{"id":8536,"date":"2026-02-22T12:32:36","date_gmt":"2026-02-22T08:32:36","guid":{"rendered":"https:\/\/eoninvestment.com\/?p=8536"},"modified":"2026-04-10T22:48:47","modified_gmt":"2026-04-10T18:48:47","slug":"var-linear-model","status":"publish","type":"post","link":"https:\/\/eoninvestment.com\/ka\/2026\/02\/22\/var-linear-model\/","title":{"rendered":"<span class=\"eon-recovered-georgian-title\" data-no-translation=\"\">VaR - \u10ec\u10e0\u10e4\u10d8\u10d5\u10d8 \u10db\u10dd\u10d3\u10d4\u10da\u10d8<\/span>"},"content":{"rendered":"<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">In the previous note about VaR, I discussed and showed how it is calculated using simulation of historical data. Now I will demonstrate how it is calculated using linear modeling.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">First, we again construct the statistics of historical data;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><a href=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-14.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"890\" height=\"504\" data-attachment-id=\"8541\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2026\/02\/22\/var-linear-model\/image-717\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-14.png?fit=890%2C504&amp;ssl=1\" data-orig-size=\"890,504\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-14.png?fit=890%2C504&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-14.png?resize=890%2C504&#038;ssl=1\" alt=\"\" class=\"wp-image-8541\" style=\"aspect-ratio:1.7659232007358012;width:504px;height:auto\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Then we calculate returns obtained from price changes \u2014 <strong>LN (t1\/t0)<\/strong>;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><a href=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-15.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"654\" height=\"283\" data-attachment-id=\"8543\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2026\/02\/22\/var-linear-model\/image-718\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-15.png?fit=654%2C283&amp;ssl=1\" data-orig-size=\"654,283\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-15.png?fit=654%2C283&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-15.png?resize=654%2C283&#038;ssl=1\" alt=\"\" class=\"wp-image-8543\" style=\"width:504px;height:auto\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">After that, we build the <strong>Variance\u2013Covariance matrix<\/strong>;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-16.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1566\" height=\"468\" data-attachment-id=\"8545\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2026\/02\/22\/var-linear-model\/image-719\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-16.png?fit=1566%2C468&amp;ssl=1\" data-orig-size=\"1566,468\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-16.png?fit=1024%2C306&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-16.png?resize=1566%2C468&#038;ssl=1\" alt=\"\" class=\"wp-image-8545\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, we compute <strong>VaR<\/strong> and the <strong>Expected Shortfall<\/strong> according to the chosen confidence interval<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><a href=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-17.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"426\" height=\"244\" data-attachment-id=\"8547\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2026\/02\/22\/var-linear-model\/image-720\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-17.png?fit=426%2C244&amp;ssl=1\" data-orig-size=\"426,244\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-17.png?fit=426%2C244&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-17.png?resize=426%2C244&#038;ssl=1\" alt=\"\" class=\"wp-image-8547\" style=\"width:318px;height:auto\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">As the number of days increases, the risk also increases:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><a href=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-18.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"752\" height=\"452\" data-attachment-id=\"8549\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2026\/02\/22\/var-linear-model\/image-721\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-18.png?fit=752%2C452&amp;ssl=1\" data-orig-size=\"752,452\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-18.png?fit=752%2C452&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/image-18.png?resize=752%2C452&#038;ssl=1\" alt=\"\" class=\"wp-image-8549\" style=\"width:566px;height:auto\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a href=\"https:\/\/eoninvestment.com\/wp-content\/uploads\/2026\/02\/21.2-var-linear-model.xlsx\">VaR \u2013 Linear Model (Excel)<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Adapted from the source:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Options, Futures &#038; Other Derivatives, John C. Hull<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>","protected":false},"excerpt":{"rendered":"<p>VaR-\u10d8\u10e1 \u10e8\u10d4\u10e1\u10d0\u10ee\u10d4\u10d1 \u10ec\u10d8\u10dc\u10d0 \u10e9\u10d0\u10dc\u10d0\u10ec\u10d4\u10e0\u10e8\u10d8 \u10d5\u10d8\u10e1\u10d0\u10e3\u10d1\u10e0\u10d4, \u10d3\u10d0 \u10d5\u10d0\u10e9\u10d5\u10d4\u10dc\u10d4 \u10e0\u10dd\u10d2\u10dd\u10e0 \u10ee\u10d3\u10d4\u10d1\u10d0 \u10db\u10d8\u10e1\u10d8 \u10d3\u10d0\u10d0\u10dc\u10d2\u10d0\u10e0\u10d8\u10e8\u10d4\u10d1\u10d0 \u10d8\u10e1\u10e2\u10dd\u10e0\u10d8\u10e3\u10da\u10d8 \u10ea\u10d8\u10e4\u10e0\u10d4\u10d1\u10d8\u10e1 \u10e1\u10d8\u10db\u10e3\u10da\u10d0\u10ea\u10d8\u10d8\u10d7, \u10d0\u10ee\u10da\u10d0 \u10d5\u10d0\u10e9\u10d5\u10d4\u10dc\u10d4\u10d1 \u10e0\u10dd\u10d2\u10dd\u10e0 \u10ee\u10d3\u10d4\u10d1\u10d0 \u10d3\u10d0\u10d0\u10dc\u10d2\u10d0\u10e0\u10d8\u10e8\u10d4\u10d1\u10d0 \u10ec\u10e0\u10e4\u10d8\u10d5\u10d8 \u10db\u10dd\u10d3\u10d4\u10da\u10d8\u10e0\u10d4\u10d1\u10d8\u10d7. \u10de\u10d8\u10e0\u10d5\u10d4\u10da \u10e0\u10d8\u10d2\u10e8\u10d8 \u10d8\u10e1\u10d4\u10d5 \u10d3\u10d2\u10d4\u10d1\u10d0 \u10d8\u10e1\u10e2\u10dd\u10e0\u10d8\u10e3\u10da\u10d8 \u10ea\u10d8\u10e4\u10e0\u10d4\u10d1\u10d8\u10e1 \u10e1\u10e2\u10d0\u10e2\u10d8\u10e1\u10e2\u10d8\u10d9\u10d0: \u10e8\u10d4\u10db\u10d3\u10d4\u10d2 \u10d5\u10d0\u10dc\u10d2\u10d0\u10e0\u10d8\u10e8\u10dd\u10d1\u10d7 \u10e4\u10d0\u10e1\u10d4\u10d1\u10d8\u10e1 \u10ea\u10d5\u10da\u10d8\u10da\u10d4\u10d1\u10d8\u10d7 [\u2026]<\/p>","protected":false},"author":12998525,"featured_media":8549,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_eon_insights_quality":"","_eon_insights_decision":"","_eon_insights_destination":"","_eon_insights_merge_group":"","_eon_insights_required_changes":"","_eon_insights_start_order":0,"_eon_featured_insight":0,"_eon_insights_map_version":"","_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[31110612,784237235,106538530],"tags":[],"eon_topic":[],"eon_learning_path":[],"eon_collection":[],"eon_level":[],"eon_content_type":[],"eon_source":[],"eon_idea":[784445705],"eon_framework":[],"class_list":["post-8536","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-excel-models","category-options-futures-other-derivatives-john-c-hull-ka","category-derivatives","eon_idea-derivatives"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.8 - 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