Liming Feng : Inverting Analytic Characteristic Functions

Posted by Jie Yang , part of the Statistics and Data Science Seminar.

At

March 28, 2012, 4 p.m.

In

SEO 636

Abstract

Analytic characteristic functions naturally arise in financial engineering applications. We explore the analyticity of such characteristic functions and propose simple but highly accurate inversion schemes. The schemes have the following advantages: (1) they are very easy to implement; one does not need to rely on commercial numerical packages; (2) despite the simplicity, they are highly accurate, with exponentially decaying errors; (3) they admit explicit error estimates that only depend on the given characteristic function; (4) multiple values of the desired quantity can be computed simultaneously using the fast Fourier transform. We illustrate the effectiveness of the schemes with financial engineering examples, including the valuation of options with barrier, lookback and early exercise features in Lévy models, as well as Monte Carlo simulation of Lévy processes with analytic characteristic functions.