{"id":718,"date":"2023-01-30T19:36:40","date_gmt":"2023-01-30T19:36:40","guid":{"rendered":"https:\/\/compfinance.ddns.net\/wordpress\/?page_id=718"},"modified":"2023-07-16T17:22:56","modified_gmt":"2023-07-16T16:22:56","slug":"financial-engineering-interest-rates-and-xva","status":"publish","type":"page","link":"https:\/\/compfinance.ddns.net\/wordpress\/financial-engineering-interest-rates-and-xva\/","title":{"rendered":"Financial Engineering (Interest Rates and xVA)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"718\" class=\"elementor elementor-718\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6559411 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6559411\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0f88077\" data-id=\"0f88077\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-2b63f5e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2b63f5e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-2c10dfa\" data-id=\"2c10dfa\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-096916f elementor-widget elementor-widget-text-editor\" data-id=\"096916f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.14.0 - 26-06-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><strong>Course description:<\/strong><br \/>The main focus of this course is the modelling of the interest rates while other asset classes like foreign exchange and inflation are also covered. Ultimately, after completing the course, the student should be able to build a multi-asset portfolio consisting of linear products and perform xVA (CVA, BCVA and FVA) and (H)Value-at-Risk computations.\u00a0<\/p><p><strong>Expected prior knowledge:<\/strong><br \/>Basic knowledge of stochastic differential equations (SDEs), numerical methods for Monte Carlo simulation, linear algebra and basic knowledge of Python programming. Prior to this course, it is highly recommended to follow the course of Computational Finance (available here).<\/p><p><strong>Workload:<\/strong> <br \/>The course consists of 14 lectures, and each lecture is divided into 45m-1h blocks. The whole course consists of 32 blocks. Homework assignments are given at the end of each lecture.<\/p><p><strong>Course Materials:<\/strong><\/p><ol><li><strong>Slides<\/strong> can be found <a href=\"https:\/\/github.com\/LechGrzelak\/FinancialEngineering_IR_xVA\">here<\/a>.<\/li><li><strong>The book used<\/strong> in the course can be get <a href=\"https:\/\/www.amazon.nl\/Mathematical-Modeling-Computation-Finance-Exercises\/dp\/1786348055\/ref=sxts_sxwds-bia-wc-rsf-ajax1_0?__mk_nl_NL=%C3%85M%C3%85%C5%BD%C3%95%C3%91&amp;crid=41NEMIHPF304&amp;cv_ct_cx=mathematical+modeling+and+computation+in+finance&amp;dchild=1&amp;keywords=mathematical+modeling+and+computation+in+finance&amp;pd_rd_i=1786348055&amp;pd_rd_r=ab446575-af67-48bf-bdcc-afc466e0a206&amp;pd_rd_w=LRCa3&amp;pd_rd_wg=mCApS&amp;pf_rd_p=7a0c348a-a275-45d8-8862-fd4e8b528823&amp;pf_rd_r=XNY9DDYB1VMP2VWNY8JS&amp;psc=1&amp;qid=1614160090&amp;sprefix=mathematical%2Caps%2C155&amp;sr=1-1-6bc49e3f-9798-4557-aecc-11e86e72dff6\">here<\/a>.<\/li><li><strong>Codes and the exercises<\/strong> for the book can be found <a href=\"https:\/\/github.com\/LechGrzelak\/QuantFinanceBook\">here<\/a>.<\/li><li><strong>YouTube Channel<\/strong> with courses can be found <a href=\"https:\/\/www.youtube.com\/computationsinfinance\">here<\/a>.<\/li><\/ol>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-69ef977\" data-id=\"69ef977\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6fa201e elementor-widget elementor-widget-image\" data-id=\"6fa201e\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.14.0 - 26-06-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.youtube.com\/playlist?list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD\" target=\"_blank\">\n\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"647\" src=\"https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/FinEngineering_1-1024x647.jpg\" class=\"attachment-large size-large wp-image-983\" alt=\"\" srcset=\"https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/FinEngineering_1-1024x647.jpg 1024w, https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/FinEngineering_1-300x189.jpg 300w, https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/FinEngineering_1-768x485.jpg 768w, https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/FinEngineering_1.jpg 1278w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\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\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-49b6e8b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"49b6e8b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-2d31ab8\" data-id=\"2d31ab8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-61d0085 elementor-widget elementor-widget-text-editor\" data-id=\"61d0085\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 1- Introduction and Overview of the Course<\/h3><p>1.1. Introduction &amp; Details Regarding the Course<br \/>1.2. Lecture 2- Understanding of Filtrations and Measures<br \/>1.3. Lecture 3- The HJM Framework<br \/>1.4. Lecture 4- Yield Curve Dynamics under Short Rate<br \/>1.5. Lecture 5- Interest Rate Products<br \/>1.6. Lecture 6- Construction of Yield Curve and Multi-Curves<br \/>1.7. Lecture 7- Pricing of Swaptions and Negative Interest Rates<br \/>1.8. Lecture 8- Mortgages and Prepayments<br \/>1.9. Lecture 9- Hybrid Models and Stochastic Interest Rates<br \/>1.10. Lecture 10- Foreign Exchange (FX) and Inflation<br \/>1.11. Lecture 11- Market Models and Convexity Adjustments<br \/>1.12. Lecture 12- Valuation Adjustments- xVA (CVA, BCVA and FVA)<br \/>1.13. Lecture 13- Value-at-Risk and Expected Shortfall<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-ab7e7c4\" data-id=\"ab7e7c4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0e4c35b elementor-widget elementor-widget-video\" data-id=\"0e4c35b\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=oX7iyvZsAak&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=1&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.14.0 - 26-06-2023 *\/\n.elementor-widget-video .elementor-widget-container{overflow:hidden;transform:translateZ(0)}.elementor-widget-video .elementor-wrapper{aspect-ratio:var(--video-aspect-ratio)}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{height:100%;width:100%;display:flex;border:none;background-color:#000}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-wrapper{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .elementor-open-inline .elementor-custom-embed-image-overlay{position:absolute;top:0;left:0;width:100%;height:100%;background-size:cover;background-position:50%}.elementor-widget-video .elementor-custom-embed-image-overlay{cursor:pointer;text-align:center}.elementor-widget-video .elementor-custom-embed-image-overlay:hover .elementor-custom-embed-play i{opacity:1}.elementor-widget-video .elementor-custom-embed-image-overlay img{display:block;width:100%}.elementor-widget-video .e-hosted-video .elementor-video{-o-object-fit:cover;object-fit:cover}.e-con-inner>.elementor-widget-video,.e-con>.elementor-widget-video{width:var(--container-widget-width);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4bca652 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4bca652\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-41930fb\" data-id=\"41930fb\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aba6c9a elementor-widget elementor-widget-text-editor\" data-id=\"aba6c9a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 2- Understanding of Filtrations and Measures<\/h3><p>2.1. Filtration<br \/>2.2. Conditional Expectations<br \/>2.3. Conditional Expectations in Python<br \/>2.4. Option Pricing Using Conditional Expectation<br \/>2.5. Convergence Experiment in Python<br \/>2.6. Concept of Numeraire<br \/>2.7. From P to Q in the Black-Scholes Model<br \/>2.8. Change of Numeraire: Stock Measure<br \/>2.9. Change of Numeraire: Dimension Reduction<br \/>2.10. The T-Forward Measure<br \/>2.11. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-271d087\" data-id=\"271d087\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-270d363 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"270d363\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-0d1eadf\" data-id=\"0d1eadf\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2ebe134 elementor-widget elementor-widget-video\" data-id=\"2ebe134\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=8A7XvKjofY8&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=2&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-19467c0\" data-id=\"19467c0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-28152fd elementor-widget elementor-widget-video\" data-id=\"28152fd\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=Vvo1kIo414w&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=3&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-336cc43 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"336cc43\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-f12ecb4\" data-id=\"f12ecb4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6eac4c3 elementor-widget elementor-widget-video\" data-id=\"6eac4c3\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=Xta1_F49noA&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=4&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-bbf90ac\" data-id=\"bbf90ac\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3cb2f6f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3cb2f6f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-95e7d85\" data-id=\"95e7d85\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d813b6e elementor-widget elementor-widget-text-editor\" data-id=\"d813b6e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 3- The HJM Framework<\/h3><p>3.1. Equilibrium vs. Term-Structure Models<br \/>3.2. The HJM Framework<br \/>3.3. The Instantaneous Forward Rate<br \/>3.4. Arbitrage Free Conditions under HJM<br \/>3.5. Ho-Lee Model and Python Simulation<br \/>3.6. Hull-White Model<br \/>3.7. Hull-White Model and Simulation in Python<br \/>3.8. