Generalized Transform Analysis of Affine Processes and Applications in Finance

Abstract

Non-linearity is an important consideration in many problems of finance and economics, such as pricing securities and solving equilibrium models. This paper provides analytical treatment of a general class of nonlinear transforms for processes with tractable conditional characteristic functions, which extends existing results on characteristic function based transforms to a substantially wider class of nonlinear functions while maintaining low dimensionality by avoiding the need to compute the density function. We illustrate the applications of the generalized transform in pricing defaultable bonds with stochastic recovery. We also use the method to analytically solve a class of general equilibrium models with multiple goods and apply this model to study the effects of time-varying labor income risk on the equity premium.

Keywords: option pricing, recovery risk, stochastic discount factor, characteristic function, Fourier transform

JEL Classification: G10, G12, G13, C5