Stats

Illustrative binary sizing uses honest empirical p=2/4 and b=18.8951 net-win multiple at the frozen P80 target: full Kelly=(bp-q)/b=47.354%, half Kelly=23.677% of the $100 book. The indivisible $18 contract is 18% of fund and 1.803% of $998.40 equity, below the 3% cap. This is a rough sizing assumption, not calibrated odds. Historical daily-path stress showed stop-first in 3/4 events at 3% loss/10% gain and 2/4 at 10%/10%; option stop paths are unobserved. Zero current bid means the nominal 50% stop is not guaranteed; premium is the loss bound. Counterexample: if true p is 1/4, Kelly remains positive only because P80 payoff is extreme, but path exits may prevent capture.

Premises:1 StartingS20.75,Oct16K20put premium.12 plus assumed.02/share friction, full all-in loss14USD;P80 legacy target1.702273 caps proceeds170.2273.2 Reversion only to19.84 pays16USD gross; break-even event probability87.5% if every other path loses all.3 To18.2977 or below, assumed target-hit probability must exceed8.2243% for positive arithmetic expectancy and10.7959% for halfKelly to fund14USD all-in at equity999.26. These are required probabilities, NOT forecasts.4 Numpy100000paths per18scenarios seed92104: pre-expiry downside probability1/5/10%, prices19.84/18.30/17, independent stop-survival1/.25. At17 and10%/fullsurvival mean+2.8593,loss90.096%,halfKelly9.667USD<14ticket;25%survival mean-9.83794,Kelly0. At5%/fullsurvival mean-5.62141. Models charge full premium even when stop assumed removed exposure: conservative risk stress, not realistic fill model. Conclusion no defensible minimum contract size from these illustrative odds; old6breakoutempiricalKelly45.97USD is no longer calibrated to cash-deal regime. This is not an indefinite simulation veto: materially new deal terms, actual independent matched event evidence or attainable repricing can change the conclusion. Primary no financing condition and long outside date do not prove failure odds zero. No actual stop/target history, no 15min option paths, American exercise not modeled. Sources https://www.sec.gov/Archives/edgar/data/1436126/000114036126037107/ef20082419_8k.htm ; https://runway.adityaperswal.workers.dev/data/option-chain/MG?feed=indicative ; script research/mg_audit.py.

Premises:1 Empiricalnormalizedsignedterminalpayoffs,cappedtarget,deductpremium+.02/sharefriction; optimize meanlogwealth over0–.99thenhalf,using999.38equity. MGOctP20.12 atP80target1.7023 mean+$14.37/contract,halfKelly45.97USD;25%payoffhaircutmean+7.28/Kelly31.98;50%haircut+.186/Kelly1.30. At3xpremiumtarget.36 mean-$8/Kelly0. MGcall.18 target.7023Kelly14.89below18minimum.2 DSXP3.13 P80target.51465 mean+5.667/Kelly119.13;25%haircut+.501/Kelly15.84(one13premiumcontract);50%haircut-4.666/Kelly0. 3xpremiumtargetmean+2.551/Kelly75.65. This generalKelly includespartialprofits; binary target-or-fullloss diagnosticKelly0doesNOTsupersede it.3 Pathstress usesactualhistorical20dailyclosepaths,N6MG/N8DSX,BSMputs,28dayexpiry/rate4%assumptions,askimpliedsigma17.8845%MG/54.4913%DSX,IVmult.75/1/1.25,spread.01/.025/.05,50%optionstop/P80target. Bootstrap100000seed92102constantIV:MGmean+18.15/+16.90/+15.89USD with5/6stops1/6targets;DSX-5.08/-10.88/-11.84 with7/8or8/8stops,1/8or0targets. Neitherdailyclosechecks norBSMcaptures15minvenueexecution,Americanexercise,IVchangesorrealbid; outcomesunvalidated, notpermanentveto.4 COSTterminalsampleallP760worthless,mean-20;TRMDP32.5signed0/11allworthlessdespiteabsoluteP80pass. ConclusiononecontractMG12orDSX13isaplausiblecappedprobeONLYwithfreshquoteandhonestexit-awareassumptions atauthorizedsession, notautomaticmodeltrade. Fullpremiumrisk<=29.9814,max4,total100;nominal50%stopisnotlossbound. Sources https://runway.adityaperswal.workers.dev/data/stock-bars andoption-chain; research/sizing.py/path_model.py. SmallNselectionandregimebreakremainbindinguncertainty.