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-ced99f0\" data-id=\"ced99f0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-2d6a667 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2d6a667\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-7a62ff3\" data-id=\"7a62ff3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a5dee9e elementor-widget elementor-widget-video\" data-id=\"a5dee9e\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=iMHukRSzJqM&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=5&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-ac3e40e\" data-id=\"ac3e40e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-abb8314 elementor-widget elementor-widget-video\" data-id=\"abb8314\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=BIZdwUDbnDo&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=6&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-74720ab elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"74720ab\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-b946cd7\" data-id=\"b946cd7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-977586b elementor-widget elementor-widget-text-editor\" data-id=\"977586b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 4- Yield Curve Dynamics under Short Rate<\/h3><p>4.1. Exact Solution for the Hull-White Model<br \/>4.2. The Affinity of the Hull-White Model<br \/>4.3. Brief Introduction to Yield Curves<br \/>4.4. Shapes and Dynamics of Yield Curve<br \/>4.5. Limitations of the 1-Factor Model and Yield Curve Dynamics<br \/>4.6. Gaussian 2-Factor Model<br \/>4.7. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-70a6f6b\" data-id=\"70a6f6b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-367e2fa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"367e2fa\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-7f82267\" data-id=\"7f82267\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9cdb15a elementor-widget elementor-widget-video\" data-id=\"9cdb15a\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=KU66_i0auXg&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=7&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-b677d0a\" data-id=\"b677d0a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-509a9ef elementor-widget elementor-widget-video\" data-id=\"509a9ef\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=JmuMixVw950&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=8&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-75e39ee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"75e39ee\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-5373d78\" data-id=\"5373d78\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b988c73 elementor-widget elementor-widget-text-editor\" data-id=\"b988c73\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 5- Interest Rate Products<\/h3><p>5.1. Simple Compounded Forward Rate<br \/>5.2. Forward Rate Agreement<br \/>5.3. Floating Rate Note<br \/>5.4. Interest Rate Swap<br \/>5.5. The Hull-White model under the T-Forward Measure<br \/>5.6. Options on Zero-Coupon Bond<br \/>5.7. Caplets and Floorlets<br \/>5.8. Pricing of Caplets\/Floorlets Under the HW Model<br \/>5.9. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-ab52ac8\" data-id=\"ab52ac8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-c22a1da elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c22a1da\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-b0a81bb\" data-id=\"b0a81bb\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3bd3829 elementor-widget elementor-widget-video\" data-id=\"3bd3829\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=6APNi-wA-O8&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=9&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-5046ebb\" data-id=\"5046ebb\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-85c135d elementor-widget elementor-widget-video\" data-id=\"85c135d\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=6yt7thVlg0U&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=10&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-46d9a53 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"46d9a53\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-44427f5\" data-id=\"44427f5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-66e332c elementor-widget elementor-widget-text-editor\" data-id=\"66e332c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 6- Construction of Yield Curve and Multi-Curves<\/h3><p>6.1. Yield Curve and its Dynamics<br \/>6.2. Mathematical Formulation<br \/>6.3. From Implied Volatilities to Building of YC<br \/>6.4. Spine Points and Optimization Routine<br \/>6.5. Analytical Example of YC Construction<br \/>6.6. Building of Yield Curve in Python<br \/>6.7. Different Interpolations and Impact on Hedging<br \/>6.8. Introduction to Multi-Curves<br \/>6.9. Multi-Curves and Connection to Default Probabilities<br \/>6.10. Python Experiment for Multi-Curves<br \/>6.11. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-bfdf0f3\" data-id=\"bfdf0f3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-fb7d0f9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fb7d0f9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-7edd3bd\" data-id=\"7edd3bd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-25b84b4 elementor-widget elementor-widget-video\" data-id=\"25b84b4\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=zEQ_I1XWcBU&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=11&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-58c1180\" data-id=\"58c1180\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c286cd7 elementor-widget elementor-widget-video\" data-id=\"c286cd7\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=ZdqNKjcRFXM&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=12&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-d9183e8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d9183e8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-c35bffb\" data-id=\"c35bffb\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9ca6dd0 elementor-widget