{"id":12433,"date":"2026-05-15T10:47:32","date_gmt":"2026-05-15T06:47:32","guid":{"rendered":"https:\/\/eoninvestment.com\/?p=12433"},"modified":"2026-05-15T11:22:10","modified_gmt":"2026-05-15T07:22:10","slug":"what-equity-prices-tell-us-about-default-risk","status":"publish","type":"post","link":"https:\/\/eoninvestment.com\/ka\/2026\/05\/15\/what-equity-prices-tell-us-about-default-risk\/","title":{"rendered":"<span class=\"eon-recovered-georgian-title\" data-no-translation=\"\">\u10e0\u10d0\u10e1 \u10d2\u10d5\u10d4\u10e3\u10d1\u10dc\u10d4\u10d1\u10d8\u10d0\u10dc \u10d0\u10e5\u10ea\u10d8\u10d8\u10e1 \u10e4\u10d0\u10e1\u10d4\u10d1\u10d8 \u10d3\u10d4\u10e4\u10dd\u10da\u10e2\u10d8\u10e1 \u10e0\u10d8\u10e1\u10d9\u10d8\u10e1 \u10e8\u10d4\u10e1\u10d0\u10ee\u10d4\u10d1?<\/span>"},"content":{"rendered":"<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83c\udfaf One weakness of credit ratings is that they are updated relatively infrequently, while credit risk itself can change significantly over short periods of time. As it turns out, equity prices can help predict default risk.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The core idea is that the value of a company\u2019s equity can be viewed as a call option on the company\u2019s assets. As a result, the probability of default can be interpreted as a function of:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>the value of the firm\u2019s assets,<\/li>\n\n\n\n<li>the volatility of those assets,<\/li>\n\n\n\n<li>and the firm\u2019s financial leverage.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This idea belongs to Robert C. Merton, who extended the Black\u2013Scholes framework into a practical model for estimating default probabilities.<br \/>(See in detail: <a href=\"https:\/\/eoninvestment.com\/ka\/2025\/03\/21\/distress-prediction\/?utm_source=chatgpt.com\">Distress Prediction and the Merton Model<\/a>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">One challenge with applying the Merton model is that we need to know:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>the market value of the firm\u2019s assets,<\/li>\n\n\n\n<li>and the volatility of those assets.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">However, these variables are not directly observable in the market.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Fortunately, Ito&#8217;s lemma allows us to infer these hidden parameters using observable market data.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ito\u2019s Lemma leads to the following relationship between asset volatility and equity volatility:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><msub><mi>E<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>d<\/mi><mn>1<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msub><mi>\u03c3<\/mi><mi>V<\/mi><\/msub><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_E E_0 = N(d_1)\\sigma_V V_0<\/annotation><\/semantics><\/math><\/div>\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 xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_E<\/annotation><\/semantics><\/math><\/td><td>Equity volatility<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>E<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">E_0<\/annotation><\/semantics><\/math><\/td><td>Current market value of equity<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><msub><mi>E<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_E E_0<\/annotation><\/semantics><\/math><\/td><td>Dollar volatility of equity<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><msub><mi>d<\/mi><mn>1<\/mn><\/msub><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">N(d_1)<\/annotation><\/semantics><\/math><\/td><td>Sensitivity of equity to asset value<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>V<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_V<\/annotation><\/semantics><\/math><\/td><td>Asset volatility<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">V_0<\/annotation><\/semantics><\/math><\/td><td>Current market value of firm assets<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>V<\/mi><\/msub><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma_V V_0<\/annotation><\/semantics><\/math><\/td><td>Dollar volatility of firm assets<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Integrating this relationship into the option pricing framework gives:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mi>E<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><msub><mi>V<\/mi><mn>0<\/mn><\/msub><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>d<\/mi><mn>1<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mi>D<\/mi><msup><mi>e<\/mi><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mi>r<\/mi><mi>T<\/mi><\/mrow><\/msup><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>d<\/mi><mn>2<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">E_0 = V_0N(d_1)-De^{-rT}N(d_2)<\/annotation><\/semantics><\/math><\/div>\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 xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>E<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">E_0<\/annotation><\/semantics><\/math><\/td><td>Current market value of equity<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">V_0<\/annotation><\/semantics><\/math><\/td><td>Current market value of firm assets<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>D<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">D<\/annotation><\/semantics><\/math><\/td><td>Debt repayment due at maturity<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>r<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">r<\/annotation><\/semantics><\/math><\/td><td>Risk-free interest rate<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math><\/td><td>Time