Option Pricing and Risk Management under Fractional Brownian Motion with Stochastic Volatility

Option Pricing and Risk Management under Fractional Brownian Motion with Stochastic Volatility | 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 Option Pricing and Risk Management under Fractional Brownian Motion with Stochastic Volatility houssam boughabi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8022981/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 paper delves into the pricing and hedging of financial derivatives within the framework of fractional Brownian motion (fBM). Traditional models often fall short in capturing market realities, particularly the long-memory and self-similarity characteristics inherent in asset prices and volatility. To address this, we extend classical option pricing theory by integrating tools from Malliavin calculus, offering a nuanced treatment of stochastic volatility under fBM. A Riccati equation governs the resulting model, allowing for analytical and numerical solutions that align with observed market behavior. Furthermore, we propose a correction term to account for residual volatility risk, providing a more practical approach to hedging. This study bridges theoretical advancements with empirical applicability, laying the groundwork for future exploration of fBM-driven financial models. JEL Classification. G13, G17, C61. Financial Mathematics Fractional Brownian Motion Stochastic Volatility Option Pricing Malliavin Calculus Full Text Additional Declarations The authors declare no competing interests. Supplementary Files code.docx Python code for estimation and Matlab code for resolving the Ricatti Equation 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. 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