elementor-widget-video\" data-id=\"9ca6dd0\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=9v1dC3lm6aI&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=13&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-cd2cdf2\" data-id=\"cd2cdf2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5170404 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5170404\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-16ac05f\" data-id=\"16ac05f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c5ada50 elementor-widget elementor-widget-text-editor\" data-id=\"c5ada50\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 7- Pricing of Swaptions and Negative Interest Rates<\/h3><p>7.1. Pricing of Caplets\/Floorlets<br \/>7.2. Pricing of Interest Rate Swaps<br \/>7.3. Pricing of Swaptions under the Black-Scholes Model<br \/>7.4. Jamshidian\u2019s Trick<br \/>7.5. Swaptions under the Hull-White Model<br \/>7.6. Negative Interest Rates<br \/>7.7. Shifted Lognormal, Shifted Implied Volatility<br \/>7.8. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-b4b4d8c\" data-id=\"b4b4d8c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-613bd62 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"613bd62\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-d590d00\" data-id=\"d590d00\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3fac311 elementor-widget elementor-widget-video\" data-id=\"3fac311\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=esmfj22HF0M&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=14&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-b9aa8aa\" data-id=\"b9aa8aa\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1fee7d3 elementor-widget elementor-widget-video\" data-id=\"1fee7d3\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=uxQO1N3qDFU&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=15&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d49569d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d49569d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-dc58e9d\" data-id=\"dc58e9d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a1d0235 elementor-widget elementor-widget-text-editor\" data-id=\"a1d0235\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 8- Mortgages and Prepayments<\/h3><p>8.1. Introduction to Mortgage Contracts<br \/>8.2. Bullet Mortgage<br \/>8.3. Bullet Mortgage: Python Experiment<br \/>8.4. Annuity Mortgage<br \/>8.5. Annuity Mortgage: Python Experiment<br \/>8.6. Prepayment determinants<br \/>8.7. CPR: Constant Prepayment Rate<br \/>8.8. Index Amortizing Swap<br \/>8.9. Inclusion of Refinancing Incentive<br \/>8.10. Stochastic Prepayment: Python Experiment<br \/>8.11. Stochastic Prepayment and Swaptions<br \/>8.12. Pipeline Risk<br \/>8.13. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-971087d\" data-id=\"971087d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-a4b6cb2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a4b6cb2\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-d71a89c\" data-id=\"d71a89c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b7ad418 elementor-widget elementor-widget-video\" data-id=\"b7ad418\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=YopnVlia_3I&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=16&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-ac763b9\" data-id=\"ac763b9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3963fc4 elementor-widget elementor-widget-video\" data-id=\"3963fc4\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=MlzhIxLyBYE&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=17&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-eeb06cf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"eeb06cf\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-bb45c4d\" data-id=\"bb45c4d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-209a9ae elementor-widget elementor-widget-video\" data-id=\"209a9ae\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=OPERBMoCkkE&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=18&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-800b523\" data-id=\"800b523\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3d9e7cc elementor-widget elementor-widget-video\" data-id=\"3d9e7cc\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=9pcnc0B0vNU&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=19&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e1da3de elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e1da3de\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-b2f21d8\" data-id=\"b2f21d8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-69b4c27 elementor-widget elementor-widget-text-editor\" data-id=\"69b4c27\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 9- Hybrid Models and Stochastic Interest Rates<\/h3><p>9.1. Hybrid Models for xVA and VaR<br \/>9.2. The Black-Scholes Hull-White Model<br \/>9.3. Implied Volatility for Models with Stochastic Interest Rates<br \/>9.4. Stochastic Vol Models with Stochastic Interest Rates<br \/>9.5. Example of a Hybrid Payoff: Diversification Product<br \/>9.6. The Heston Hull-White Hybrid Model<br \/>9.7. Monte Carlo Simulation for Hybrid Models<br \/>9.8. Monte Carlo Simulation of the Heston-Hull-White Model<br \/>9.9. