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A simple model of deferred callability in defaultable debt

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  • Mjøs, Aksel
  • Persson, Svein-Arne

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.

Suggested Citation

  • Mjøs, Aksel & Persson, Svein-Arne, 2010. "A simple model of deferred callability in defaultable debt," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1350-1357, December.
  • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1350-1357
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    1. Guha, Rajiv & Sbuelz, Alessandro & Tarelli, Andrea, 2020. "Structural recovery of face value at default," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1148-1171.
    2. Atreya, Nikhil & Mjøs, Aksel & Persson, Svein-Arne, 2015. "Making Bank: Why High Bank Leverage is Optimal - for the Bank's Shareholders," Discussion Papers 2015/33, Norwegian School of Economics, Department of Business and Management Science.

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