Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2005/22: Callable Risky Perpetual Debt: Options, Pricing And Bankruptcy Implications

Aksel Mjøs () and Svein-Arne Persson ()
Additional contact information
Aksel Mjøs: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway
Svein-Arne Persson: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: Issuances of perpetual risky debt are often motivated by capital requirements for financial institutions. However, observed market practice indicates that actual maturity equals first possible call date. We analyze callable risky perpetual debt including an initial protection period before the debt may be called. To this end we develop European barrier option pricing formulas in a Black and Cox (1976) environment. The total market value of debt including the call option is expressed as a portfolio of barrier options and perpetual debt with a time dependent barrier. We analyze how the issuer’s optimal bankruptcy decision is affected by the existence of the call option using closed-form approximations. In accordance with intuition, our model quantifies the increased coupon and the decreased bankruptcy level caused by the embedded option. We show that the option will be exercised even at fairly low asset levels at the time of expiry.

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

JEL-codes: G13; G32; G33

33 pages, December 23, 2005

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