Premises:1 Oct16P95 atindicative.18,target1.93,assumed.02friction givesnetwin1.73/share; allincost.20.2 Borrow2/17signedterminalpositives as an explicitly optimistic assumedtargetprobability; it is not observed target-before-50%stop probability. HalfKelly equity allocation=55.9488USD withidealstoploss.11allin versus7.8205USD withfull.20loss.3 Onecontractpremium18/allincost20 andcap30; below-onecontract allocations cannot be roundedup. Conclusion: freshspread/path-awarehonestodds required at authorizedentry; fullpremiumbudget and50%stop remainmandatory. Neither scenarios establishtradeprobabilitynorpermanentcashveto. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; latestcontract metadataOI7 asSep17,zeroindicativebid asSep18,observations31094 and current sizing observation.

Premises:1 NumPyseed92100 draws100000 signed NKE reactions from12frozen events; spot35.51,K31,premium.30,+.02assumedfriction; max(K-S*(1+r),0). Mean net-$2.2825,median-$32,loss83.315%,proceeds>=3premium16.685%.2 This terminal intrinsic scenario excludesremainingtimevalue,IV,50%pathstops and executablequotes, so neither lossfrequency nor targetfrequency is a live probability. NKEsize0 independently becausegatefails.3 On frozen HALON17/THN4 signed terminalrows, capintrinsic at indicatedP80target beforedeductingpremium+.02: HALOP95target1.93 mean+$2.7059; HALOC130target1.83 -$3.4706; THP18target6.20 -$25; THC27target3.58 +$143.8632. Uncappedmeans greatly overstate target-limitedstrategy; even cappedendpointvalues omitpathstop. Conclusion: no new calibratedKellyortradeodds; preserve grosspasses for honestfreshsession sizing. Existing3658series depletion/full-loss sensitivity remainsapplicable, not rerun. Stop50% is required but fullpremium<=30 is hardrisk. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; observations31092 and signed scenarios thisrun.

Premises:1 NumPyseed9200802,N100000resamplesof11signedWORearningsclose-reactions; frozenS57.38,K55put,ask2.14,+.02friction.2 MapK-S*(1+r)positivepart; meancontractnet-156.32USD,median-216,loss90.716%,zero-intrinsic63.5%,terminal3xpremium0%.3 This is empiricalterminalintrinsicscenario,NOT optionfill/PnLforecast; remainingtimevalue,IV,50%stopandadverseselectionexcluded. Quantizedsize0because214premium>30capregardlessmodel. Conclusion: no live Kelly or exitodds established; do notbuyhypotheticalcheapfillsbecausebootstraplooksbetter. Newoptions simulationsunnecessary forunchangedHALO/TH: prior3658fullpremiumandshared-lossstress retained,notrerun. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; /data/option-chain/WOR?feed=indicative .

Premises:1 NumPyseed9200602,100000paths/scenario,20sequentialpairs,initialfund100,noaddedcapital; premiums23+18,targetsaleproceeds183+358,1USDroundtripfeeeach,reserve43beforepair.2 Binaryp5/10/15%perlegASSUMED,loss50%or100%;commonuniformmixture0/.5/1 preservesmarginals and stresses dependence.3 p10%/half-loss independent meanfund413.71 butmedian32.50 and57.76%unabletofundnextpair; perfectlysharedmean323.51/median32.50/unable72.883%. Full-lossindependent mean175.58,median14,unable79.461%;shared86.257%. P95peak-to-troughdrawdowns270/382.5USDhalf-loss mayexceedinitial100 aftermodeledwins,notinitialprincipalrisk.4 BreakeventargetprobHALO7.289%half-loss/13.115%full-loss;TH2.865/5.307%. AtASSUMEDp10%,HALOhalfKelly26.91USDhalf-lossbut0full-loss;TH66.11/23.47before30cap. Conclusion: size cannotignore fullpremiumlossor minimumcontractgranularity; model sensitivity is not prediction,newmandatoryveto,or validatedtradeodds. No portfolio deploymentselected. Fullpremiumhardcap30,total100,max4. Source stock-derivedtargetlevels https://runway.adityaperswal.workers.dev/data/stock-bars

Premises:1 NumPy seed92004,20000 paths, four sampled5-session blocks from last252 logreturns,20 steps/25 calendar days toOct16,unchangedspot. BSM constantIV fit to HALO.23/TH.18 asks:33.414/68.513%,rate4%; targets1.83/3.58,50%premium stop, fills capped at target,1USD assumed roundtripfee.2 At no exit markdown, HALO/TH means+4.90/+4.50USD,loss87.97/93.23%,halfKelly22.95/11.50USD of1000equity, below onecontractcost24/19 respectively.20%mark discount changes means-1.19/+.57 andhalfKelly0/1.50USD. Zero-mean underlying paths already lose-1.54/-2.93 without markdown.3 Constantbidratio<=.5 triggers model immediate loss before movement: HALOzero-bid-24USD,TH.07/.18 -12USD. Actual venue mark unknown; indicative ratiosnotactualbidasks.4 Conditional cheaperfills:HALO.15 with.8markratio mean+9.05/halfKelly39.35,cost16;TH.13 with.8ratio+8.16/halfKelly21.80,cost14. RetainingTH.3889ratio instead yields-3.19/halfKelly0. Thus .13 onlyfixesinitialspread-stoparithmetic,notwholeholdingexpectancy. Pricegriduses samevaluationbutassumeslimitfillswithoutadverseselection; cannotcallpriceimprovement attainable. TH separategrid MonteCarlo differs slightly due RNG sequence; no bestdrawchosen. Conclusion: no calibrated positive sizing at observed indicative asks; fresh pricing and honest odds can change it. Fullpremium cap30,total100,max4; quarter30probe7.50unavailable attheseprices. Models sensitivity only,notnewmandatorygateorproofcashforever; historical terminalKelly isoptimisticrelative toexitpolicy. Source /data/stock-bars,/data/option-chain/HALO andTH; allrows30343–47 andlimitbatches.

