{"id":710,"date":"2023-01-30T19:31:35","date_gmt":"2023-01-30T19:31:35","guid":{"rendered":"https:\/\/compfinance.ddns.net\/wordpress\/?page_id=710"},"modified":"2023-07-16T16:54:54","modified_gmt":"2023-07-16T15:54:54","slug":"computational-finance","status":"publish","type":"page","link":"https:\/\/compfinance.ddns.net\/wordpress\/computational-finance\/","title":{"rendered":"Computational Finance"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"710\" class=\"elementor elementor-710\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-dfb3193 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dfb3193\" 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-c9b3cda\" data-id=\"c9b3cda\" 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-c23422b elementor-widget elementor-widget-text-editor\" data-id=\"c23422b\" 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 style=\"margin-bottom: var(--content-spacing); font-size: 16px; text-align: start;\"><strong>Course Description:<\/strong><br \/><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">The course aims to improve the student\u2019s knowledge of computational methods in\u00a0<\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">finance. Numerical algorithms and partial differential equations, in particular in the field of\u00a0<\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">modelling asset prices and in option pricing, are presented. The student learns to apply methods\u00a0<\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">in a computer project.\u00a0<\/span><\/p><p style=\"font-size: 16px; text-align: start;\"><strong>Expected Prior Knowledge:<\/strong><br \/><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">Basic knowledge of partial differential equations (PDEs), numerical methods for solving\u00a0<\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">PDEs, of linear algebra and of the basic of numerical linear algebra, computing tool: Python.<br \/><br \/><\/span><strong>Course Materials:<\/strong><\/p><ol><li style=\"font-size: 16px; text-align: start;\"><strong>Slides<\/strong> can be <a href=\"https:\/\/github.com\/LechGrzelak\/Computational-Finance-Course\">found here<\/a>.<\/li><li style=\"font-size: 16px; text-align: start;\"><strong>The book<\/strong> used in the course can be <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\">get here<\/a>.<\/li><li style=\"font-size: 16px; text-align: start;\"><strong>Codes and the exercises<\/strong> for the book can be found <a href=\"https:\/\/github.com\/LechGrzelak\/QuantFinanceBook\">here<\/a>.<\/li><li style=\"font-size: 16px; text-align: start;\"><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-top-column elementor-element elementor-element-2a64abe\" data-id=\"2a64abe\" 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-748ef44 elementor-widget elementor-widget-image\" data-id=\"748ef44\" 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=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB\" target=\"_blank\">\n\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"737\" src=\"https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/CompFinanceCourse-1024x737.jpg\" class=\"attachment-large size-large wp-image-921\" alt=\"\" srcset=\"https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/CompFinanceCourse-1024x737.jpg 1024w, https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/CompFinanceCourse-300x216.jpg 300w, https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/CompFinanceCourse-768x553.jpg 768w, https:\/\/compfinance.ddns.net\/wordpress\/wp-content\/uploads\/2023\/07\/CompFinanceCourse.jpg 1191w\" 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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-85ebf1d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"85ebf1d\" 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-f9c3ac9\" data-id=\"f9c3ac9\" 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-7f34937 elementor-widget elementor-widget-text-editor\" data-id=\"7f34937\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 1- Introduction and Overview of Asset Classes<\/strong><\/span><\/h3><p><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.1. Introduction<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.2. *Background Knowledge, Materials for the course (book etc.)<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.3. *Outline of the Course<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.4. *Grading<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.5. Financial Engineering<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.6. Financial Markets and Different Asset Classes<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.7. Stocks and Dividends<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.8. Interest Rates<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.9. Volatility<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.10. Options &amp; Payoffs<\/span><\/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-847b175\" data-id=\"847b175\" 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-5d3254c elementor-widget elementor-widget-video\" data-id=\"5d3254c\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=IRMn6JQvU8A&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&amp;index=1&amp;t=1s&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-66cf2e4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"66cf2e4\" 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-7ceafc4\" data-id=\"7ceafc4\" 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-5f22ac8 