A Model of Deferred Callability in Defaultable Debt

19 Pages Posted: 27 May 2009

See all articles by Aksel Mjøs

Aksel Mjøs

Norwegian School of Economics (NHH) - Department of Finance

Svein-Arne Persson

Norwegian School of Economics (NHH)

Date Written: May 25, 2009

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 Classification: G12, G13, G33

Suggested Citation

Mjøs, Aksel and Persson, Svein-Arne, A Model of Deferred Callability in Defaultable Debt (May 25, 2009). NHH Dept. of Finance & Management Science Discussion Paper No. 2009/4. Available at SSRN: https://ssrn.com/abstract=1409673 or http://dx.doi.org/10.2139/ssrn.1409673

Aksel Mjøs

Norwegian School of Economics (NHH) - Department of Finance ( email )

Helleveien 30
N-5045 Bergen
Norway

Svein-Arne Persson (Contact Author)

Norwegian School of Economics (NHH) ( email )

Helleveien 30
Bergen, NO-5045
Norway
47-55-95-90-00 (Phone)
47-55-95-96-47 (Fax)

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