{"id":4062,"date":"2021-03-01T11:45:20","date_gmt":"2021-03-01T11:45:20","guid":{"rendered":"https:\/\/detralytics.com\/?p=4062"},"modified":"2026-06-22T14:47:49","modified_gmt":"2026-06-22T14:47:49","slug":"a-heath-jarrow-morton-model-compliant-with-solvency-ii-promises-and-pitfalls","status":"publish","type":"post","link":"https:\/\/detralytics.com\/en\/publications\/a-heath-jarrow-morton-model-compliant-with-solvency-ii-promises-and-pitfalls\/","title":{"rendered":"A Heath-Jarrow-Morton model compliant with Solvency II? Promises and pitfalls"},"content":{"rendered":"\t\t
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A health-jarrow-morton model compliant with solvency iI? promises and pitfalls<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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DetraNote 2021-1<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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In this working paper, we adapt the Heath-Jarrow Morton (HJM) framework by considering a constraint of convergence of future forward rates toward a constant exogeneous rate set e.g. by a regulator. This limit rate, called \u201cultimate forward risk\u201d or UFR, was introduced by the EIOPA in 2015 to extrapolate the initial yield curve for maturities beyond the last liquid point. We show that adding a constraint of convergence in the HJM model impacts not only the term structure of interest rates but also the future variance of zero-coupon bonds.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Sector: <\/b>Insurance<\/p>\n

Authors:<\/b> Simon Boigelot &<\/span>
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Donatien Hainaut<\/p>\n

Publisher:<\/b> Detralytics<\/p>\n

Date:<\/b> March 2021<\/p>\n

Language:<\/b> English<\/p>\n

Pages:<\/b> 25<\/p>\n

Reference :<\/b> Detra Note 2021-1<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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About the authors<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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Simon Boigelot<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Simon is a TCP Actuarial Consultant and Sales Lead at Detralytics. Prior to joining the company, Simon worked at Belfius Bank as a Senior Quantitative Risk Analyst. His tasks ranged from pricing of financial products to Risk Management. Before that, Simon did two internships, at WTW and Deloitte.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Donatien\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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Donatien Hainaut<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Donatien Hainaut is a Scientific Advisor at Detralytics and a professor at UCLouvain (Belgium), where he serves as the Director of the Master’s program in Data Science with a statistical orientation. Prior to this, he held several academic positions, including Associate Professor at Rennes School of Business and ENSAE in Paris. He also has extensive industry experience, having worked as a Risk Officer, Quantitative Analyst, and ALM Officer.<\/p>\n

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Donatien is a Qualified Actuary and holds a PhD in the field of Asset and Liability Management. His current research focuses on contagion mechanisms in stochastic processes and the applications of neural networks in insurance.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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We adapt the Heath-Jarrow Morton (HJM) framework by considering a constraint of convergence of future forward rates toward a constant exogeneous rate set e.g. by a regulator.<\/p>\n","protected":false},"author":1,"featured_media":2167,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[137,133],"tags":[131],"class_list":["post-4062","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-137","category-publications","tag-detranote"],"yoast_head":"\nDetra Note : A Heath-Jarrow-Morton model compliant with Solvency II?<\/title>\n<meta name=\"description\" content=\"In this working paper, we adapt the Heath-Jarrow Morton (HJM) framework by considering a constraint of convergence of future forward rates toward a constant exogeneous rate set e.g. by a regulator.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/detralytics.com\/en\/publications\/a-heath-jarrow-morton-model-compliant-with-solvency-ii-promises-and-pitfalls\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Detra Note : A Heath-Jarrow-Morton model compliant with Solvency II?\" \/>\n<meta property=\"og:description\" content=\"In this working paper, we adapt the Heath-Jarrow Morton (HJM) framework by considering a constraint of convergence of future forward rates toward a constant exogeneous rate set e.g. by a regulator.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/detralytics.com\/en\/publications\/a-heath-jarrow-morton-model-compliant-with-solvency-ii-promises-and-pitfalls\/\" \/>\n<meta property=\"og:site_name\" content=\"detralytics.com\" \/>\n<meta property=\"article:published_time\" content=\"2021-03-01T11:45:20+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-06-22T14:47:49+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/detralytics.com\/wp-content\/uploads\/2021\/03\/DETRAnote_simon.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"794\" \/>\n\t<meta property=\"og:image:height\" content=\"1123\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Detralytics\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Detralytics\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/detralytics.com\\\/publications\\\/a-heath-jarrow-morton-model-compliant-with-solvency-ii-promises-and-pitfalls\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/detralytics.com\\\/publications\\\/a-heath-jarrow-morton-model-compliant-with-solvency-ii-promises-and-pitfalls\\\/\"},\"author\":{\"name\":\"Detralytics\",\"@id\":\"https:\\\/\\\/detralytics.com\\\/#\\\/schema\\\/person\\\/afceedbd1f9efae3aff3db243bb1890d\"},\"headline\":\"A Heath-Jarrow-Morton model compliant with Solvency II? 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