A Model of Deferred Callability in Defaultable Debt
AbstractBanks and other financial institutions raise hybrid capital as part of their risk capital. Hybrid capital has no maturity, but, similarily to most corporate debt, includes an embedded issuer's call option. To obtain acceptance as risk capital, the first possible exercise date of the embedded call is contractually deferred by several years, generating a protection period. The existence of this call feature affects the issuer's optimal bankruptcy decision, in addition to the value of debt. We value the call feature as a European option on perpetual defaultable debt. We do this by first modifying the underlying asset process to incorporate a time dependent bankruptcy level before the expiration of the embedded option. We identify a call option on debt as a fixed number of put options using a modified exercise price on a modified asset, which is lognormally distributed, as opposed to the market value of debt. To include the possibility of default before the expiration of the option we apply barrier options results. The formulas are quite general and may be used for valuing both embedded and third-party options. All formulas are developed in the seminal and standard Black-Scholes-Merton model and, thus, standard analytical tools such as 'the greeks', are immediately available.
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Bibliographic InfoPaper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2009/4.
Length: 28 pages
Date of creation: 25 May 2009
Date of revision:
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Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
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Fax: +47 55 95 96 50
Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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Callable perpetual debt; barrier options;
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation
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