elementor-widget elementor-widget-text-editor\" data-id=\"5f22ac8\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 2- Stock, Options and Stochastics<\/strong><\/span><\/h3><p>2.1. Trading of Options and Hedging<br \/>2.2. Commodities<br \/>2.3. Currencies and Cryptos<br \/>2.4. Value of Call and Put Options and Hedging<br \/>2.5. Modeling of Asset Prices and Randomness<br \/>2.6. Stochastic Processes for Stock Prices<br \/>2.7. Ito\u2019s Lemma for Solving SDEs<\/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-c4ba9fc\" data-id=\"c4ba9fc\" 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-bc506e4 elementor-widget elementor-widget-video\" data-id=\"bc506e4\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=_8GUNJZwAQ0&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0ea1bd4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0ea1bd4\" 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-e88d5fe\" data-id=\"e88d5fe\" 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-0ca633d elementor-widget elementor-widget-text-editor\" data-id=\"0ca633d\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 3- Option Pricing and Simulation in Python<\/strong><\/span><\/h3><p>3.1. Stock Paths and Simulation in Python<br \/>3.2. Black-Scholes model<br \/>3.3. Hedging with the Black-Scholes model<br \/>3.4. Martingales and Option Pricing<br \/>3.5. Coding of Martingales in Python<br \/>3.6. Risk Neutral Valuation and Feynman-Kac Formula<br \/>3.7. Measures and Impact on a Drift<br \/>3.8. Closed-Form Solution for Black-Scholes model<\/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-8e22a4d\" data-id=\"8e22a4d\" 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-b441c26 elementor-widget elementor-widget-video\" data-id=\"b441c26\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=MhmZaHWGWHc&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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-top-section elementor-element elementor-element-2d38551 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2d38551\" 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-5463ead\" data-id=\"5463ead\" 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-7ce8c40 elementor-widget elementor-widget-text-editor\" data-id=\"7ce8c40\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 1- Introduction and Overview of Asset Classes<\/strong><\/span><\/h3><p><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.1. Introduction<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.2. *Background Knowledge, Materials for the course (book etc.)<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.3. *Outline of the Course<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.4. *Grading<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.5. Financial Engineering<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.6. Financial Markets and Different Asset Classes<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.7. Stocks and Dividends<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.8. Interest Rates<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.9. Volatility<br \/><\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.10. Options &amp; Payoffs<\/span><\/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-7f58e0a\" data-id=\"7f58e0a\" 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-76c3bce elementor-widget elementor-widget-video\" data-id=\"76c3bce\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=IRMn6JQvU8A&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&amp;index=1&amp;t=1s&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-top-section elementor-element elementor-element-276bb67 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"276bb67\" 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-6406642\" data-id=\"6406642\" 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-e688a94 elementor-widget elementor-widget-text-editor\" data-id=\"e688a94\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 4- Implied Volatility<\/strong><\/span><\/h3><p>4.1. Key Elements for Pricing Derivatives<br \/>4.2. Black-Scholes Implied Volatility<br \/>4.3. Newton-Raphson Method and Implementation in Python<br \/>4.4. Time-Dependent Volatility Parameter, \u03c3(t)<br \/>4.5. Implied Volatility Surface<br \/>4.6. Deficiencies of the Black-Scholes Model<\/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-5600bda\" data-id=\"5600bda\" 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-dc1b1cd elementor-widget elementor-widget-video\" data-id=\"dc1b1cd\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=XKaBN-sgIA0&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b7fee17 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b7fee17\" 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-a0ea8d8\" data-id=\"a0ea8d8\" 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-422044a elementor-widget elementor-widget-text-editor\" data-id=\"422044a\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 5- Jump Processes<\/strong><\/span><\/h3><p><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">5.1. Inclusion of Jumps in the Stock Process<br \/>5.2. Poisson Process and Implementation in Python<br \/>5.3. It\u02c6o\u2019s Lemma and Jumps<br \/>5.4. Jumps and Asset Dynamics under the Q-Measure<br \/>5.5. Partial Integro-Differential Equations<br \/>5.6. Different Jump Distributions and Implied Volatility<br \/>5.7. Expectation and Jump Processes<br \/>5.8. Characteristic Function for a Jump Process<\/span><span style=\"font-size: