precision must preserve majorobserveddependence.2 Forecast loss andvariance calibration are not option profits.3 Position sizing needs actual costedoption p,avgwin,avgloss. numpy seed7090602,50000 common-index circular4-window blockbootstrap resamples83 nonoverlapping5session holdoutwindows simultaneously across7ETFs. This is MonteCarlo resampling offorecastobservations, NOT riskneutralpaths or optionexit simulation. Each path computes perassetmeanlossdifference,ratio sum(realizedvariance)/sum(predictedvariance),and equalassetmean. Pooleddifference-.0272720856,95interval[-.084595064,.028682371]. Bonferroni sevenasset95 intervals onlyTLTuppernegative-.001400933; sensitive toblocklength andnonstationarity, not distribution-free proof. GLDvariance-ratio95[1.432672,2.802439],IBIT[.471998,.800341] show modelerror overwhelms simulationnoise. All83dates/581rows,intervals and7x7correlations recorded. Initial5000perassetbootstrap results also recorded but50000commonindex ismain dependence-aware audit, not independent corroboration. Explicit sizing gate: quarterKelly=max(0,.25*(p-(1-p)/(W/L))) can be computed only for empirically defensible optionoutcomes; ownoptiontrades0,actualoptionholdout0,p/W/Lunknown,allocation0. No winprobability0 is asserted. OptionexitMonteCarlo intentionally NOT run aftervalue/targetfailure; simulating under favorableposthocvol would manufacture evidence. No optionreturn,drawdown,winrate or exitodds claimed. Source venueadjustedstockbars; scripts uncertainty.py/analyze.py; observations saved successfully after splitting oversizedjournalbatches.

Premises:1 A numericalpricingcross-checkshouldrecovercash-dividendEuropeanparity.2 Risk-neutral terminalpayoffsdo notestimateactualwinprobabilityorplannedexitreturns.3 Failedvalue/riskgatesbartrade-sizingpaths. N500000numpy pathsseed7092026,independentstandardnormaldrawsbefore/afterex. S46.15,r.04,sigma.4081799262,T14/365,td13.7291667/365,D2.61. Spre=Sexp((r-.5sig²)td+sig sqrt(td)Z1);Spost=max(Spre-D,0);ST=Spostexp((r-.5sig²)(T-td)+sig sqrt(T-td)Z2). Discountpayoffs exp(-rT)max(sign*(ST-K),0). SepK46EuropeanC=.603604336(SE.002064965),P=2.992489208(SE.003961243);C-P=-2.388884872vsanalytic S-PV(D)-Kexp(-rT)=-2.385554805;parityMCSE.005213506,difference-.64SE. AmericanFDcall1.565900includesexerciseprivilege andneednotmatchEuropeanMC. PutFD2.992254closebecauseits earlyexerciseincrement smallhere. AffordableK25/29/30/31putvalues0,.000000871,.000002868,.000015226;zeroK25hitsdoesnotprovezerotailprobability. RiskneutralITM frequencies0,.000002,.000002,.000024are NOTempiricalwinrates. These areGaussianmodeldiagnostics,omitgeopoliticaljumps,stochasticvolatility,spreadchangesand15minexitdelays; MCprecisiondoesnotremove modelerror. Conclusion: arithmetic/modelcross-checksupportsdividendmechanism; simulationcannotestablishquarterKelly orprofitabletailstrategy. Noexitoddsoractualoptionbacktestclaimed; owntrades0,actualoptionholdout0,size0. Sources frozenSep4inputs https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=FRO&timeframe=1Day&feed=iex&adjustment=all ; issuerD https://ml-eu.globenewswire.com/Resource/Download/59431810-8e9c-4a39-b3d0-cc2dd63da402 ; scripts research_fro/mc.py andverify.py.

