CAT Bond Pricing in Uncertain Environment

Document Type : Research Paper

Authors

Department of Applied Mathematics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran

Abstract

Catastrophe bonds are among the essential instruments in providing a financial hedge for insurance companies and their policyholders. Catastrophic events are rare, and the shortage of data turns using probability theory indefensible. On the other hand, uncertainty theory is a reliable alternative to deal with these kinds of indeterminacies. We model the problem of pricing catastrophe bonds as an uncertain optimization problem where the maximization of the cedent insurance company’s profit is constrained to the uncertain measure of ruin defined for the investors. Consequently, one could provide a tradeoff between being profitable for the ceding company and having reasonable protection for the investors. A solution to the optimization problem will be considered as the spread over the LIBOR, leading to a complete determination of the bond price. The results suggest the practicality of the model, especially the application of uncertainty theory in pricing catastrophe bonds. Finally, the uncertain ruin index is calculated for a real-world problem, and the results are compared with those obtained by probability theory.

Keywords

Main Subjects


Article Title [فارسی]

قیمت‌گذاری اوراق فاجعه در محیط نایقینی

Authors [فارسی]

  • وریا وکیلی
  • علیرضا غفاری حدیقه
گروه ریاضی کاربردی، دانشکده علوم، دانشگاه شهید مدنی آذربایجان، تبریز، ایران
Abstract [فارسی]

اوراق فاجعه یکی  از اصلی‌ترین ابزارها برای پوشش مالی شرکت‌های بیمه  و مشتریان آنها‌ است. وقایع فاجعه‌آمیز به‌ندرت اتفاق می‌افتند و کمبود داده‌های اولیه باعث می‌شود استفاده از نظریه احتمال در مطالعه آنها غیرممکن باشد. ازطرفی، نظریه نایقینی جایگزین قابل‌ اتکایی است که می‌توان در این گونه مسائل از آن استفاده کرد. ما مساله قیمت‌گذاری اوراق فاجعه را در قالب یک مساله بهینه سازی نایقین مدل‌بندی می‌کنیم، که در آن هدف بیشینه کردن سود شرکت بیمه با شرط ممانعت از ورشکستگی سرمایه‎‌گذاران است. به این ترتیب، می‌توان بین سودآور بودن قراردادها برای شرکت بیمه و محافظت از سرمایه سرمایه‌گذاران  توازن ایجاد کرد. جواب مساله بهینه‌سازی به عنوان مازاد بر سود لایبور لحاظ خواهد شد، که خود منجر به تعیین قیمت اوراق می­شود. نتایج محاسبتی نشان از کارایی عملی مدل، و به ویژه کارایی نظریه نایقینی در مساله قیمت‌گذاری اوراق فاجعه دارند. درنهایت، شاخص ورشکستگی از دیدگاه نظریه نایقینی برای یک مساله واقعی محاسبه شده و با نتایج استخراج شده از نظریه احتمال مقایسه می‌شود.

Keywords [فارسی]

  • باند CAT
  • قیمت گذاری اوراق بهادار مرتبط با بیمه؛ نظریه عدم قطعیت؛ برنامه نویسی نامطمئن
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