Convertible bonds are hybrid securities unifying both debt and equity features. Hence, for the valuation of convertible bonds we need a model which enables us to describe both aspects of these securities correctly. To this end, we introduce the Jump to Default Extended Constant Elasticity of Variance Model that yields closed-form valuation formulas. This model is suitable since it merges a reduced-form approach and an extension of the Black-Scholes Model which means in particular the Jump to Default Extended Diffusions and the Constant Elasticity of Variance Model, respectively. Due to the relation between the solution of the stochastic differential equation that describes the stock price movements in this model and the family of Bessel processes we are able to derive analytically tractable valuation formulas for survival probabilities and basic contingent claims. Furthermore, we apply the developed results to price European- and American-style convertible bonds. To price the latter we adjust a trinomial tree approach to our model. Finally, we accomplish a sensitivity analysis for the several input parameters to show their impact on the instantaneous volatility and the default probability as well as on the price of the convertible bonds.     «

Convertible bonds are hybrid securities unifying both debt and equity features. Hence, for the valuation of convertible bonds we need a model which enables us to describe both aspects of these securities correctly. To this end, we introduce the Jump to Default Extended Constant Elasticity of Variance Model that yields closed-form valuation formulas. This model is suitable since it merges a reduced-form approach and an extension of the Black-Scholes Model which means in particular the Jump to Def...     »