Premises: 1. Model probabilities are conditional, not empirical option winrates. 2. The intended exit must have a positive realistic payoff before path simulation can justify it. 3. Full premium remains at risk. The registered52step15minexit-pathstudy was cut at its feasibility gate, not run: range-basedtargets<=entryasks inindicatorsanalysis. Do notreplaceit with an expiryhold strategy. Separate terminal diagnostic NumPyseed2026090608,N100000,9sessionsT=9/252,S23.67; ST=Sexp(-.5sigma²T+sigma sqrtT Z+J_i-logmeanexpJ),Jdrawsuniformlyfrom16trainingearningsloggaps,commonrandomnumbersforcomparisons. Baselineevent sigma46.9262%; adverse.5J,.8sigma;diffusionJ0,vol42.5200%. Payoff100max(ST-K,0)callor100max(K-ST,0)put less100ask andfixedassumedroundtrip$.20/$1.30. Ignoresdiscount/cashinterestinphysicalP&L,Americanexercise,exerciseclosingexecution,tax,rareunseenjumps andeventdependence; not anexecutionbacktest. CallsK37.5 ask.05 andputsK17.5 ask.06. Event $.20scenario call mean-$5.189230,win.011% (11/100000),avgwin$92.707951,avgloss$5.20,fullpremiumloss99.989%,MCSE$.004165; putmean-$5.870908,win.552%,avgwin$53.102472,avgloss$6.198248,fullpremiumloss99.39%,MCSE$.017642. Raisingfeeto1.30 shiftsmeans-$1.10. Adversemeans-$5.20/-$6.198126 at$.20;diffusion-$5.20/-$6.197772. All12scenariosrecorded; nonepositive. qKelly=max(0,[p-(1-p)/(W/L)]/4)=0throughout. Zeroobservedwins in someMCsamplesisnottruezerotailprobability; modeluncertaintydominatesMCSE. Risks$5/.06*100pluscostfit8.5099butnegativeexpectancyandunvalidatedquotesmeanszeroallocation. Actualoptionhistorysample0 and owntradehistory0. Source https://runway.adityaperswal.workers.dev/data/option-chain/CHWY?feed=indicative andadjustedstockbars;18individualissuerdateURLs recorded.

Premises:1 mark exits at bids after fees;2 target must fit measured range and reward/risk;3 Monte Carlo precision is conditional model precision, not empirical edge. First choose largest baseline net among145affordablecontracts with>=4sessions (allbaseline netnegative): Sep18K62call bid.01ask.02. Two-session1.5ATR14 rise=.987857 gives modeledbid target .02 after rounding down; equals entry beforefees, so no admissible base-hit trade. stop0 is only zero-bid diagnostic, not a recommended venue exit. Blend100kpath mean-$1.462946, win10.301%,avgwin$.165684,avgloss$1.649978;HARmean-$1.225398;low-$1.661492 at$.20assumedfee. Secondary counterexample chosen after results: largest HAR net among same>=4session set, Sep18K60.5call bid.04ask.07. S58.10,K60.5,n9sessions,r.04,q.0138,midcalibratedmarkIV.145572289,halfspread.015. Two-session1.5ATR move gives rawbid.119338,target roundeddown.11;stop.03. Target profit beforefee$4 againstpremium$7, already below1.5RR; with$.20cost 3.80/7.20=.52778, also below1.5 usingplanned$4stoploss. No trade. NumPyseed2026090606,100000paths,52steps; dt=1/(252*26),dlogS=-.5sigma²dt+sigma sqrt(dt)Z, common draws acrossscenarios. Aftereachstep bid=max(BSM at decreasingT, fixedmarkIV minusinitialhalfspread,0). First stop/target hit exits at observed modeledbid; rest end2sessions. Blend physicalvol12.30249%: win11.486%,avgwin$4.39266,avgloss$4.47374,mean-$3.45535,stop86.398%,target10.609%,time2.993%. HAR15.99295%: win15.786%,avgwin4.84070,avgloss4.61075,mean-3.11874,stop83.762%,target15.578%. Low9.84199%mean-3.73230. Fee$1.30 instead$.20 reduces eachmean$1.10; all12scenarios qKelly=max(0,(p-(1-p)/(W/L))/4)=0. Fullpremium7+1.30=8.30 affordable, but allocation0. Zero observedfullpremiumloss in some simulated cases does not bound realgaploss. Limitations: staticIV/spread, no overnight/holidayjumps, Americanexercise, queuing or real liquidity; targetovershoot fills optimistic. Actual option backtestN0. No removal/widening of exits to rescuemean. Source https://runway.adityaperswal.workers.dev/data/option-chain/XLF?feed=indicative and adjustedstock-bars; all12scenariofigures recorded.

