[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124380-en":3,"doc-seo-124380-105":30,"detail-sidebar-cat-0-en-105":95},{"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":4,"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},124380,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","Calibration of Option Price Models with Machine Learning - Bachelor’s Degree Final Thesis","Financial option pricing is commonly modeled through mathematical frameworks such as Black-Scholes and Heston, yet both face practical limitations. Black-Scholes relies on constant volatility, reducing accuracy in real applications. Heston introduces stochastic volatility, but its calibration is computationally demanding and difficult to scale. This thesis presents a Calibrating Neural Network (CaNN) that learns Heston parameters from implied volatility (IV) surfaces using deep learning and optimization-based calibration, then performs extensive synthetic and market-data evaluations. It also discusses neural-network challenges, hyperparameter uncertainty, interpretability, data demands, and regulatory and socioeconomic implications.","Bachelor’s Degree in Applied Mathematics and Computing  \n2022-2023  \nBachelor’s Degree Final Thesis  \nCalibration of Option Price Models with  \nMachine Learning  \nCarlos Suárez Pardo  \nSupervisor  \nFrancisco Manuel Bernal Martínez Leganés, June 18th 2023  \nThis work is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works license  \nABSTRACT  \nThe complex, yet fascinating, world of financial option pricing has traditionally been tackled with mathematical models, such as the Black-Scholes and Heston models. However, these models are not without their limitations. The Black-Scholes model assumes constant volatility, which is a simplification that limits its accuracy in practical applications. The Heston model overcomes this by incorporating stochastic volatility; however, calibrating it is a complex and computationally intensive task, which hinders its scalability and efficiency. In light of these challenges, this thesis introduces a novel approach to option pricing calibration that leverages the power of machine learning, specifically, neural networks.  \nThis thesis explores a paradigm shift that was first introduced by Oosterlee and collaborators in [1] . This shift combines the best of two worlds: the interpretability and reliability of option pricing models, along with the computational advantages of a deep learning-based approach. This exploration begins with the theoretical underpinnings of options and their pricing and then shifts to the application of machine learning and the potential it offers in this context.  \nThe focus of this work is the development of a Calibrating Neural Network (CaNN), designed to master the multidimensional calibration of the Heston model. The CaNN is trained on Implied Volatility (IV) surfaces rather than prices, capitalizing on their abundant availability and the rich information they contain, making them an excellent indicator of model accuracy. The training process involves a feedforward pass, with attention to the ANN architecture and learning of the map. A backward pass follows in order to calibrate the Heston parameters by applying various optimization algorithms to the trained model, evaluating them, and comparing them.  \nThe methodology presented is exhaustively tested. Using synthetic data for initial training, validation, calibration, and evaluation, promising results are displayed, which motivates an extension of the approach to a more ambitious application over market data, something not considered in Oosterlee’s reference paper. This extension, for which difficulties and implications are discussed, represents a genuine novel contribution coming from the thesis. However, this paper does not shy away from addressing the known challenges of adopting neural networks, such as lack of interpretability, uncertainty in the optimal choice of hyper-parameters, and dependency on large amounts of data. Finally, it also presents an overview of the potential socioeconomic impact, as well as the regulatory considerations required for the application of this technology in options trading.  \nKeywords: machine learning, deep learning, quantitative finance, option pricing models, stochastic volatility models, calibration, multi-layer perceptron, implied volatility, Heston model, BlackScholes model, neural network, financial engineering  \nACKNOWLEDGMENTS  \nI would like to express my gratitude to my supervisor, Francisco, for his persistent support, mentorship, and inspiration throughout the course of this project. His knowledge of the matter coupled with the motivation to expand the horizons together made the development an enriching experience. I would also like to thank my university colleagues and classmates that helped me get through the 4 years of coursework for which this thesis symbolizes the culmination.  \nCONTENTS  \n1. INTRODUCTION ......................................... 1  \n1.1. Financial Derivatives ...................................... 