Before describing the contents of this issue of The Journal of Computational Finance, I would like to take this opportunity to welcome two neweditorial board members to our team. Professor Karel In 't Hout from the Department of Mathematics at the University of Antwerp is a leading expert in the area of partial differential equations (PDEs) for financial applications and numerical PDE discretization methods. Professor Mike Ludkovski of the Department of Statistics and Applied Probability at the University of California Santa Barbara is a leading expert in the area of Monte Carlo simulation methods, among many other topics. It is great that the board's expertise is expanding in these important areas for The Journal of Computational Finance.
This issue consists of four papers discussing several different numerical approaches. Three of them deal with some form of stochastic volatility in underlying asset dynamics. We also have a corrigendum in the present issue, for "Robust and accurate Monte Carlo simulation of (cross-) Gammas for Bermudan swaptions in the LIBOR market model", which appeared in Volume 17 (Issue 3) of the journal in 2014. The authors, RalfKorn and Qian Liang, describe a flawin their suggested pure pathwise method for calculation of (cross-) Gammas of a Bermudan swaption in the LIBOR market model. The reason for the flaw is an incorrect interchange of expectation and differentiation.
In the first paper in this issue, "Efficient Monte Carlo for discrete variance contracts", Nicolas Merener and Leonardo Vicchi, from Argentina and Brazil, respectively, develop an efficient Monte Carlo method for the valuation of financial contracts on discretely realized variance. Under a general stochastic volatility model the variance contract price is represented by a high-dimensional integral.A two-dimensional manifold that represents most of the uncertainty in realized variance and a precise integration based on quasi-random numbers give interesting insights.
Our second paper, "A chaos expansion approach for the pricing of contingent claims" by Hideharu Funahashi and Masaaki Kijima from the Tokyo Metropolitan University in Japan, presents an approximation method based on Wiener-Ito chaos expansion for the pricing of European-style contingent claims. The method is applicable for continuous Markov processes, and the resulting approximation formula requires (at most) three-dimensional numerical integration. The accuracy of the approximation remains highly satisfactory, even in the case of high-volatility and long-maturity contracts.
The third paper, "Multicurrency extension of the quasi-Gaussian stochastic volatility interest rate model" by Leslie Ng, deals with a Heston-type stochastic volatility process having a constant elasticity of variance local volatility component for foreign exchange dynamics. An approximation is presented for European foreign exchange options, and some insights regarding correlations and model calibration are given.
In the issue's fourth paper, "The density of distributions from the Bondesson class" by German Bernhart, Jan-Frederik Mai, Steffen Schenk and Matthias Scherer, a representation for the density of distributions from the Bondesson class is presented. This represents a large subclass of positive, infinitely divisible distributions. Many parametric families of infinitely divisible distributions can be assigned to the Bondesson class, eg, the inverse Gaussian, Gamma,Weibull and lognormal distributions. In particular, the paper discusses numerical stability. The oscillating integrand and the infinite integration bounds of the Bromwich Laplace inversion integral are circumvented so that discretization and truncation errors are reduced.
I wish you very enjoyable reading of this issue of The Journal of Computational Finance.
Cornelis W. Oosterlee
CWI - Dutch Center for Mathematics and Computer Science, Amsterdam