Premises: evaluateplannedbidexits,notonlyterminalfairvalue; usephysicalpathsindependentofthemarkIV; allscenarioresultsconditionaluntilvalidatedagainstactualoptionhistory. FixedNFLXSep11K72put S78.25,Fridaybid.02ask.03,4remainingtradingsessions; midcalibratedsessionIV32.94478%,rate4%,q0. Initialterminal2-sessionGBM withfixedIV/halfspread.005 andfees.20percontract givesblendphysicalvol38.03027%win16.93%,avgwin18.2765,avgloss2.9420,mean+.6503; trainingwinsorvol35.93251%mean-.04315,lowvol30.15233%mean-1.54882. Positiveunboundedtailmeanisnotbase-hitvalidation. Explicitexitdiagnostic: 1.5ATR14decline=3.4575underlyingpoints over2sessions givesBSMbid.091519,roundtargetdown.09; stop.01belowinitialbid.02. Targetnetprofit5.80versusfullpremium+assumedfees3.20=1.8125RR. Notanorder. NumPyseed2026090605,100000paths,52equal15minute-likegridsteps over2/252years; commonnormaldrawsforallvolscenarios, dlogS=-.5sigma²dt+sigma√dtZ. RemainingTdecreases4/252to2/252; modeledbid=max(BSM-.005,0). Firstbid<=.01stopor>=.09target exitsatmodeledobservedbid, othersatend. Blendwin16.382%,avgwin7.399572,avgloss2.460156,mean-.844935; stop83.514%,target16.252%,time.234%. Winsorwin15.161%,mean-.972319; lowwin11.074%,mean-1.383048. qKelly=max(0,(p-(1-p)/(avgwin/avgloss))/4)=0allscenarios. This matchesneitherhistoricaloptionliquiditynoractualclosurevariance: continuousvariancegridcompressesovernight,IV/spreadfixed,noovernightjump/stochasticIV/latency/Americanpathmodel. Favorableovershootfillsassumed,notpromised. Stopsdonotboundfullpremiumrisk; onecontract3+feesaffordablebutedgezero. Source https://runway.adityaperswal.workers.dev/data/option-chain/NFLX?feed=indicative ; https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=NFLX&timeframe=1Day&adjustment=all&feed=iex . Reject, donotremoveexitstoaccommodateoptimisticmean.

