Callable Risky Perpetual Debt with Protection Period

28 Pages Posted: 6 Mar 2005 Last revised: 28 Sep 2008

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: December 23, 2005


Issuances in the USD 260 Bn global market of perpetual risky debt are often motivated by capital requirements for financial institutions. We analyze callable risky perpetual debt emphasizing an initial protection ('grace') period before the debt may be called. The total market value of debt including the call option is expressed as a portfolio of perpetual debt and barrier options with a time dependent barrier. We also analyze how an issuer's optimal bankruptcy decision is affected by the existence of the call option by using closed-form approximations. The model quantifies the increased coupon and the decreased initial bankruptcy level caused by the embedded option. Examples indicate that our closed form model produces reasonably precise coupon rates compared to numerical solutions. The credit-spread produced by our model is in a realistic order of magnitude compared to market data.

Keywords: Callable perpetual debt, embedded options, barrier options, optimal bankruptcy

JEL Classification: G13, G32, G33

Suggested Citation

Mjøs, Aksel and Persson, Svein-Arne, Callable Risky Perpetual Debt with Protection Period (December 23, 2005). NHH Dept. of Finance & Management Science Discussion Paper No. 22/2005, Available at SSRN: or

Aksel Mjøs

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

Helleveien 30
N-5045 Bergen

Svein-Arne Persson (Contact Author)

Norwegian School of Economics (NHH) ( email )

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

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