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A Model of Deferred Callability in Defaultable Debt

Author

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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)

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.

Suggested Citation

  • Mjøs, Aksel & Persson, Svein-Arne, 2009. "A Model of Deferred Callability in Defaultable Debt," Discussion Papers 2009/4, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2009_004
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    File URL: http://hdl.handle.net/11250/163968
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    Cited by:

    1. Mjøs, Aksel & Persson, Svein-Arne, 2010. "Callable risky perpetual debt with protection period," European Journal of Operational Research, Elsevier, vol. 207(1), pages 391-400, November.

    More about this item

    Keywords

    Callable perpetual debt; barrier options;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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