Premises:1 buyatask/sellatbid;2 highphysicalvolatilitydoesnotguaranteeIVrepricing;3 simulatedmeansarenotvalidatedwin/lossedge. HypotheticalSep4snapshots: SNAPOct2K4.5put S5.48,bid.01ask.03,ATR14.316429,19sessions; MARASep18K8.5put S11.30,bid.01ask.02,ATR14.979286,9sessions. CalibrateBSMtosession-clockmidpoint withr4%,q0, impliedvol48.93596%SNAP/78.62248%MARA; do notcarryfeedIVacrossclockswithoutrecalibration. NumPyseed2026090602,100000terminalGBMdraws percontract/scenario; zeroexpectedstockreturn,5sessions, physicalvol0.8min(RV21,RV63,EWMA) orfixedvarianceblendforecast; markIVunchangedorhalfwaytoforecast. Terminalbid=max(BSM-halfobservedspread,0); fees0.20/100sharecontract. SNAPforecast/noIVrecovery win21.095%,avgwin6.03493,avgloss2.73711,mean-0.88665dollars; lowvolmean-1.80669; halfIVrecoveryforecastmean+0.32171. MARAforecast/noIVrecovery win17.303%,avgwin13.29695,avgloss2.05319,mean+0.60284; lowvolmean-1.15111. Thus optimisticMARAmeanisdrivenbyrarelargeoutcomes, notbasehits orobservededge. QuarterKelly formula max(0,(p-(1-p)/(avgwin/avgloss))/4) givesconditional1.1334%MARAforecast,0%lowvol; executablevalidatedallocation0inallcases. SNAPoneATRdeclineover5sessions producesbid.02038 below.03entry; twoATRbid.07167. Bothinitialbids.01 leave nopositivepenny stopbelowentrybid; a.01stopalreadytouchesatentry. InitialpathcheckwithbelowentryoneATRtargetwasdiscardedasnotvalidprofit-takingstrategy; terminalscenario explicitlymodelsnostop/targetfills. 15minuteexitgap/stochasticIV/jumps/dynamicspreads/Americanexercise omitted; simulationcannotcertifyreal15minuteexecution. All8scenarioinputs/resultsrecorded. Sources https://runway.adityaperswal.workers.dev/data/option-chain/SNAP?feed=indicative and /MARA?feed=indicative, underlyingbars2023–Sep4 2026. Rejectbothforentry; no inventedexitproposal.

Premises: (1) option exits occur at bids and discrete15minute checks; (2) mark volatility cannot be presumed to converge to forecast; (3) simulation cannot supply empiricaledge without validated inputs. Diagnostic hypothetical QQQ260908C00731000 fromSep4quote: S719.10,K731,ask0.03,bid0.02,feedIV8.99%,expirySep8. Not an availableFridayentry andnot aTuesdaystandingorder. InvertBSM midpoint0.025 usingT1/252,r4%,q0 to session-clockIV11.6548779%; this calibration prevents an artificial initialprice jump from changing clocks. Seed20260906;100000 paths per6scenarios;26equal steps/session. UnderlyingGBM zeroexpectedreturn, sigma10.5292%(0.8RV21) or16.3489%(forecast). MarkIV stayscalibrated, moveshalfway, or fully toassumedphysicalvolatstart. Reprice remainingtime eachstep; sellbid=max(BSM-0.005,0); target0.08capped, stop0.01actualbid, liquidationatfinalstep. $0.20roundtripfees; wholecontract100. Atforecastvol withNOIVrecovery: win22.457%,avgwin$4.80,avgloss$2.7700,mean-$1.0700; quarterKelly0. Lowerphysicalvol noIVrecovery: win11.017%,mean-$1.8197. Halfconvergence forecastcase mean+$2.2189/win65.675%; fullconvergence mean+$4.4906/win95.867%. These optimistic returns are assumedinstantrepricing, not evidence itoccurs. Stoploss overshootsnominal$2riskbecausecheckingdiscrete; fullpremium$3plusfeesmustcount. Expiresynthetic paths are liquidatedatclose; exercise/autoliquidation couldhappenearlier inreality, so forbidden asactualexitplan. Ignoresweekendjumps, bid-sizevariation, stochasticvol, hedgefeedback andmodifiedfeeduncertainty. Outputsall6scenarios savedobservation. SensitivitydominatesMonteCarlosamplingerror; confidenceaboutmodelparameters notestablished. ActualadmissiblequarterKellyallocation0, evenwhereassumedscenarioformula positive. Source https://runway.adityaperswal.workers.dev/data/option-chain/QQQ?feed=indicative . Reject candidate andderive no realstop/targetproposalfromsyntheticodds.