Stochastic Regularization in Financial Markets: Implications for Volatility and Stability

Stochastic Regularization in Financial Markets: Implications for Volatility and Stability | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Stochastic Regularization in Financial Markets: Implications for Volatility and Stability Nam Anh Quach This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8805306/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This research examines a stochastic-transport-based regularization framework in financial markets and its effects on volatility, tail risk, and systemic stability. We represent asset price dynamics as a nonlinear transport system influenced by divergence-free stochastic transport fields that incorporate market microstructure effects, including heterogeneous execution and routing variability. In this context, we derive the corresponding Itô dynamics and recognize an emergent deterministic second-order operator—viewed as a latent dissipation mechanism—that regulates gradient amplification in state space. We establish evidence for (i) an energy–variance equilibrium indicating that transport noise introduces an additional nonnegative dissipation pathway in expectation, and (ii) a coercivity criterion on the transport covariance that produces an effective stability threshold comparable to viscosity in physical transport systems. These findings are consistent with the hypothesis that stochastic transport mitigates unstable feedback mechanisms, including trend following, leverage targeting, and endogenous liquidity stress. The empirical study of high-frequency XAUUSD data corroborates the proposed mechanism. During times of heightened market impact and liquidity constraints, we notice systematic, state-dependent rises in an effective viscosity-like stabilization term proxy obtained from detrended price increments, aligning with noise-induced regularization during periods of stress. Numerical investigations on modeled multi-asset systems further illustrate that the proposed approach mitigates drawdown severity, diminishes volatility clustering, and improves portfolio resilience during shock propagation. Stochastic transport market microstructure volatility regularization systemic risk nonlinear feedback stability thresholds Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8805306","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":599486920,"identity":"3fb7cf23-3d6f-4bd9-9541-e55922bc811e","order_by":0,"name":"Nam Anh Quach","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYLACxgYQycP4+E8FkGZmbiBaC7MBzxmQFkbitbBJ8LYhuDiBOfvpxM+FO6wT+9vPHpCQnFcbzd8O1PKjYhtOLZY9uZulZ55JT5xxJi/BwHDb8dwZhxkbGHvO3MapxeBA7gZp3rbDiQ03eAwSErcdy20AamFmbMOj5fzbzb9BWuYDtRw4OOdY7nyCWm7kbgPbsuEGj2FjY0NN7gbCWt5us+ZtSzfeeCbHmJnh2IHcjUAtB/H65Xzu5tu8bday846fMf/NUFOXO+/84YMPflTg1gIFzDDGYTB5gJB6ZC11RCgeBaNgFIyCkQYAJ8Fh8iX1/zgAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Nam","middleName":"Anh","lastName":"Quach","suffix":""}],"badges":[],"createdAt":"2026-02-06 09:53:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8805306/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8805306/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104779248,"identity":"2b9f6a1a-4e25-4133-983a-c2979f8a1814","added_by":"auto","created_at":"2026-03-17 07:37:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1204338,"visible":true,"origin":"","legend":"","description":"","filename":"StochasticRegularizationinFinancialMarketsImplicationsforVolatilityandStability.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8805306/v1_covered_f33d2c8b-7f98-446e-a9e5-5540966f2f24.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Stochastic Regularization in Financial Markets: Implications for Volatility and Stability","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Stochastic transport, market microstructure, volatility regularization, systemic risk, nonlinear feedback, stability thresholds","lastPublishedDoi":"10.21203/rs.3.rs-8805306/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8805306/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research examines a stochastic-transport-based regularization framework in financial markets and its effects on volatility, tail risk, and systemic stability. We represent asset price dynamics as a nonlinear transport system influenced by divergence-free stochastic transport fields that incorporate market microstructure effects, including heterogeneous execution and routing variability. In this context, we derive the corresponding It\u0026ocirc; dynamics and recognize an emergent deterministic second-order operator\u0026mdash;viewed as a latent dissipation mechanism\u0026mdash;that regulates gradient amplification in state space.\u003c/p\u003e \u003cp\u003eWe establish evidence for (i) an energy\u0026ndash;variance equilibrium indicating that transport noise introduces an additional nonnegative dissipation pathway in expectation, and (ii) a coercivity criterion on the transport covariance that produces an effective stability threshold comparable to viscosity in physical transport systems. These findings are consistent with the hypothesis that stochastic transport mitigates unstable feedback mechanisms, including trend following, leverage targeting, and endogenous liquidity stress.\u003c/p\u003e \u003cp\u003eThe empirical study of high-frequency XAUUSD data corroborates the proposed mechanism. During times of heightened market impact and liquidity constraints, we notice systematic, state-dependent rises in an effective viscosity-like stabilization term proxy obtained from detrended price increments, aligning with noise-induced regularization during periods of stress. Numerical investigations on modeled multi-asset systems further illustrate that the proposed approach mitigates drawdown severity, diminishes volatility clustering, and improves portfolio resilience during shock propagation.\u003c/p\u003e","manuscriptTitle":"Stochastic Regularization in Financial Markets: Implications for Volatility and Stability","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-03 12:36:16","doi":"10.21203/rs.3.rs-8805306/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bd2cceed-7ea5-4675-a506-75c0281f3ee9","owner":[],"postedDate":"March 3rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-03T12:36:18+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-03 12:36:16","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8805306","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8805306","identity":"rs-8805306","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}