{"id":8734,"date":"2026-03-15T10:59:27","date_gmt":"2026-03-15T06:59:27","guid":{"rendered":"https:\/\/eoninvestment.com\/?p=8734"},"modified":"2026-04-10T16:43:11","modified_gmt":"2026-04-10T12:43:11","slug":"garch-model","status":"publish","type":"post","link":"https:\/\/eoninvestment.com\/ka\/2026\/03\/15\/garch-model\/","title":{"rendered":"<span class=\"eon-recovered-georgian-title\" data-no-translation=\"\">GARCH \u10db\u10dd\u10d3\u10d4\u10da\u10d8<\/span>"},"content":{"rendered":"<h1 class=\"wp-block-heading\">GARCH (1,1) and Volatility Clustering<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Financial markets exhibit an important property: <strong>volatility clustering<\/strong> \u10d3\u10d0 <strong>reversion toward a long-run average<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In other words, large movements tend to be followed by large movements, and calm periods tend to be followed by calm periods. However, over time volatility tends to move back toward a long-term average level.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To capture this behavior, the <strong>GARCH(1,1)<\/strong> model is commonly used.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In a previous post we discussed <strong>Moving Average (MA)<\/strong> \u10d3\u10d0 <strong>Exponentially Weighted Moving Average (EWMA)<\/strong> methods. Both attempt to estimate the current volatility of an asset\u2019s returns using historical data.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>MA cannot capture volatility clustering<\/strong>,<\/li>\n\n\n\n<li><strong>EWMA cannot capture mean reversion<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">What GARCH Means<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>GARCH<\/strong> stands for:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Generalized Autoregressive Conditional Heteroskedasticity<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The name sounds complicated, but the idea is quite simple.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Word<\/th><th>Meaning<\/th><\/tr><\/thead><tbody><tr><td>Generalized<\/td><td>an extension of an earlier model (ARCH)<\/td><\/tr><tr><td>Autoregressive<\/td><td>volatility depends on its own past values<\/td><\/tr><tr><td>Conditional<\/td><td>depends on past information<\/td><\/tr><tr><td>Heteroskedasticity<\/td><td>variance is not constant<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u10db\u10d0\u10e0\u10e2\u10d8\u10d5\u10d0\u10d3:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>today\u2019s volatility depends on the long-run volatility, yesterday\u2019s volatility, and yesterday\u2019s shock.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">The Core Formula<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The model updates the variance (the square of volatility) using the equation<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><msubsup><mi>\u03c3<\/mi><mi>t<\/mi><mn>2<\/mn><\/msubsup><mo>=<\/mo><mi>\u03c9<\/mi><mo>+<\/mo><mi>\u03b1<\/mi><msubsup><mi>u<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><mo>+<\/mo><mi>\u03b2<\/mi><msubsup><mi>\u03c3<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_t^2 = \\omega + \\alpha u_{t-1}^2 + \\beta \\sigma_{t-1}^2<\/annotation><\/semantics><\/math>where:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Symbol<\/th><th>Meaning<\/th><\/tr><\/thead><tbody><tr><td><math><semantics><mrow><msub><mi>u<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">u_{t-1}<\/annotation><\/semantics><\/math>ut\u22121\u200b<\/td><td>yesterday\u2019s return<\/td><\/tr><tr><td><math><semantics><mrow><msubsup><mi>u<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">u_{t-1}^2<\/annotation><\/semantics><\/math>ut\u221212\u200b<\/td><td>the size of yesterday\u2019s shock<\/td><\/tr><tr><td><math><semantics><mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_{t-1}^2<\/annotation><\/semantics><\/math>\u03c3t\u221212\u200b<\/td><td>yesterday\u2019s variance<\/td><\/tr><tr><td><math><semantics><mrow><mi>\u03c9<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\omega<\/annotation><\/semantics><\/math>\u03c9<\/td><td>base