1  \n1.2. Option Pricing","cbCaicu0MKtQYYJX","https://ap.wps.com/l/cbCaicu0MKtQYYJX","pdf",4510683,1,70,"English","en",105,"# Introduction\n## Financial Derivatives\n## Option Pricing Models\n### Black-Scholes Model\n### Heston Model\n## Overview\n## Machine Learning Background\n### Deep Learning\n### The Multi-Layer Perceptron\n### MLP Architecture\n### MLP Training\n# Methodology: Calibrating Neural Network\n## Choice of Output and Mapping Function\n## CaNN Training\n## CaNN Calibration\n# Setup and Results\n## Setup: Fundamental Methods and Data Generation\n## Forward Training\n## Forward Evaluation\n## Calibration\n## Results over Market Data\n# Feasibility Analysis\n## Regulatory Framework\n## Socioeconomic Impact\n# Conclusions","[{\"question\":\"Why are Black-Scholes and Heston models difficult to use in practice?\",\"answer\":\"Black-Scholes assumes constant volatility, limiting accuracy. Heston includes stochastic volatility, but parameter calibration is complex and computationally intensive, reducing scalability and efficiency.\"},{\"question\":\"What is the core method introduced in the thesis?\",\"answer\":\"The thesis develops a Calibrating Neural Network (CaNN) that calibrates the Heston model by learning from implied volatility (IV) surfaces rather than option prices.\"},{\"question\":\"How does CaNN training and calibration work?\",\"answer\":\"CaNN uses a feedforward pass to learn a mapping from IV surface information via the ANN architecture, then applies a backward/optimization step to calibrate Heston parameters and evaluate different optimization algorithms through comparisons.\"},{\"question\":\"What feasibility aspects are discussed beyond the experiments?\",\"answer\":\"The work addresses known neural-network challenges such as limited interpretability and hyperparameter uncertainty, and discusses additional considerations including socioeconomic impact and regulatory requirements for options trading.\"}]","Calibration of Option Price Models with Machine Learning - Bachelor’s Degree Final Thesis | PDF",1785821898,176,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":90,"head_meta":92,"extra_data":94,"updated_unix":28},"calibration-of-option-price-models-with-machine-learning-bachelors-degree-final-thesis","",{"@graph":36,"@context":89},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/calibration-of-option-price-models-with-machine-learning-bachelors-degree-final-thesis/124380/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81,85],{"name":72,"@type":73,"acceptedAnswer":74},"Why are Black-Scholes and Heston models difficult to use in practice?","Question",{"text":75,"@type":76},"Black-Scholes assumes constant volatility, limiting accuracy. Heston includes stochastic volatility, but parameter calibration is complex and computationally intensive, reducing scalability and efficiency.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the core method introduced in the thesis?",{"text":80,"@type":76},"The thesis develops a Calibrating Neural Network (CaNN) that calibrates the Heston model by learning from implied volatility (IV) surfaces rather than option prices.",{"name":82,"@type":73,"acceptedAnswer":83},"How does CaNN training and calibration work?",{"text":84,"@type":76},"CaNN uses a feedforward pass to learn a mapping from IV surface information via the ANN architecture, then applies a backward/optimization step to calibrate Heston parameters and evaluate different optimization algorithms through comparisons.",{"name":86,"@type":73,"acceptedAnswer":87},"What feasibility aspects are discussed beyond the experiments?",{"text":88,"@type":76},"The work addresses known neural-network challenges such as limited interpretability and hyperparameter uncertainty, and discusses additional considerations including socioeconomic impact and regulatory requirements for options trading.","https://schema.org",{"og:url":52,"og:type":91,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":93,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":96},[97,101,105,108,113,118,123,126,131,134,138],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":21,"slug":107},"Exam","exam",{"id":109,"doc_module":4,"doc_module_name":46,"category_name":110,"show_sort_weight":111,"slug":112},5,"Comic",60,"comic",{"id":114,"doc_module":4,"doc_module_name":46,"category_name":115,"show_sort_weight":116,"slug":117},6,"Technology",50,"technology",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":121,"slug":122},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":124,"slug":125},30,"research-report",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":129,"slug":130},9,"Religion & Spirituality",20,"religion-spirituality",{"id":129,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":129,"slug":133},"World Cup","world-cup",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":135,"slug":137},10,"Lifestyle","lifestyle",{"id":139,"doc_module":4,"doc_module_name":46,"category_name":140,"show_sort_weight":109,"slug":141},19,"General","general"]