A valuation model of deferred callability in defaultable debt

Abstract

In this thesis a model is developed for valuing risky perpetual debt with an embedded American call option that can be exercised after a protection period. These features are relevant for a hybrid capital instrument typically issued by banks and other financial institutions, partly as an outcome of regulatory requirements. There exist a large market for this instrument, the outstanding amount of hybrid capital securities was $ 376 billion in 2005 (Mjøs and Persson, 2007). The model is based on a model by Mjøs and Persson (2010) where similar debt is valued, but where as a simplification the option is assumed to be a European type of option. Market practice indicates that this hybrid capital instrument is issued with an American option and a step-up coupon rate, in this sense the model developed in this thesis is more realistic than Mjøs and Persson’s model because it incorporates these characteristics. An important result from this thesis is that the value of risky perpetual debt with an embedded American call option differs from the value of similar debt with a European call option. This is interesting because considering market practice and the characteristics of the two options would imply otherwise.