[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117519-en":3,"doc-seo-117519-105":30,"detail-sidebar-cat-0-en-105":96},{"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},117519,687197207057,"Sage","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Credit Exposure Modelling Using Differential Machine Learning - Master’s Thesis 2023","Exposure modelling plays a central role in counterparty credit risk management, requiring banks to invest substantial computation to quantify future uncertainty. This thesis applies differential machine learning, a neural-network approach introduced by Huge and Savine in 2020, to approximate trade pricing from Monte Carlo paths using pathwise gradients. Training uses market variables instead of hidden model state. Simulations from Heston-type models estimate future exposure distributions for European-option portfolios. Stress testing under varying model–scenario compatibility shows that low compatibility reduces prediction accuracy.","Credit Exposure Modelling Using Differential Machine Learning  \nMaster’s thesis in Engineering Mathematics and Computational Science  \nSAMUEL WAGNER MÅNS KARPú  \nDEPARTMENT OF MATHEMATICAL SCIENCES  \nChalmers University of Technology Gothenburg, Sweden 2023  \n[www.chalmers.se](www.chalmers.se)  \nMaster’s thesis 2023  \nCredit Exposure Modelling Using Differential Machine Learning  \nSamuel Wagner, Måns Karpú  \nú Faculty of Engineering (LTH), Lund University  \nDepartment of Mathematical Sciences Division of Applied Mathematics and Statistics Chalmers University of Technology Gothenburg, Sweden 2023  \nCredit Exposure Modelling Using Differential Machine Learning SAMUEL WAGNER  \nMÅNS KARPú  \n© SAMUEL WAGNER, MÅNS KARP, 2023 .  \nSupervisors:  \nJesper Christiansen, Danske Bank Brian Fuglsbjerg, Danske Bank  \nCarl Lindberg, Department of Mathematical Sciences  \nExaminer:  \nAnnika Lang, Department of Mathematical Sciences  \nMaster’s Thesis 2023  \nDepartment of Mathematical Sciences Division of Applied Mathematics and Statistics Chalmers University of Technology  \nSE-412 96 Gothenburg Telephone +46 31 772 1000  \nCover: Example twin network structure central to the differential machine learning framework.  \nTypeset in LATEX  \nPrinted by Chalmers Reproservice Gothenburg, Sweden 2023  \nCredit Exposure Modelling Using Differential Machine Learning SAMUEL WAGNER, MÅNS KARPú  \nDepartment of Mathematical Sciences Chalmers University of Technology  \nAbstract  \nExposure modelling is a critical aspect of managing counterparty credit risk, and banks worldwide invest significant time and computational resources in this task. One approach to modelling exposure involves pricing trades with a counterparty in numerous potential future market scenarios. Suitable for this type of pricing is a framework presented in 2020 by Huge and Savine, which they call differential machine learning. It approximates the pricing function with a neural network that trains on Monte Carlo paths and the gradients along these paths. This thesis aims to demonstrate the application of differential machine learning in the context of exposure modelling. To better comply with this context, training is done on market variables, rather than some hidden model state. Simulated data is used from Heston type models to estimate the future exposure distribution of a portfolio consisting of European options. The conducted experiments reveal that training the machine learning model on market observables yields similar results to those obtained when training on hidden model states. Furthermore, the exposure modelling approach is subject to stress testing by evaluation of its performance under different levels of compatibility between the pricing model and future market scenarios in which the portfolio is priced. Results show that low compatibility leads to decreased accuracy of the predicted exposure distributions.  \nKeywords: Counterparty credit risk, Differential machine learning, Exposure modelling, Heston model, Option pricing.  \nAcknowledgements  \nFirstly, we would like to thank our industry supervisors at Danske Bank, Copenhagen, Brian Fuglsbjerg and Jesper Christiansen, for their time and patience throughout the project. Furthermore, we would like to thank our academic supervisors Erik Lindström and Carl Lindberg for insightful feedback and guidance. Lastly, we would like to express our gratitude towards our two examiners, Annika Lang at Chalmers University of Technology and Magnus Wiktorsson at the Faculty of Engineering at Lund University for allowing us to write this thesis together, despite coming from different universities.  \nSamuel Wagner & Måns Karp, June 2023  \nContents  \n1 Introduction 1  \n1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1  \n1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2  \n1.3 Previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3  \n1.4 Procedural overview . . . .","cbCaioZFbCuQKYeg","https://ap.wps.com/l/cbCaioZFbCuQKYeg","pdf",4027177,1,73,"English","en",105,"# Introduction\n## Background\n## Objective\n## Previous work\n## Procedural overview\n# Theory\n## Exposure Modelling\n## Basel Regulation\n## Exposure Metrics\n## Heston Model\n## Multi-Asset Heston Model\n## Neural Networks\n## Differential Machine Learning\n## Differential PCA\n# Methods\n## Exposure Modelling Using Differential Machine Learning\n## Example Settings\n## Sample Generation in the Heston Model\n## Sample Generation in the Multi-Asset Heston Model\n## Pathwise Gradients\n## Differential Machine Learning Hyperparameter Settings\n## Changing the Q-model Parameters\n## Performance Measuring\n# Results\n## Heston Model\n## Multi-Asset Heston Model\n## Netting set dependent on 2 underlying assets\n## Netting set dependent on 16 underlying assets","[{\"question\":\"What is the main goal of the thesis?\",\"answer\":\"The thesis demonstrates how differential machine learning can be applied to exposure modelling for counterparty credit risk, aiming to estimate future exposure distributions for a portfolio.\"},{\"question\":\"How is differential machine learning trained in this work?\",\"answer\":\"Training is performed on market variables rather than hidden model state, using neural-network approximation trained on Monte Carlo paths and gradients along these paths.\"},{\"question\":\"What models and instruments are used for the experiments?\",\"answer\":\"Experiments use simulated data from Heston-type models and estimate future exposure distributions for a portfolio consisting of European options.\"},{\"question\":\"How does model–scenario compatibility affect results?\",\"answer\":\"Stress testing evaluates performance under different compatibility levels between the pricing model and future market scenarios, showing that lower compatibility decreases the accuracy of predicted exposure distributions.\"}]","Credit Exposure Modelling Using Differential Machine Learning - Master’s Thesis 2023 | PDF",1785676594,184,{"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":91,"head_meta":93,"extra_data":95,"updated_unix":28},"credit-exposure-modelling-using-differential-machine-learning-masters-thesis-2023","",{"@graph":36,"@context":90},[37,54,69],{"@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/credit-exposure-modelling-using-differential-machine-learning-masters-thesis-2023/117519/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-02",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82,86],{"name":73,"@type":74,"acceptedAnswer":75},"What is the main goal of the thesis?","Question",{"text":76,"@type":77},"The thesis demonstrates how differential machine learning can be applied to exposure modelling for counterparty credit risk, aiming to estimate future exposure distributions for a portfolio.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How is differential machine learning trained in this work?",{"text":81,"@type":77},"Training is performed on market variables rather than hidden model state, using neural-network approximation trained on Monte Carlo paths and gradients along these paths.",{"name":83,"@type":74,"acceptedAnswer":84},"What models and instruments are used for the experiments?",{"text":85,"@type":77},"Experiments use simulated data from Heston-type models and estimate future exposure distributions for a portfolio consisting of European options.",{"name":87,"@type":74,"acceptedAnswer":88},"How does model–scenario compatibility affect results?",{"text":89,"@type":77},"Stress testing evaluates performance under different compatibility levels between the pricing model and future market scenarios, showing that lower compatibility decreases the accuracy of predicted exposure distributions.","https://schema.org",{"og:url":52,"og:type":92,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":94,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":97},[98,102,106,110,115,120,125,128,133,136,140],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"Exam",70,"exam",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},5,"Comic",60,"comic",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},6,"Technology",50,"technology",{"id":121,"doc_module":4,"doc_module_name":46,"category_name":122,"show_sort_weight":123,"slug":124},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":126,"slug":127},30,"research-report",{"id":129,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":131,"slug":132},9,"Religion & Spirituality",20,"religion-spirituality",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":131,"slug":135},"World Cup","world-cup",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":137,"slug":139},10,"Lifestyle","lifestyle",{"id":141,"doc_module":4,"doc_module_name":46,"category_name":142,"show_sort_weight":111,"slug":143},19,"General","general"]