{"id":298,"date":"2026-07-19T16:20:31","date_gmt":"2026-07-19T16:20:31","guid":{"rendered":"https:\/\/eclass.co.ke\/class\/lesson\/9-4-structural-models-of-corporate-credit-risk\/"},"modified":"2026-07-19T17:41:26","modified_gmt":"2026-07-19T17:41:26","slug":"9-4-structural-models-of-corporate-credit-risk","status":"publish","type":"eclass_lesson","link":"https:\/\/eclass.co.ke\/class\/lesson\/9-4-structural-models-of-corporate-credit-risk\/","title":{"rendered":"9.4 Structural models of corporate credit risk"},"content":{"rendered":"<p>Structural models aim to understand the economics of a company&#x27;s liabilities and build on the insights of option pricing theory.<\/p>\n<ul>\n<li>Structural models are called &quot;structural&quot; because they are based on the structure of a company&#x27;s balance sheet.<\/li>\n<\/ul>\n<h3>9.4.1 Structural Models Estimations<\/h3>\n<p>EXPECTED LOSS Structural models can help estimate expected loss and the present value of expected loss.<\/p>\n<p>Expected loss is equal to the following:<\/p>\n<p>E(loss) KN( ) A ( )N( )<\/p>\n<p>Where:<\/p>\n<p>( ) ( )<\/p>\n<p>( )<\/p>\n<p>sqrt sqrtT t At is the value of assets at time t; K is the face value of debt; N(.) is the cumulative standard normal distribution function with mean 0 and variance 1; T &#8211; t is the debt&#x27;s maturity of debt; u and sigma are the annual expected return and volatility of the company&#x27;s assets, respectively.<\/p>\n<p>The assumptions of the model are:<\/p>\n<ul>\n<li>The company&#x27;s assets trade in frictionless markets that are arbitrage free,<\/li>\n<li>The riskless rate of interest, r, is constant over time, and<\/li>\n<li>The time T value of the company&#x27;s assets has a lognormal distribution with mean uT and variance sigma2T.<\/li>\n<\/ul>\n<p>PRESENT VALUE OF EXPECTED LOSS Present value of expected loss is calculated as follows:<\/p>\n<p>P(t T) (t T) ( )N( ) A N( )<\/p>\n<p>Where l ( ) r(T t)<\/p>\n<p>(T t)<\/p>\n<p>sqrtT t sqrtT t P(t T) ( )<\/p>\n<p>r is the risk-free rate of interest.<\/p>\n<p>Calculating expected loss Example: Assume a company has the following values: At = $1,000; ut=0.03 per year; r =0.01 per year; K = $700; time to maturity of debt, T &#8211; t = 1 year; and sigma = 0.3 per year. Estimate the expected loss and the present value of the expected loss on this debt:<\/p>\n<p>l ( )<\/p>\n<p>( )<\/p>\n<p>sqrt sqrt Using normal distribution table N( ) , N( )<\/p>\n<p>E( oss)<\/p>\n<p>The present value of expected loss is calculated by:<\/p>\n<p>l ( )<\/p>\n<p>( )<\/p>\n<p>sqrt sqrt Using a normal distribution table N( ) , N( )<\/p>\n<p>P(t T) (t T)<\/p>\n<ul>\n<li>The $1.50 difference between expected loss and present value of expected loss includes both a discount for the time value of money and the risk premium required by the market to bear the risk of credit loss.<\/li>\n<li>In this case, the present value of the expected loss exceeds the expected loss. This means that the risk premium must dominate the difference because the time-value-of- money discount will reduce the present value of the expected loss compared with the expected loss. In other words, in the absence of a risk premium, the present value of the expected loss will be less than the expected loss.<\/li>\n<\/ul>\n<h3>9.4.2 Reasons for equity being viewed as a call option on the company&#x27;s assets<\/h3>\n<ul>\n<li>In a structural model, the company&#x27;s equity can be viewed as a European call option on the assets of the company, with a strike price equal to the debt&#x27;s face value<\/li>\n<li>The link between option pricing theory and structural models comes from the call option analogy for equity<\/li>\n<li>The company&#x27;s owners (equity holders) have limited liability.<\/li>\n<li>If the equity holders default on the debt payment at time T, the debtholders&#x27; only recourse is to the company&#x27;s assets. They have no additional claim on the equity holders&#x27; personal wealth<\/li>\n<\/ul>\n<h3>Lesson Wrap-Up<\/h3>\n<p>This lesson should leave you able to explain the structural models of corporate credit risk in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.<\/p>\n<h3>Review Prompts<\/h3>\n<ol>\n<li>Explain structural models estimations in your own words.<\/li>\n<li>Explain reasons for equity being viewed as a call option on the company&#x27;s assets in your own words.<\/li>\n<li>State one exam-style risk, valuation, or market implication of the structural models of corporate credit risk.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Structural models aim to understand the economics of a company&#x27;s liabilities and build on the insights of option pricing theory. Structural models are called &quot;structural&quot; because they are based on the structure of a company&#x27;s balance sheet. 9.4.1 Structural Models Estimations EXPECTED LOSS Structural models can help estimate expected loss and the present value of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-298","eclass_lesson","type-eclass_lesson","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson\/298","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson"}],"about":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/types\/eclass_lesson"}],"author":[{"embeddable":true,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/comments?post=298"}],"version-history":[{"count":2,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson\/298\/revisions"}],"predecessor-version":[{"id":434,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson\/298\/revisions\/434"}],"wp:attachment":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/media?parent=298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}