inherit; text-align: inherit; background-color: var(--palettecolor7); color: var(--color); font-family: var(--fontFamily); font-style: var(--fontStyle, inherit); font-weight: var(--fontWeight); letter-spacing: var(--letterSpacing); text-transform: var(--textTransform);\">1.10. Options &amp; Payoffs<\/span><\/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-855e2cc\" data-id=\"855e2cc\" 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-209847c elementor-widget elementor-widget-video\" data-id=\"209847c\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=gLIb2SOoSXc&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c81c17d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c81c17d\" 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-18b65fa\" data-id=\"18b65fa\" 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-590d8f1 elementor-widget elementor-widget-text-editor\" data-id=\"590d8f1\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 6- Affine Jump Diffusion Processes<\/strong><\/span><\/h3><p>6.1. How to Choose a Pricing Method?<br \/>6.2. Fourier Transformation- Motivation<br \/>6.3. Characteristic Function for the Black-Scholes Model<br \/>6.4. Affine Diffusion Processes<br \/>6.5. Characteristic Function for High Dimensions<br \/>6.6. Affine Jump Diffusion Processes<\/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-a3b40fc\" data-id=\"a3b40fc\" 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-f890440 elementor-widget elementor-widget-video\" data-id=\"f890440\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=OJCBjGUyg2U&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b8f6bdd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b8f6bdd\" 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-7a1cbed\" data-id=\"7a1cbed\" 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-bc7f34f elementor-widget elementor-widget-text-editor\" data-id=\"bc7f34f\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 7- Stochastic Volatility Models<\/strong><\/span><\/h3><p>7.1. Towards Stochastic Volatility<br \/>7.2. The Stochastic Volatility Model of Heston<br \/>7.3. Correlated Stochastic Differential Equations<br \/>7.4. Ito\u2019s Lemma for Vector Processes<br \/>7.5. Pricing PDE for the Heston Model<br \/>7.6. Impact of SV Model Parameters on Implied Volatility<br \/>7.7. Black-Scholes vs. Heston Model<br \/>7.8. Characteristic Function for the Heston Model<\/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-c2dfec0\" data-id=\"c2dfec0\" 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-32dbec9 elementor-widget elementor-widget-video\" data-id=\"32dbec9\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=HG3s2StHB3k&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-241edd3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"241edd3\" 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-6211799\" data-id=\"6211799\" 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-f952997 elementor-widget elementor-widget-text-editor\" data-id=\"f952997\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 8- Fourier Transformation for Option Pricing<\/strong><\/span><\/h3><p>8.1. Fourier Transformation<br \/>8.2. FFT- Fast Fourier Transformation in Python<br \/>8.3. The COS Method and Density Recovery<br \/>8.4. Implementation of the COS Method in Python<br \/>8.5. European Option Pricing with Characteristic Function<br \/>8.6. Pricing Experiments Using COS Method in Python<\/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-5d18e18\" data-id=\"5d18e18\" 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-cab654d elementor-widget elementor-widget-video\" data-id=\"cab654d\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=qVqAeijw6aQ&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-105dd57 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"105dd57\" 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-f326af0\" data-id=\"f326af0\" 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-fe50743 elementor-widget elementor-widget-text-editor\" data-id=\"fe50743\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 9- Monte Carlo Simulation<\/strong><\/span><\/h3><p>9.1. Monte Carlo and Integration via Sampling<br \/>9.2. Examples of Stochastic Integrals in Python<br \/>9.3. Smoothness of a Payoff and Impact on Convergence<br \/>9.4. Types of Convergence<br \/>9.5. Option Pricing and Standard Error<br \/>9.6. Euler Discretization<br \/>9.7. Milstein Discretization<\/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-a6faeb5\" data-id=\"a6faeb5\" 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-c32da33 elementor-widget elementor-widget-video\" data-id=\"c32da33\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=MJw1tg43uJE&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ec83825 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ec83825\" 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-55edab7\" data-id=\"55edab7\" 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-e6257cb elementor-widget elementor-widget-text-editor\" data-id=\"e6257cb\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 10- Monte Carlo Simulation of the Heston Model<\/strong><\/span><\/h3><p>10.1. Option Pricing with Monte Carlo<br \/>10.2. Simulation of the CIR Process<br \/>10.3. Exact Simulation of the CIR Model<br \/>10.4. Almost Exact Simulation of the Heston Model<br \/>10.5. The Heston Model and Simulation in Python<\/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-16ad754\" data-id=\"16ad754\" 