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-2e662de\" data-id=\"2e662de\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-14ff82a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"14ff82a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-17d4925\" data-id=\"17d4925\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4528b68 elementor-widget elementor-widget-video\" data-id=\"4528b68\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=tBlhfqtyGAY&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=20&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-0305f2a\" data-id=\"0305f2a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bd574ff elementor-widget elementor-widget-video\" data-id=\"bd574ff\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=nxg2lAmJEkk&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=21&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-df3b32f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"df3b32f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-a7a8d18\" data-id=\"a7a8d18\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-53c3a85 elementor-widget elementor-widget-text-editor\" data-id=\"53c3a85\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 10- Foreign Exchange (FX) and Inflation<\/h3><p>10.1. Introduction to Foreign Exchange<br \/>10.2. Forward FX Contract<br \/>10.3. Cross-Currency Swaps<br \/>10.4. Pricing of FX Options, the Black-Scholes Case<br \/>10.5. The Heston FX Model<br \/>10.6. Pricing of FX Options with Stochastic Interest Rates<br \/>10.7. Introduction to Inflation<br \/>10.8. Pricing of Inflation Forwards and Swaps<br \/>10.9. Modeling of Inflation with SDEs<br \/>10.10. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-bcfcd09\" data-id=\"bcfcd09\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-ad22ec8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ad22ec8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-d1802d8\" data-id=\"d1802d8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7617981 elementor-widget elementor-widget-video\" data-id=\"7617981\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=yCRbQD5MXz8&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=22&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-61923b8\" data-id=\"61923b8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a93a057 elementor-widget elementor-widget-video\" data-id=\"a93a057\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=qn1Pux9c4Wc&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=23&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-4292491 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4292491\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-48b7254\" data-id=\"48b7254\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1537d63 elementor-widget elementor-widget-video\" data-id=\"1537d63\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=HToejNJNkFc&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=24&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-47cf56a\" data-id=\"47cf56a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fca2a88 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fca2a88\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-37cf026\" data-id=\"37cf026\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9b2eb0a elementor-widget elementor-widget-text-editor\" data-id=\"9b2eb0a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 11- Market Models and Convexity Adjustments<\/h3><p>11.1. A bit of History<br \/>11.2. Libor Market Model Specifications<br \/>11.3. Libor Rate Dynamics, from P \u2192 QT<br \/>11.4. Lognormal LMM and Measure Changes<br \/>11.5. LMM Under the Terminal and Spot Measures<br \/>11.6. Stochastic Volatility LMM<br \/>11.7. Smile and Skew in the LMM (Displaced Diffusion)<br \/>11.8. Freezing Technique<br \/>11.9. Convexity Correction<br \/>11.10. Convexity and Inclusion of Volatility Smile and Skew<br \/>11.11. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-aaab060\" data-id=\"aaab060\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-4d3182f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4d3182f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-347f43a\" data-id=\"347f43a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3993f08 elementor-widget elementor-widget-video\" data-id=\"3993f08\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=ib86CRvNdPE&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=25&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-df8005a\" data-id=\"df8005a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5e07fd7 elementor-widget elementor-widget-video\" data-id=\"5e07fd7\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=vDFB2K7VsWs&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=26&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1fefa96 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1fefa96\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-d0b8bb2\" data-id=\"d0b8bb2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d7a71a3 elementor-widget elementor-widget-text-editor\" data-id=\"d7a71a3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 12- Valuation Adjustments- xVA (CVA, BCVA and FVA)<\/h3><p>12.1. Introduction and Basics of CVA<br \/>12.2. Exposures and Potential Future Exposure<br \/>12.3. Expected Exposures<br \/>12.4. Expected Exposures and Closed Form Solutions<br \/>12.5. Generation of Exposures with Python (1D Case)<br \/>12.6. Exposure Generation for Portfolio of Assets<br \/>12.7. Unilateral Credit Value Adjustment (CVA)<br \/>12.8. Approximations in Calculation of CVA<br \/>12.9. Bilateral Credit Value Adjustment (BCVA)<br \/>12.10. Funding Value Adjustment (FVA)<br \/>12.11. Trade Attributions in (B)CVA<br \/>12.12. