[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119952-en":3,"doc-seo-119952-105":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},119952,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Machine-learning regression methods for American-style path-dependent contracts - paper overview","Evaluating financial derivatives with early-termination features is difficult, especially when payoffs depend on past price paths. The paper studies Asian options, look-back options, and callable certificates, comparing regression-based pricing and sensitivity estimation using both traditional polynomial basis functions and modern machine learning. It analyzes randomized recurrent and feedforward neural networks, and introduces a signature-based approach based on underlying price dynamics. Delta and Gamma are computed with Chebyshev interpolation, and results show comparable or improved accuracy and efficiency for Asian and look-back options, with randomized neural networks performing best for callable certificates.","arXiv :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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  \n3.3 Signature methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  \n3.3.1 Truncated signature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  \n3.3.2 Randomized signature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14  \n3.4 Sensitivity computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16  \n3.4. 1 Finite-difference method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16  \n3.4.2 Regression method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16  \n3.4.3 Chebyshev method .................................... 17  \n3.4.4 Algorithm comparison for American put Gamma ................... 17  \n4 Numerical techniques 18  \n4.1 Price dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18  \n4.2 Risk factors and features . . . . . . . . . . ","cbCaivfWK5NqmTD7","https://ap.wps.com/l/cbCaivfWK5NqmTD7","pdf",1082514,1,60,"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\n## Product description\n## Snowball payoff\n## Lock-in payoff\n# Conclusion and Further Developments","[{\"question\":\"Which option types and products are analyzed in the study?\",\"answer\":\"The paper focuses on Asian options, look-back options, and callable certificates with early-termination features.\"},{\"question\":\"How does the paper compare traditional regression with machine learning approaches?\",\"answer\":\"It compares polynomial basis regression methods against modern machine learning regressors, including randomized feedforward/recurrent neural networks and signature-based methods.\"},{\"question\":\"How are Delta and Gamma sensitivities computed?\",\"answer\":\"Delta and Gamma are computed using Chebyshev interpolation, alongside regression or neural network pricing/sensitivity workflows.\"}]","Machine-learning regression methods for American-style path-dependent contracts - 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