to debt maturity<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>e<\/mi><mrow><mo>\u2212<\/mo><mi>r<\/mi><mi>T<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">e^{-rT}<\/annotation><\/semantics><\/math><\/td><td>Discount factor<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><msub><mi>d<\/mi><mn>1<\/mn><\/msub><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">N(d_1)<\/annotation><\/semantics><\/math><\/td><td>Risk-adjusted asset participation in equity value<\/td><\/tr><tr><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><msub><mi>d<\/mi><mn>2<\/mn><\/msub><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">N(d_2)<\/annotation><\/semantics><\/math>N(d2\u200b)<\/td><td>Risk-neutral survival-related component<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, the probability of default is calculated as:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mi>D<\/mi><mo>=<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><msub><mi>d<\/mi><mn>2<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">PD = N(-d_2)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mi>d<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><mfrac><mrow><\/mrow><mrow><mi>ln<\/mi><mo>\u2061<\/mo><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>V<\/mi><mn>0<\/mn><\/msub><mi>\/<\/mi><mi>D<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>r<\/mi><mo>\u2212<\/mo><msubsup><mi>\u03c3<\/mi><mi>V<\/mi><mn>2<\/mn><\/msubsup><mi>\/<\/mi><mn>2<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>T<\/mi><\/mfrac><\/mrow><mrow><msub><mi>\u03c3<\/mi><mi>V<\/mi><\/msub><msqrt><mi>T<\/mi><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">d_2 = \\frac{\\ln(V_0\/D)+(r-\\sigma_V^2\/2)T}{\\sigma_V\\sqrt{T}}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Important Note<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">An important nuance is that this framework produces a <strong>risk-neutral probability of default<\/strong>, not a real-world default probability.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In reality, the true probability of default would usually be lower because the model uses:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>option-pricing formulas,<\/li>\n\n\n\n<li>and the risk-free rate as the discount rate.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Nevertheless, the model remains highly useful in practice because it provides strong relative ranking signals across firms and allows markets to continuously reprice credit risk.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/eoninvestment.com\/wp-content\/uploads\/2026\/05\/hull_merton_default_probability_example.xlsx\">\ud83d\udcca Excel \u2013 Default Probability Calculator<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udcda Source:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Options, Futures, and Other Derivatives<\/p>","protected":false},"excerpt":{"rendered":"<p>\ud83c\udfaf \u10e1\u10d0\u10d9\u10e0\u10d4\u10d3\u10d8\u10e2\u10dd \u10e0\u10d4\u10d8\u10e2\u10d8\u10dc\u10d2\u10d4\u10d1\u10d8\u10e1 \u10dc\u10d0\u10d9\u10da\u10dd\u10d5\u10d0\u10dc\u10d8 \u10db\u10ee\u10d0\u10e0\u10d4 \u10d8\u10db\u10d0\u10e8\u10d8\u10d0 \u10e0\u10dd\u10db \u10db\u10d0\u10d7\u10d8 \u10d2\u10d0\u10dc\u10d0\u10ee\u10da\u10d4\u10d1\u10d0 \u10ee\u10d3\u10d4\u10d1\u10d0 \u10d3\u10d0\u10d1\u10d0\u10da\u10d8 \u10e1\u10d8\u10ee\u10e8\u10d8\u10e0\u10d8\u10d7, \u10db\u10d0\u10e8\u10d8\u10dc \u10e0\u10dd\u10ea\u10d0 \u10e1\u10d0\u10d9\u10e0\u10d4\u10d3\u10d8\u10e2\u10dd \u10e0\u10d8\u10e1\u10d9\u10d4\u10d1\u10d8 \u10e8\u10d4\u10d8\u10eb\u10da\u10d4\u10d1\u10d0 \u10db\u10dd\u10d9\u10da\u10d4\u10d5\u10d0\u10d3\u10d8\u10d0\u10dc \u10de\u10d4\u10e0\u10d8\u10dd\u10d3\u10e8\u10d8 \u10db\u10dc\u10d8\u10e8\u10d5\u10dc\u10d4\u10da\u10dd\u10d5\u10dc\u10d0\u10d3 \u10e8\u10d4\u10d8\u10ea\u10d5\u10d0\u10da\u10dd\u10e1. \u10e0\u10dd\u10d2\u10dd\u10e0\u10ea \u10d0\u10e6\u10db\u10dd\u10e9\u10dc\u10d3\u10d0 \u10d0\u10e5\u10ea\u10d8\u10d8\u10e1 \u10e4\u10d0\u10e1\u10d4\u10d1\u10e1 \u10e8\u10d4\u10e3\u10eb\u10da\u10d8\u10d0\u10d7 \u10d3\u10d4\u10e4\u10dd\u10da\u10e2\u10d8\u10e1 \u10ec\u10d8\u10dc\u10d0\u10e1\u10ec\u10d0\u10e0\u10db\u10d4\u10e2\u10e7\u10d5\u10d4\u10da\u10d4\u10d1\u10d0. \u10d0\u10e5 \u10d8\u10d3\u10d4\u10d0 \u10d8\u10db\u10d0\u10e8\u10d8 \u10db\u10d3\u10d2\u10dd\u10db\u10d0\u10e0\u10d4\u10dd\u10d1\u10e1, [\u2026]<\/p>","protected":false},"author":12998525,"featured_media":0,"comment_status":"closed","ping_status":"closed","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_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[784237235,37372],"tags":[],"eon_topic":[],"eon_learning_path":[],"eon_collection":[],"eon_level":[],"eon_content_type":[],"eon_source":[],"eon_idea":[784445690],"eon_framework":[],"class_list":["post-12433","post","type-post","status-publish","format-standard","hentry","category-options-futures-other-derivatives-john-c-hull-ka","category-risk","eon_idea-risk"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>What Equity Prices Tell Us About Default Risk - Eon Investment<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/eoninvestment.com\/ka\/2026\/05\/15\/what-equity-prices-tell-us-about-default-risk\/\" \/>\n<meta property=\"og:locale\" content=\"ka_GE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What Equity Prices Tell Us About Default Risk - Eon Investment\" \/>\n<meta property=\"og:description\" content=\"\ud83c\udfaf \u10e1\u10d0\u10d9\u10e0\u10d4\u10d3\u10d8\u10e2\u10dd \u10e0\u10d4\u10d8\u10e2\u10d8\u10dc\u10d2\u10d4\u10d1\u10d8\u10e1 \u10dc\u10d0\u10d9\u10da\u10dd\u10d5\u10d0\u10dc\u10d8 \u10db\u10ee\u10d0\u10e0\u10d4 \u10d8\u10db\u10d0\u10e8\u10d8\u10d0 \u10e0\u10dd\u10db \u10db\u10d0\u10d7\u10d8 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