[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124403-en":3,"doc-seo-124403-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},124403,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Leveraging Machine Learning for High-Dimensional Option Pricing within the Uncertain Volatility Model - SEO Summary","This paper investigates machine learning methods for pricing high-dimensional options under the Uncertain Volatility Model (UVM). The UVM captures volatility unpredictability by using lower/upper bounds for volatility and bounds for correlation, producing confidence intervals for future uncertain parameters. Two ML-based approaches are proposed: GTU uses Gaussian Process regression with backward-in-time selection solved via expectation computations on a multidimensional tree and Sequential Quadratic Programming, while NNU trains neural networks to output worst-case volatility and correlation for Monte Carlo valuation. Results indicate improved precision for option pricing and risk management in high-dimensional settings.","arXiv :2407 . 13213v2 [ q-fin .CP] 5 Jun 2025  \nLeveraging Machine Learning for High-Dimensional Option Pricing within the Uncertain Volatility Model  \nLudovic Goudenège∗  \nAndrea Molent†  \nAntonino Zanette‡  \nAbstract  \nThis paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM) . The UVM is a robust framework that accounts for the inherent unpredictability of market volatility by setting upper and lower bounds on volatility and the correlation among underlying assets. By leveraging historical data and extreme values of estimated volatilities and correlations, the model establishes a confidence interval for future volatility and correlations, thus providing a more realistic approach to option pricing. By integrating advanced Machine Learning algorithms, we aim to enhance the accuracy and efficiency of option pricing under the UVM, especially when the option price depends on a large number of variables, such as in basket or path-dependent options. In this paper, we consider two approaches based on Machine Learning. The first one, termed GTU, evolves backward in time, dynamically selecting at each time step the most expensive volatility and correlation for each market state. Specifically, it identifies the particular values of volatility and correlation that maximize the expected option value at the next time step, and therefore, an optimization problem must be solved. This is achieved through the use of Gaussian Process regression, the computation of expectations via a single step of a multidimensional tree and the Sequential Quadratic Programming optimization algorithm. The second approach, referred to as NNU, leverages neural networks and frames pricing in the UVM as a control problem. Specifically, we train a neural network to determine the most adverse volatility and correlation for each simulated market state, generated via random simulations. The option price is then obtained through Monte Carlo simulations, which are performed using  \n∗ Féderation de Mathématiques de CentraleSupélec-CNRS FR3487, [France-](France-ludovic.goudenege@math.cnrs.fr)[ludovic.goudenege@math.cnrs.fr](France-ludovic.goudenege@math.cnrs.fr)  \n†Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Udine, Italy [andrea.molent@uniud.it](andrea.molent@uniud.it)  \n‡Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Udine, Italy [antonino.zanette@uniud.it](antonino.zanette@uniud.it)  \nthe values for the uncertain parameters provided by the neural network. The numerical results demonstrate that the proposed approaches can significantly improve the precision of option pricing and risk management strategies compared with methods already in the literature, particularly in high-dimensional contexts.  \nKeywords: Machine Learning, Gaussian Process Regression, Neural Networks, Option Pricing, Uncertain Volatility Model, Stochastic Control.  \n1 Introduction  \nThe Uncertain Volatility Model represents a significant advancement in financial modeling, specifically for the pricing and hedging of derivative securities in markets characterized by uncertain volatility. Developed initially by [Avellaneda et al., 1995], the UVM addresses the limitations of traditional models like the Black-Scholes, which assume constant volatility over the life of an option. Instead, the UVM assumes that volatility fluctuates within a known range, providing a more realistic framework for financial markets where volatility is inherently unpredictable.  \nThe core idea of the UVM is to set lower and upper bounds on volatility, denoted as σmin and σmax. These bounds can be inferred from historical data or extreme values of implied volatilities from liquid options. The model uses these bounds to establish a confidence interval within which the future volatility is expected to lie. This approach acknowledges the inherent uncertainty in predicti","cbCaianN9HVp2hCW","https://ap.wps.com/l/cbCaianN9HVp2hCW","pdf",772929,1,39,"English","en",105,"# 1 Introduction\n## Uncertain Volatility Model and motivation\n## Volatility bounds and confidence intervals\n## BlackScholes-Barenblatt PDE under UVM\n## Superhedging and worst-case volatility\n## Risk management and numerical analysis\n# 2 Proposed ML approaches\n## GTU: backward evolution and optimization\n## Gaussian Process regression and tree-based expectations\n## NNU: neural network control and Monte Carlo pricing","[{\"question\":\"What problem does the Uncertain Volatility Model address in option pricing?\",\"answer\":\"It addresses the limitation of constant-volatility assumptions by modeling volatility as fluctuating within known bounds and incorporating uncertainty in correlation across underlying assets.\"},{\"question\":\"How does the GTU approach select volatility and correlation for each market state?\",\"answer\":\"GTU evolves backward in time and, at each step, chooses the volatility and correlation that maximize the expected option value at the next time step, requiring optimization and expectation evaluation.\"},{\"question\":\"How does the NNU method obtain an option price under uncertainty?\",\"answer\":\"NNU trains a neural network to determine the most adverse volatility and correlation for simulated market states, then uses those outputs in Monte Carlo simulations to compute the option price.\"}]","Leveraging Machine Learning for High-Dimensional Option Pricing within the Uncertain Volatility Model - 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