[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119457-en":3,"doc-seo-119457-105":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},119457,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Machine-learning regression methods for American-style path-dependent contracts - Journal article abstract","Evaluating financial products with early-termination clauses, especially those with path-dependent structures, remains challenging in practice. The paper studies Asian options, look-back options, and callable certificates, comparing regression-based pricing and sensitivity computation approaches. It contrasts randomized recurrent and feedforward neural networks with traditional polynomial basis functions, and introduces a signature-based method based on the underlying price process. For Delta and Gamma, Chebyshev interpolation is used within the sensitivity workflow. Results indicate machine learning can match traditional accuracy and efficiency for Asian and look-back options, while randomized neural networks perform best for callable certificates.","Gambara, Matteo, Livieri, Giulia & Pallavicini, Andrea (2025) Machine-learning regression methods for American-style path-dependent contracts. Quantitative Finance, 25(6), 895-918. [https://doi.org/10.1080/14697688.2025.2517272](https://doi.org/10.1080/14697688.2025.2517272)  \n[https://researchonline.lse.ac.uk/id/eprint/128600/](https://researchonline.lse.ac.uk/id/eprint/128600/)  \nVersion: Accepted Version  \nLicence: Creative Commons: Attribution 4 .0  \nThis document is the author’s accepted version of the journal article. There may be differences between this version and the published version.  \nThis author accepted manuscript has been made open access under the LSE open access publications policy and distributed under a Creative Commons: Attribution 4.0 license.  \nLSE Research Online is the repository for research produced by the London School of Economics and Political Science. For more information, please refer to our Policies  \npage or contact [lseresearchonline@lse.ac.uk](lseresearchonline@lse.ac.uk)  \narXiv :2311 . 16762v2 [ q-fin .PR] 18 Jul 2025  \nMachine-learning regression methods  \nfor American-style path-dependent contracts ∗  \nM. Gambara†, G. Livieri‡, A. Pallavicini§  \nFirst Version: January 31, 2023 . This version: July 21, 2025  \nAbstract  \nEvaluating financial products with early-termination clauses, in particular those with path-dependent structures, is challenging. This paper focuses on Asian options, look-back options, and callable certificates. We will compare regression methods for pricing and computing sensitivities, highlighting modern machine learning techniques against traditional polynomial basis functions. Specifically, we will analyze randomized recurrent and feedforward neural networks, along with a novel approach using signatures of the underlying price process. For option sensitivities like Delta and Gamma, we will incorporate Chebyshev interpolation. Our findings show that machine learning algorithms often match the accuracy and efficiency of traditional methods for Asian and look-back options, while randomized neural networks are best for callable certificates. Furthermore, we apply Chebyshev interpolation for Delta and Gamma calculations for the first time in Asian options and callable certificates.  \nJEL classification codes: C63, G13 .  \nAMS classification codes: 65C05, 91G20, 91G60 .  \nKeywords: Amerasian options, Look-back options, Callable certificates, Early termination, Random networks, Signature methods, Least-square Monte Carlo, Chebyshev Greeks.  \n∗ The authors report no potential competing interests. The opinions expressed in this document are solely those of the authors and do not represent in any way those of their present and past employers.  \n†Inait SA, Address: Av. du Tribunal-Fédéral 34, 1005, Lausanne, Switzerland. Email address: [matteo.gambara@gmail.com](matteo.gambara@gmail.com).  \n‡The London School of Economics and Political Science, Department of Statistics. Address: Houghton St, London WC2A 2AE, United Kingdom. Email address: [g.livieri@lse.ac.uk](g.livieri@lse.ac.uk).  \n§ Intesa Sanpaolo, Financial Engineering. Address: largo Mattioli 3, Milano 20121, Italy. Email address: [andrea.pallavicini@intesasanpaolo.com](andrea.pallavicini@intesasanpaolo.com).  \nContents  \n1 Introduction 5  \n1. 1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7  \n2 Financial products with early termination 8  \n2.1 Asian and look-back payoffs ................................... 8  \n2.2 Early exercise and early termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9  \n3 Pricing techniques 9  \n3. 1 Least-square Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10  \n3.2 Randomized neural networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10  \n3.2. 1 R-FFNN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11  \n3.2.2 R-RNN . . . . .","cbCaimoMc1rPIuze","https://ap.wps.com/l/cbCaimoMc1rPIuze","pdf",1150665,1,61,"English","en",105,"# Introduction\n## Notation\n# Financial products with early termination\n## Asian and look-back payoffs\n## Early exercise and early termination\n# Pricing techniques\n## Least-square Monte Carlo\n## Randomized neural networks\n## Signature methods\n## Sensitivity computation\n# Numerical techniques\n## Price dynamics\n## Risk factors and features\n## Configuration of random networks\n## Configuration of signature methods\n# Numerical investigations\n## Asian options\n## Look-back options\n# Callable certificates","[{\"question\":\"Which financial products are analyzed for early-termination and path dependence?\",\"answer\":\"The paper focuses on Asian options, look-back options, and callable certificates. These contracts all feature path-dependent structures or early termination effects that make valuation difficult.\"},{\"question\":\"How do the regression methods differ from traditional polynomial basis functions?\",\"answer\":\"The study compares regression approaches using randomized recurrent and feedforward neural networks against traditional polynomial basis function techniques. It also considers regression via signatures of the underlying price process.\"},{\"question\":\"How are Delta and Gamma sensitivities computed in the proposed workflow?\",\"answer\":\"For Delta and Gamma, the paper incorporates Chebyshev interpolation into the sensitivity computation. It applies this Chebyshev approach for Asian options and callable certificates.\"}]","Machine-learning regression methods for American-style path-dependent contracts - Journal article abstract | PDF",1785724401,154,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-regression-methods-for-american-style-path-dependent-contracts-journal-article-abstract","",{"@graph":36,"@context":85},[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/machine-learning-regression-methods-for-american-style-path-dependent-contracts-journal-article-abstract/119457/",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","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Which financial products are analyzed for early-termination and path dependence?","Question",{"text":75,"@type":76},"The paper focuses on Asian options, look-back options, and callable certificates. These contracts all feature path-dependent structures or early termination effects that make valuation difficult.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do the regression methods differ from traditional polynomial basis functions?",{"text":80,"@type":76},"The study compares regression approaches using randomized recurrent and feedforward neural networks against traditional polynomial basis function techniques. It also considers regression via signatures of the underlying price process.",{"name":82,"@type":73,"acceptedAnswer":83},"How are Delta and Gamma sensitivities computed in the proposed workflow?",{"text":84,"@type":76},"For Delta and Gamma, the paper incorporates Chebyshev interpolation into the sensitivity computation. It applies this Chebyshev approach for Asian options and callable certificates.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]