Robust Option Pricing with Characteristic Functions and the B-Spline Order of Density Projection

Abstract

This paper extends and refines the method of option pricing by frame projection of risk-neutral densities to incorporate general B-splines, including the cubic basis, and general payoff structures. We introduce a coefficient stabilization method which substantially improves convergence for higher order splines. This stabilization has subsequently provided robust implementations for exotic option extensions of the method. After demonstrating the greater robustness of a fixed-width truncation rule over generally accepted cumulant based approaches, we devise a novel Hilbert transform based approach for the selection of truncated density supports, applicable to any density approximation method, which facilitates greater control over realized pricing errors. Robustness of B-spline frame projection is demonstrated by an extensive set of experiments which guide the selection of splines of various orders and subsequent parameter decisions. Finally, we provide formulas for digital and forward starting options.