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A Model of Deferred Callability in Defaultable Debt

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  • Mjøs, Aksel

    ()
    (Institute for Research in Economics and Business Administration)

  • Persson, Svein-Arne

    ()
    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

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    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.

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    Bibliographic Info

    Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2009/4.

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    Length: 28 pages
    Date of creation: 25 May 2009
    Date of revision:
    Handle: RePEc:hhs:nhhfms:2009_004

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    Keywords: Callable perpetual debt; barrier options;

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