Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2009/4: A Model of Deferred Callability in Defaultable Debt

Aksel Mjøs () and Svein-Arne Persson ()
Additional contact information
Aksel Mjøs: Institute for Research in Economics and Business Administration, Postal: Institute for Research in Economics and Business Administration, Breiviksveien 40, N-5045 Bergen, Norway
Svein-Arne Persson: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: Banks 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.

Keywords: Callable perpetual debt; barrier options

JEL-codes: G12; G13; G33

28 pages, May 25, 2009

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