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-f143000 elementor-widget elementor-widget-video\" data-id=\"f143000\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=c4XTHxpGP1g&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-755cb53 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"755cb53\" 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-912157e\" data-id=\"912157e\" 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-bd759eb elementor-widget elementor-widget-text-editor\" data-id=\"bd759eb\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 11- Hedging and Monte Carlo Greeks<\/strong><\/span><\/h3><p>11.1. Hedging with the Black-Scholes Model<br \/>11.2. Dynamic Hedging- Python Experiment<br \/>11.3. Hedging with Jumps<br \/>11.4. Delta, Gamma and Vega Hedging<br \/>11.5. Monte Carlo Sensitivity: Finite Difference<br \/>11.6. Monte Carlo Sensitivity: Pathwise Sensitivities<br \/>11.7. Monte Carlo Sensitivity: Likelihood Ratio Method<\/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-1b681c6\" data-id=\"1b681c6\" 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-a050ea0 elementor-widget elementor-widget-video\" data-id=\"a050ea0\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=pKFD6JWOJ5A&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-879bc6e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"879bc6e\" 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-fa22b65\" data-id=\"fa22b65\" 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-2b5102a elementor-widget elementor-widget-text-editor\" data-id=\"2b5102a\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 12- Forward Start Options and Model of Bates<\/strong><\/span><\/h3><p>12.1. Forward-Start Options<br \/>12.2. Characteristic Function for Pricing of Forward Start Options<br \/>12.3. Forward Start Options under the Black-Scholes Model<br \/>12.4. Forward Start Options under the Heston Model<br \/>12.5. Forward Implied Volatility with Python<br \/>12.6. The Bates Model<br \/>12.7. Variance Swaps<\/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-50a4410\" data-id=\"50a4410\" 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-8a8e77e elementor-widget elementor-widget-video\" data-id=\"8a8e77e\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=6MqOajy7rFs&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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-top-section elementor-element elementor-element-47574c5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"47574c5\" 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-9495926\" data-id=\"9495926\" 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-a5a9f8e elementor-widget elementor-widget-text-editor\" data-id=\"a5a9f8e\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 13- Exotic Derivatives<\/strong><\/span><\/h3><p>13.1. Overview of Payoffs in the Industry<br \/>13.2. Binaries and Digitals<br \/>13.3. Path-Dependent Options: Barrier Options<br \/>13.4. Asian Options<br \/>13.5. Multi-Asset Options<\/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-52be34c\" data-id=\"52be34c\" 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-0731d5e elementor-widget elementor-widget-video\" data-id=\"0731d5e\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=CNq9asJ_UkA&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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-top-section elementor-element elementor-element-a0a0984 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a0a0984\" 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-49db2ad\" data-id=\"49db2ad\" 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-699ec30 elementor-widget elementor-widget-text-editor\" data-id=\"699ec30\" 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><span style=\"text-decoration: underline;\"><strong>Lecture 14- Summary of the Course<\/strong><\/span><\/h3><p>14.1. 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-afdd911\" data-id=\"afdd911\" 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-29272bd elementor-widget elementor-widget-video\" data-id=\"29272bd\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=WkTewla837M&amp;list=PL6zzGYGhbWrPaI-op1UfNl0uDglxdkaOB&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\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 course aims to improve the student\u2019s knowledge of computational methods in\u00a0finance. Numerical algorithms and partial differential equations, in particular in the field of\u00a0modelling asset prices and in option pricing, are presented. The student learns to apply methods\u00a0in a computer project.\u00a0 Expected Prior Knowledge:Basic knowledge of partial differential equations (PDEs), numerical methods for solving\u00a0PDEs, of linear algebra and of the basic of numerical linear algebra, computing tool: Python. Course Materials: Slides can be found here. The book used in the course can be get here. Codes and the exercises for the book can be found here. Youtube Channel with\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-710","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\/710","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=710"}],"version-history":[{"count":70,"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/pages\/710\/revisions"}],"predecessor-version":[{"id":981,"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/pages\/710\/revisions\/981"}],"wp:attachment":[{"href":"https:\/\/compfinance.ddns.net\/wordpress\/wp-json\/wp\/v2\/media?parent=710"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}