Statistics and Data Science Seminar
Liming Feng
University of Illinois at Urbana-Champaign
Inverting Analytic Characteristic Functions
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.
Wednesday March 28, 2012 at 4:00 PM in SEO 636