Premises: hypotheticalSep21unchangedspot,20daily steps toOct16/25calendar days,NumPy30000paths/scenario seed92002. Bootstrap last252signedlogdailyreturns IID at.75/1/1.5scale, constantBSMIV calibrated toask and4%rate. HALOC130paid.23fitIV33.414%,P95paid.18IV38.114%,THC27paid.18IV68.513%;RV60HALO45.30/TH58.40%. Optionstop50%; modeledtargets filled no better than target, exitfriction.01/share+1USDroundtripfee. 3xpremium targets meanHALOC -8.90/-3.58/+1.78USD,THC -7.89/-4.71/+.02; apparent positive initialMC thatcreditedovershoots wasreplaced. P80targets independentlyderivedfrom3593 HALOC1.83 andTHC3.58 yieldmean -8.27/+1.42/+16.26 and-3.54/+7.28/+28.75;baseline targethits10.657%/4.557%,stops89.257%/91.873%,fullpremiumloss3.617%/5.847%. HALOPtarget1.93baseline -10.21USD,prefercallifquotedriskpass. These are uncalibrated regime-sensitive models, notconfidenceor executablebacktest; daily bars omit15minpath,quotesize/zero-bid,Americanfeatures andIVchanges. Stockreturns have positivehistoricaldrift: stationarity assumption canfail. Simulatedmarginalprofitdoesnotvalidate certainty. Keep wholepremium23/18 (<30 each),potential41total<100,max4; worstcase41+costs despitehalfpremiumstops. TerminalintrinsicKelly49.7/235.25USD unreliable; hardcap30 binds. Prospective singlecontracts are minimumgranularity, quarter30probe7.50unavailable. No ordersclosed; refreshcapital andactualquoteinentryrun. Source /data/stock-bars,/data/option-chain/HALO,TH?feed=indicative;30184–89.

Premises: S46.67 K37.5 paid.23, indicativeIV55.94%, N11 empirical signed reactions3554. NumPy50k paths/scenario, seed92000,20businesssteps Sep21–Oct16, eventstep12 Oct6; zero-drift GBM26/40/60% ordinaryvol, empiricalevent replaces dailyreturn. BSM put floored intrinsic,4% rate assumption, preIV55.94%,postIVscenario; initialmodel.23647 vsask.23. Daily stop.115,target.69, exit .01/share friction plus1USD roundtripfee. Hypothetical hold-through means+3.27/+8.81/+7.67USD, targets4.83/11.78/22.62%,but current20.14% hurdle exceeds10.02%median so this hold policy is outside mandate. Mandate-consistent forced Oct5 day11 exit means-13.81/-9.02/+.88USD, targets.556/7.006/20.698%. These uncalibrated daily marks omit American/dividend details and15-minute quote/liquidity risk. Full-premium loss remains possible despite half-premium stop. Separate empiricalterminalintrinsic after.02 friction:2/11wins, meanintrinsic.650308, grid halfKelly6.704% equity; it omits timevalue/path and uses same observed tails, so not live odds. It cannot override failedgate; actualsize0, future onepremium<=30,total100,max4. Crucial counterexample: higher price of a nearerstrike may passmedian when cheapenough; reprice rather than claim modelprofits at an impermissible hold. Sources https://runway.adityaperswal.workers.dev/data/option-chain/LW?feed=indicative ; stockbars and issuerOct6date29824.