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-4c38169\" data-id=\"4c38169\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-c07f06b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c07f06b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-4153c99\" data-id=\"4153c99\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8048440 elementor-widget elementor-widget-video\" data-id=\"8048440\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=yG4EdykJViY&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=27&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-bba1bcf\" data-id=\"bba1bcf\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e23503b elementor-widget elementor-widget-video\" data-id=\"e23503b\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=WOG4bt1pw68&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=28&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-96a2299 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"96a2299\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-e834d93\" data-id=\"e834d93\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-664e523 elementor-widget elementor-widget-video\" data-id=\"664e523\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=pQsvOfIpnVw&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=29&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-75a459f\" data-id=\"75a459f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-933a995 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"933a995\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-4a2ac52\" data-id=\"4a2ac52\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9f157e8 elementor-widget elementor-widget-text-editor\" data-id=\"9f157e8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 13- Value-at-Risk and Expected Shortfall<\/h3><p>13.1. Value at Risk (VaR), Stressed VaR (SVaR)<br \/>13.2. Coherent Risk Measures<br \/>13.3. Expected Shortfall<br \/>13.4. Historical VaR (HVar) and Python Experiment<br \/>13.5. Missing Data, Arbitrage and Re-Gridding<br \/>13.6. VaR Computation with Monte Carlo<br \/>13.7. Backtesting<br \/>13.8. Summary of the Lecture + Homework<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-fa65ce5\" data-id=\"fa65ce5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-b7eaffa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b7eaffa\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-5cec2e2\" data-id=\"5cec2e2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-12a4a1f elementor-widget elementor-widget-video\" data-id=\"12a4a1f\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=0BDPmUbHnr4&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=30&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-6fd27c4\" data-id=\"6fd27c4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-86e3f9f elementor-widget elementor-widget-video\" data-id=\"86e3f9f\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=jaR3n--J5HE&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=31&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4ef2dae elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4ef2dae\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-49c8f27\" data-id=\"49c8f27\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0dd0201 elementor-widget elementor-widget-text-editor\" data-id=\"0dd0201\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Lecture 14- The Summary of the Course<\/h3><p>14.1. The Summary of the Course<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-d438e92\" data-id=\"d438e92\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9078bae elementor-widget elementor-widget-video\" data-id=\"9078bae\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=kpC1pwN-ldA&amp;list=PL6zzGYGhbWrMpjEKDtnrHWyIj-oVLKCYD&amp;index=32&amp;ab_channel=ComputationsinFinance&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\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<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Course description:The main focus of this course is the modelling of the interest rates while other asset classes like foreign exchange and inflation are also covered. Ultimately, after completing the course, the student should be able to build a multi-asset portfolio consisting of linear products and perform xVA (CVA, BCVA and FVA) and (H)Value-at-Risk computations.\u00a0 Expected prior knowledge:Basic knowledge of stochastic differential equations (SDEs), numerical methods for Monte Carlo simulation, linear algebra and basic knowledge of Python programming. Prior to this course, it is highly recommended to follow the course of Computational Finance (available here). Workload: The course consists of\u2026<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-718","page","type-page","status-publish","hentry"],"blocksy_meta":{"styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":5}},"_links":{"self":[{"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/pages\/718","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/comments?post=718"}],"version-history":[{"count":43,"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/pages\/718\/revisions"}],"predecessor-version":[{"id":1025,"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/pages\/718\/revisions\/1025"}],"wp:attachment":[{"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/media?parent=718"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}