A simple model of deferred callability in defaultable debt |
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Authors: | Aksel Mjøs Svein-Arne Persson |
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Institution: | Department of Finance and Management Science, The Norwegian School of Economics and Business Administration, Helleveien 30, NO-5045 Bergen, Norway |
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Abstract: | Banks and other financial institutions issue hybrid capital as part of their risk capital. Hybrid capital has no maturity, but, similarly 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. 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 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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Keywords: | Callable perpetual debt Barrier options Hybrid capital |
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