Unified Credit-Equity Modeling

This chapter surveys a modeling framework for the unified valuation of corporate debt, credit, and equity derivatives.In this framework, the defaultable stock price is seen as the fundamental observable state variable. Corporate debt, credit, and equity derivatives on a given firm are seen as contingent claims on the defaultable stock. We model the defaultable stock price as a jump-to-default extended diffusion. In particular, we survey the jump-todefault extended constant elasticity of variance (JDCEV) model of Carr and Linetsky (2006) and the time-changed JDCEV model of Mendoza-Arriaga, Carr, and Linetsky (2009) with state-dependent jumps exhibiting leverage effect and stochastic volatility.