variance level<\/td><\/tr><tr><td><math><semantics><mrow><mi>\u03b1<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha<\/annotation><\/semantics><\/math>\u03b1<\/td><td>reaction to new shocks<\/td><\/tr><tr><td><math><semantics><mrow><mi>\u03b2<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\beta<\/annotation><\/semantics><\/math>\u03b2<\/td><td>volatility persistence<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Here<math display=\"block\"><semantics><mrow><mi>\u03c9<\/mi><mo>=<\/mo><msub><mi>V<\/mi><mi>L<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03b1<\/mi><mo>\u2212<\/mo><mi>\u03b2<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\omega = V_L (1-\\alpha-\\beta)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where<math display=\"block\"><semantics><mrow><msub><mi>V<\/mi><mi>L<\/mi><\/msub><mo>\u2248<\/mo><mtext>the&nbsp;long-run&nbsp;average&nbsp;variance&nbsp;of&nbsp;returns<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">V_L \\approx \\text{the long-run average variance of returns}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Unlike EWMA, <strong>GARCH includes a long-run average variance<\/strong>, which can be written as<math display=\"block\"><semantics><mrow><msub><mi>V<\/mi><mi>L<\/mi><\/msub><mo>=<\/mo><mfrac><mi>\u03c9<\/mi><mrow><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03b1<\/mi><mo>\u2212<\/mo><mi>\u03b2<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">V_L = \\frac{\\omega}{1-\\alpha-\\beta}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The corresponding long-run volatility is<math display=\"block\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>L<\/mi><\/msub><mo>=<\/mo><msqrt><msub><mi>V<\/mi><mi>L<\/mi><\/msub><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_L = \\sqrt{V_L}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This represents the volatility level <strong>toward which the model tends to move over time<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However, it is important to understand that volatility will not stay close to this level every day. The long-run variance simply acts like <strong>gravity<\/strong>, slowly pulling volatility toward equilibrium over time.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Why Volatility Clustering Appears<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Looking again at the GARCH equation<math display=\"block\"><semantics><mrow><msubsup><mi>\u03c3<\/mi><mi>t<\/mi><mn>2<\/mn><\/msubsup><mo>=<\/mo><mi>\u03c9<\/mi><mo>+<\/mo><mi>\u03b1<\/mi><msubsup><mi>u<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><mo>+<\/mo><mi>\u03b2<\/mi><msubsup><mi>\u03c3<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_t^2 = \\omega + \\alpha u_{t-1}^2 + \\beta \\sigma_{t-1}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If volatility is high today, the next period will still contain the term<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>\u03b2<\/mi><msubsup><mi>\u03c3<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">\\beta \\sigma_{t-1}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Because <strong>\u03b2 is usually large (0.85\u20130.95)<\/strong>, volatility declines only gradually. This persistence creates <strong>volatility clustering<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mathematically, the weight applied to past shocks becomes<math display=\"block\"><semantics><mrow><mi>\u03b1<\/mi><msup><mi>\u03b2<\/mi><mi>i<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha \\beta^{i}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">which means the influence of shocks <strong>decays exponentially through time<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Parameter Interpretation<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">For daily financial data we often observe parameter values in the following ranges:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Parameter<\/th><th>Typical Range<\/th><\/tr><\/thead><tbody><tr><td>\u03b1<\/td><td>0.05 \u2013 0.12<\/td><\/tr><tr><td>\u03b2<\/td><td>0.85 \u2013 0.94<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">For the model to be stable we require<math display=\"block\"><semantics><mrow><mi>\u03b1<\/mi><mo>+<\/mo><mi>\u03b2<\/mi><mo><<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha + \\beta < 1<\/annotation><\/semantics><\/math>\u03b1+\u03b2<1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If this sum is very close to one, the impact of shocks disappears very slowly. In real financial markets the value is often <strong>between 0.95 and 0.99<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Note also that if<math display=\"block\"><semantics><mrow><mi>\u03c9<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\omega = 0<\/annotation><\/semantics><\/math>\u03c9=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">then <strong>GARCH reduces to EWMA<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Why It Is Called GARCH (1,1)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The general notation is <strong>GARCH(p,q)<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>p<\/strong> = number of past shocks included<\/li>\n\n\n\n<li><strong>q<\/strong> = number of past variance estimates included<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Thus <strong>GARCH(1,1)<\/strong> means the model uses:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>the most recent <strong>squared return<\/strong><\/li>\n\n\n\n<li>the most recent <strong>variance estimate<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Despite its simplicity, <strong>GARCH(1,1) is the most widely used volatility model in finance.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Example<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The chart below is constructed using historical data for <strong>Tesla (TSLA)<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1310\" height=\"541\" data-attachment-id=\"8750\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2026\/03\/15\/garch-model\/image-740\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/03\/image-14.png?fit=1310%2C541&amp;ssl=1\" data-orig-size=\"1310,541\" 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\/03\/image-14.png?fit=1024%2C423&amp;ssl=1\" class=\"wp-image-8750\" style=\"width: 700px\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2026\/03\/image-14.png?resize=1310%2C541&#038;ssl=1\" alt=\"\"\/><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a href=\"https:\/\/eoninvestment.com\/wp-content\/uploads\/2026\/03\/22.2-garch-11.xlsx\">Excel model: GARCH(1,1)<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There is one interesting detail that explains why <strong>GARCH sometimes moves further away from equilibrium than EWMA<\/strong>, even though intuitively we might expect the opposite.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Intuitively we think:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">EWMA \u2192 inertia<br \/>GARCH \u2192 inertia + gravity<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore we might expect <strong>GARCH to stay closer to equilibrium<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However, the graph shows something different.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The reason is that <strong>EWMA reacts more slowly to shocks<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s compare the formulas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">EWMA:<math display=\"block\"><semantics><mrow><msubsup><mi>\u03c3<\/mi><mi>t<\/mi><mn>2<\/mn><\/msubsup><mo>=<\/mo><mi>\u03bb<\/mi><msubsup><mi>\u03c3<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><mo stretchy=\"false\">)<\/mo><msubsup><mi>u<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_t^2 = \\lambda\\sigma_{t-1}^2 + (1-\\lambda)u_{t-1}^2<\/annotation><\/semantics><\/math>\u03c3t2\u200b=\u03bb\u03c3t\u221212\u200b+(1\u2212\u03bb)ut\u221212\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">GARCH:<math display=\"block\"><semantics><mrow><msubsup><mi>\u03c3<\/mi><mi>t<\/mi><mn>2<\/mn><\/msubsup><mo>=<\/mo><mi>\u03c9<\/mi><mo>+<\/mo><mi>\u03b1<\/mi><msubsup><mi>u<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><mo>+<\/mo><mi>\u03b2<\/mi><msubsup><mi>\u03c3<\/mi><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_t^2 = \\omega + \\alpha u_{t-1}^2 + \\beta\\sigma_{t-1}^2<\/annotation><\/semantics><\/math>\u03c3t2\u200b=\u03c9+\u03b1ut\u221212\u200b+\u03b2\u03c3t\u221212\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now look at the weights.