Characteristic functions of affine processes via calculus of their operator symbols

Abstract

The characteristic functions of multivariate Feller processes with generator of affine type, and with smooth symbol functions have an explicit representation in terms of power series with rational number coefficients and with monmoms consisting of powers of the the symbol functions and formal derivatives of the symbol functions. The power series repesentations are convergent globally in time and on bounded domains of arbitrary size. Generalized symbol functions can be derived leading to power series expansions which are convergent on arbitrary domains in special cases. The rational number coefficients can be efficiently computed by an integer recursion. As a numerical consequence characteristic functions of multivariate affine processes can be efficiently computed from the symbol function avoiding computation of the generalized Riccati equations (an observation first made recently in a more general context).