Pricing path-dependent equity and credit derivatives within a general hybrid equity-credit framework: A unified CTMC approximation approach

Abstract

We propose a unified closed-form approximation approach to pricing path-dependent equity and credit derivatives such as defaultable single- and double-barrier options and equity default swaps (EDSs) under jump-to-default extended exponential Lévy models with local volatilities. This rich class of hybrid equity-credit models allows for state-dependent volatilities, state-dependent default intensities, and general Lévy types with either finite or infinite activities and with either finite or infinite variations, and includes many important hybrid equity-credit models as special cases. The convergences of the closed-form approximation pricing formulas are theoretically proved, and the corresponding convergence rates are also theoretically established. Numerical results indicate that our pricing method is accurate and efficient under a wide range of hybrid equity-credit models.