This issue of The Journal of Computational Finance consists of several papers with a focus on transform-based derivatives pricing techniques, particularly Fourier techniques, and on Lévy processes.
In the first paper in this issue, "Fourier transform algorithms for pricing and hedging discretely sampled exotic variance products and volatility derivatives under additive processes", Wendong Zheng and YueKuenKwok develop efficient Fourier techniques for volatility derivatives under, for example, time-inhomogeneous Lévy processes. Their numerical algorithms are versions of the so-called Fourier space time-stepping method applied to nonlinear path-dependent payoff structures.
Another transform technique - the fast Gauss transform - is central to the issue's second paper: "Application of the improved fast Gauss transform to option pricing under jump-diffusion processes" by Takayuki Sakuma and Yuji Yamada. The techniques introduced in the paper are based on the so-called fast multipole method, which is a highly efficient technique from computational physics. The authors demonstrate its applicability in computational finance.
Our third paper, "Efficient variations of the Fourier transform in applications to option pricing" by Svetlana Boyarchenko and Sergei Levendorski˘ı, aims to clarify relationships and connections among popular methods for pricing European options based on Fourier expansions of the payoff function and the trapezoidal rule. Based on this clarification, new method variations are proposed and optimal parameter choices are suggested.
The fourth paper in the issue is "Option calibration of exponential Lévy models: confidence intervals and empirical results" by Jakob Söhl and Mathias Trabs. They discuss an efficient calibration procedure based on a spectral estimation procedure for Lévy models of finite jump activity. Based on finite sample variances, confidence intervals are defined for the volatility, the jump density and the drift.
Finally, we were very recently informed that Jade Mitchell, our journals manager and primary publisher contact, is leaving Incisive Media. Jade has been extremely helpful with the journal's editorial process, and we thank her deeply for all her help and wish her the very best for the future.
I wish you enjoyable reading of this issue of The Journal of Computational Finance.
CWI - Dutch Center for Mathematics and Computer Science, Amsterdam
Fourier transform algorithms for pricing and hedging discretely sampled exotic variance products and volatility derivatives under additive processes