Generalized Transform Analysis of Affine Processes and Applications in Finance

Nonlinearity is an important consideration in many problems of finance and economics, such as pricing securities, computing equilibrium, and conducting structural estimations. We extend the transform analysis in Duffie, Pan, and Singleton (2000) by providing analytical treatment of a general class of nonlinear transforms for processes with tractable conditional characteristic functions. We illustrate the applications of the generalized transform method in pricing contingent claims and solving general equilibrium models with preference shocks, heterogeneous agents, or multiple goods. We also apply the method to a model of time-varying labor income risk and study the implications of stochastic covariance between labor income and dividends for the dynamics of the risk premiums on financial wealth and human capital.