Discussion Papers, Department of Finance and Management Science, Norwegian School of Economics (NHH)
No 2009/4:
A Model of Deferred Callability in Defaultable Debt
Aksel Mjøs ()
and Svein-Arne Persson ()
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; (follow links to similar papers)
JEL-Codes: G12; G13; G33; (follow links to similar papers)
28 pages, May 25, 2009
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