Premises: 11 close-event reactions3513; S15.13,K14,indicativeask.23/IV.3516 fromchain. NumPy50k paths each,seed91908,20businessdaysSep21-Oct16,eventstep8Sep30; empiricalreaction replaces ordinaryreturn on eventday, otherdayszero-driftGBM22.5/35/50%annualvol. BSM put flooredintrinsic,preIV.3516/postIVscenario vol,r4%assumed;initialmodel.168158 differsask.23,so this is exit-policy sensitivity notfair-valueproof. Daily modeledstop.115,target.69,elseexpiry;exit.01/sharefriction+$1roundtrip. MeanPnL -12.3303/-6.1652/+.1245USD;target5.052/13.464/21.866%,stop93.924/85.970/78.006%;P05-23.2405/-20.4268/-21.2576USD. Uncalibrateddailyprices omitAmericanexercise/dividendboundary andactual15-minute liquidity; probabilities are model outputs, not live estimates. Empirical terminalintrinsic logutility grid halfKelly0 after.02friction. Conclusion size0 forfailedmandate; evenpositivehigh-volscenario doesnotrescueP80gate. Futurequalifyingticket fullpremium<=30, total<=100,max4;50%stop doesnot cap gaploss. Source https://runway.adityaperswal.workers.dev/data/stock-bars and option-chain/CAG?feed=indicative .

Premises:13observedovernightgaps29472–84; S7.99;10tradingsteps fromMondaySep21 throughOct2, eventstep4ThursdaySep24 issuer https://investors.blackberry.com/ . Correctedstep4 supersedesinitialstep3 outputs29595–97. NumPy50kpaths/scenario seed91906; stockzeroexpecteddrift GBM40/60/80%annualvol, oneIIDempiricalgap injectedday4; rate4%assumption. BSMputflooredintrinsic,pre-eventindicativeIV84.03%K7/98.70%K7.5, posteventIV40/60/80%; noAmericanexerciseboundary calibration. Exitdaily modeledmark<=.5paid or>=max(3paid,P80intrinsic),elseexpiry; actual15minquote/liquidityandgapstop executionunvalidated. $1roundtrip+.01/shareexitslippage. K7p.20 target.60 means-$13.6358/-10.8047/-6.7817,stop95.850/92.566/87.452%,target3.234/6.130/11.384%. K7.5 hypotheticalp.20 target.60 means-$7.1241/+$1.7658/+$10.9070;stop83/71.85/60.444%,target13.416/25.566/37.804%. CurrentK7.5ask.46 costs46>30cap; means-$30.4092/-23.0016/-15.1475. Cheap.20 is notquotedattainable. ModelP05 oftenfullpremium+fee despitehalf-premiumstop. Separate13signedclose intrinsicpayoff logutilitygrid halfKelly0 forK7p.20 andK7.5p.20/.23/.46 after.02friction. Intrinsicexcludesremainingtimevalue,so notproof trueoptionEVnegative; cannotclaimpositivecalibratedsize. Currentliveallocation0, hardonepremium<=30,total<=100,max4; quarterprobe cannotrescue invalidquote/failedmandate. Riskfullpremium,notmodelstop. Source https://runway.adityaperswal.workers.dev/data/option-chain/BB?feed=indicative andstock-bars.

Premises: historical10overnight gaps from observations29367–76, Sep18 S2.84, Oct16putK2.5. 30,000NumPy paths/volscenario seed91904, Monday-entry-to-expiry19trading steps; sample one historical GAP atstep3 then diffuse daily; use gaps rather than nextdayclose move to avoid adding intradayreaction twice. Vol scenarios40/60/80% annualized; zero stock drift, risk-free4% assumption; preevent option IV108.28% from indicativequote, posteventIV=scenario realizedvol. BSM put floored atintrinsic approximates American mark; no verified optimal exercise surface. Exit at daily observed model mark below0.5premium or above P80target.552156, else horizon. Gaps may pass stop; exitprice not stopguarantee. Fees1USDroundtrip and.01/shareexitslippage. At premium.13 mean dollarPnL -5.2523/-2.5318/+1.1347, stop80.4167/77.89/73.8533%, target7.2333/11.8667/17.7267%, win17.9433/20.62/24.9133%. At.28 allnegative(-18.5996,-16.2792,-13.7725); already failsmandate. At.11 means-3.2232/-.5282/+3.1574. These are assumption sensitivity, NOT calibrated venue execution probabilities: historicalsample10, resamplingIID,mixedregimes,indicativeIV,daily not15min marks, modeledliquidity. P05 loss .13case14USD includingfees; premium stillwhole13USD risk, not6.50stop. Separate empirical intrinsic-only Kelly grid on10signed nextdayclose moves: at.10 meanpayoff.116659,profit30%,halfKelly1.77%account; at.11 halfKelly.70%account; at.13/.28 halfKelly0. Intrinsic-only excludes remainingtimevalue; friction lowersKelly further. It does NOT prove no positive optionexpectancy at.13, but cannot support a confident size. One .11contract costs11USD vs7USD intrinsic halfKelly =>granularity matters. Start100fundcash/1000account, hardpremium30/lot,total100,max4. No live size; a future cheap probe requires honestly stated netodds/size under currentcapital andprice. Data sources https://runway.adityaperswal.workers.dev/data/stock-bars and https://runway.adityaperswal.workers.dev/data/option-chain/SFIX?feed=indicative .