{"id":8622,"date":"2012-03-30T14:43:00","date_gmt":"2012-03-30T12:43:00","guid":{"rendered":"https:\/\/casmef.luiss.it\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/"},"modified":"2026-07-30T14:44:40","modified_gmt":"2026-07-30T12:44:40","slug":"equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi","status":"publish","type":"casmef_publication","link":"https:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/","title":{"rendered":"Equity Options, Credit Default Swaps e Leverage: Un Semplice Modello a Volatilit\u00e0 Stocastica per i Derivati Azionari e Creditizi"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Abstract: Lo scopo di questo lavoro \u00e8 quello di definire un modello che permetta ai traders di stimare il valore dei derivati azionari e creditizi nell\u2019ambito dello stesso schema teorico. Le formule chiuse proposte consentono ai traders di valutare equity, equity options e credit default swaps (CDSs) in modo coerente. Il modello pu\u00f2 anche essere utilizzato per risolvere il problema inverso, ossia quello di estrarre informazioni sensibili al rischio di credito dalle quotazioni di mercato dei derivati azionari e creditizi. In particolare, \u00e8 possibile stimare il leverage aziendale, cos\u00ec com\u2019\u00e8 percepito dai traders. Queste finalit\u00e0 sono state perseguite con un modello \u00e0 la Leland (1994), in cui gli azionisti dispongono di un\u2019opzione americana perpetua che consente loro di dichiarare in qualsiasi istante il fallimento della societ\u00e0. Dopo aver sostenuto che il debito pu\u00f2 essere modellato in termini di un\u2019unica emissione obbligazionaria perpetua e definito il leverage, abbiamo dimostrato la natura stocastica dell\u2019equity volatility e abbiamo ricavato le term structures delle probabilit\u00e0 d\u2019insolvenza e dei CDS spreads utilizzando la first-passage time distribution function. Abbiamo poi ricavato nuove formule per le equity calls e le equity puts. Queste formule, che dipendono dal leverage, L, e utilizzano la funzione di distribuzione normale univariata, sono coerenti con il volatility skew osservato nel mercato delle equity options e convergono verso le equazioni Black-Scholes Merton (BSM) per L ! 1. Tutte le lettere greche sono funzioni elementari delle corrispondenti lettere del modello BSM. Il lavoro si chiude<br>con due applicazioni: Lehman Brothers e General Motors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Barone G. CASMEF Working Paper Series. 2012;(5). <\/p>\n","protected":false},"template":"","publication_type":[559],"class_list":["post-8622","casmef_publication","type-casmef_publication","status-publish","hentry"],"acf":{"pub_unit":7855,"pub_file":8621},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Equity Options, Credit Default Swaps e Leverage: Un Semplice Modello a Volatilit\u00e0 Stocastica per i Derivati Azionari e Creditizi - Casmef<\/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:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equity Options, Credit Default Swaps e Leverage: Un Semplice Modello a Volatilit\u00e0 Stocastica per i Derivati Azionari e Creditizi - Casmef\" \/>\n<meta property=\"og:description\" content=\"Barone G. CASMEF Working Paper Series. 2012;(5).\" \/>\n<meta property=\"og:url\" content=\"https:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/\" \/>\n<meta property=\"og:site_name\" content=\"Casmef\" \/>\n<meta property=\"article:modified_time\" content=\"2026-07-30T12:44:40+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/publications\\\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\\\/\",\"url\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/publications\\\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\\\/\",\"name\":\"Equity Options, Credit Default Swaps e Leverage: Un Semplice Modello a Volatilit\u00e0 Stocastica per i Derivati Azionari e Creditizi - Casmef\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/#website\"},\"datePublished\":\"2012-03-30T12:43:00+00:00\",\"dateModified\":\"2026-07-30T12:44:40+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/publications\\\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/publications\\\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/publications\\\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Equity Options, Credit Default Swaps e Leverage: Un Semplice Modello a Volatilit\u00e0 Stocastica per i Derivati Azionari e Creditizi\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/#website\",\"url\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/\",\"name\":\"Casmef\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/#organization\",\"name\":\"Casmef\",\"url\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/casmef.luiss.it\\\/wp-content\\\/uploads\\\/2026\\\/07\\\/Logo-CASMEF.svg\",\"contentUrl\":\"https:\\\/\\\/casmef.luiss.it\\\/wp-content\\\/uploads\\\/2026\\\/07\\\/Logo-CASMEF.svg\",\"caption\":\"Casmef\"},\"image\":{\"@id\":\"https:\\\/\\\/casmef.luiss.it\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Equity Options, Credit Default Swaps e Leverage: Un Semplice Modello a Volatilit\u00e0 Stocastica per i Derivati Azionari e Creditizi - Casmef","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/","og_locale":"en_US","og_type":"article","og_title":"Equity Options, Credit Default Swaps e Leverage: Un Semplice Modello a Volatilit\u00e0 Stocastica per i Derivati Azionari e Creditizi - Casmef","og_description":"Barone G. CASMEF Working Paper Series. 2012;(5).","og_url":"https:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/","og_site_name":"Casmef","article_modified_time":"2026-07-30T12:44:40+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/","url":"https:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/","name":"Equity Options, Credit Default Swaps e Leverage: Un Semplice Modello a Volatilit\u00e0 Stocastica per i Derivati Azionari e Creditizi - Casmef","isPartOf":{"@id":"https:\/\/casmef.luiss.it\/en\/#website"},"datePublished":"2012-03-30T12:43:00+00:00","dateModified":"2026-07-30T12:44:40+00:00","breadcrumb":{"@id":"https:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/casmef.luiss.it\/en\/publications\/equity-options-credit-default-swaps-e-leverage-un-semplice-modello-a-volatilita-stocastica-per-i-derivati-azionari-e-creditizi\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/casmef.luiss.it\/en\/"},{"@type":"ListItem","position":2,"name":"Equity Options, Credit Default Swaps e Leverage: Un Semplice Modello a Volatilit\u00e0 Stocastica per i Derivati Azionari e Creditizi"}]},{"@type":"WebSite","@id":"https:\/\/casmef.luiss.it\/en\/#website","url":"https:\/\/casmef.luiss.it\/en\/","name":"Casmef","description":"","publisher":{"@id":"https:\/\/casmef.luiss.it\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/casmef.luiss.it\/en\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/casmef.luiss.it\/en\/#organization","name":"Casmef","url":"https:\/\/casmef.luiss.it\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/casmef.luiss.it\/en\/#\/schema\/logo\/image\/","url":"https:\/\/casmef.luiss.it\/wp-content\/uploads\/2026\/07\/Logo-CASMEF.svg","contentUrl":"https:\/\/casmef.luiss.it\/wp-content\/uploads\/2026\/07\/Logo-CASMEF.svg","caption":"Casmef"},"image":{"@id":"https:\/\/casmef.luiss.it\/en\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/casmef.luiss.it\/en\/wp-json\/wp\/v2\/casmef_publication\/8622","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/casmef.luiss.it\/en\/wp-json\/wp\/v2\/casmef_publication"}],"about":[{"href":"https:\/\/casmef.luiss.it\/en\/wp-json\/wp\/v2\/types\/casmef_publication"}],"acf:post":[{"embeddable":true,"href":"https:\/\/casmef.luiss.it\/en\/wp-json\/wp\/v2\/casmef_observatory\/7855"}],"wp:attachment":[{"href":"https:\/\/casmef.luiss.it\/en\/wp-json\/wp\/v2\/media?parent=8622"}],"wp:term":[{"taxonomy":"publication_type","embeddable":true,"href":"https:\/\/casmef.luiss.it\/en\/wp-json\/wp\/v2\/publication_type?post=8622"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}