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">RiskMetrics EWMA uses<math display=\"block\"><semantics><mrow><mi>\u03bb<\/mi><mo>=<\/mo><mn>0.94<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\lambda = 0.94<\/annotation><\/semantics><\/math>\u03bb=0.94<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">which means the weight on the shock is<math display=\"block\"><semantics><mrow><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mn>0.06<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1-\\lambda = 0.06<\/annotation><\/semantics><\/math>1\u2212\u03bb=0.06<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Typical GARCH parameters (Hull example) are<math display=\"block\"><semantics><mrow><mi>\u03b1<\/mi><mo>=<\/mo><mn>0.13<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>\u03b2<\/mi><mo>=<\/mo><mn>0.86<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha = 0.13,\\quad \\beta = 0.86<\/annotation><\/semantics><\/math>\u03b1=0.13,\u03b2=0.86<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus the shock weight in <strong>EWMA is about 6%<\/strong>, while in <strong>GARCH it is about 13%<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In other words, <strong>GARCH reacts roughly twice as strongly to shocks<\/strong>, which is why its path can move further away from equilibrium.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At the same time, <strong>\u03c9 is usually very small<\/strong>, meaning the gravitational pull toward the long-run average is quite weak in the short run.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\u10d0\u10d3\u10d0\u10de\u10e2\u10d8\u10e0\u10d4\u10d1\u10e3\u10da\u10d8\u10d0 \u10ec\u10e7\u10d0\u10e0\u10dd\u10d3\u10d0\u10dc:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>John C. Hull \u2014 Options, Futures and Other Derivatives<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>","protected":false},"excerpt":{"rendered":"<p>\u10e4\u10d8\u10dc\u10d0\u10dc\u10e1\u10e3\u10e0 \u10d1\u10d0\u10d6\u10e0\u10d4\u10d1\u10e1 \u10d4\u10e0\u10d7\u10d8 \u10db\u10dc\u10d8\u10e8\u10d5\u10dc\u10d4\u10da\u10dd\u10d5\u10d0\u10dc\u10d8 \u10d7\u10d5\u10d8\u10e1\u10d4\u10d1\u10d0 \u10d0\u10ee\u10d0\u10e1\u10d8\u10d0\u10d7\u10d4\u10d1\u10d7: \u10db\u10d4\u10e0\u10e7\u10d4\u10dd\u10d1\u10d8\u10e1 \u10d9\u10da\u10d0\u10e1\u10e2\u10d4\u10e0\u10d8\u10d6\u10d0\u10ea\u10d8\u10d0 (Volatility Clustering), \u10d3\u10d0 \u10d2\u10e0\u10eb\u10d4\u10d5\u10d0\u10da\u10d3\u10d8\u10d0\u10dc\u10d8 \u10e1\u10d0\u10e8\u10e3\u10d0\u10da\u10dd\u10e1\u10d9\u10d4\u10dc \u10e0\u10d4\u10d5\u10d4\u10e0\u10e1\u10d8\u10d0. \u10d0\u10dc\u10e3, \u10d3\u10d8\u10d3 \u10e0\u10e7\u10d4\u10d5\u10d4\u10d1\u10e1 \u10db\u10dd\u10f0\u10e7\u10d5\u10d4\u10d1\u10d0 \u10d3\u10d8\u10d3\u10d8 \u10e0\u10e7\u10d4\u10d5\u10d4\u10d1\u10d8, \u10db\u10e8\u10d5\u10d8\u10d3 \u10de\u10d4\u10e0\u10d8\u10dd\u10d3\u10d4\u10d1\u10e1 \u2013 \u10db\u10e8\u10d5\u10d8\u10d3\u10d8 \u10de\u10d4\u10e0\u10d8\u10dd\u10d3\u10d4\u10d1\u10d8, \u10db\u10d0\u10d2\u10e0\u10d0\u10db \u10e1\u10d0\u10d4\u10e0\u10d7\u10dd \u10d3\u10dd\u10dc\u10d4 \u10e1\u10d0\u10e8\u10e3\u10d0\u10da\u10dd\u10e1\u10d9\u10d4\u10dc \u10db\u10d8\u10d8\u10e1\u10ec\u10e0\u10d0\u10e4\u10d8\u10e1. \u10d0\u10db \u10db\u10dd\u10db\u10d4\u10dc\u10e2\u10d8\u10e1 [\u2026]<\/p>","protected":false},"author":12998525,"featured_media":0,"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-8734","post","type-post","status-publish","format-standard","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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