Before we describe the contents of the current issue of The Journal of Computational Finance, let me say a few words. For two years we have been managed and assisted by Incisive Media Journals Manager Dawn Hunter, who did her work with great accuracy and care. She helped us take our first steps into the e-paper handling system in April 2015. She has now left Incisive Media, and we wish her all the best for her future career. Dawn, thanks for the accurate handling of all your work and for your cooperation!
That being said, in front of you is the September 2017 issue of The Journal of Computational Finance. In the following four research papers, four different numerical techniques are advocated for a variety of applications in finance, for which efficient computations are mandatory. Interestingly, the underlying asset dynamics appear to be based on Lévy processes in three of the papers in this issue.
The title of Geng Deng, Tim Dulaney, Craig McCann and Mike Yan’s paper, the first in this issue, is self-explanatory: “Efficient valuation of equity-indexed annuities under Lévy processes using Fourier cosine series”. An efficient version of the COS method is proposed for pricing equity-indexed annuities, which are deferred annuities that increase in value over time according to crediting and realized index returns. The value of the contract is based on a series of terms containing characteristic functions, so the COS method can be applied to calculate the contract’s present value as well as annuity market sensitivities.
“A generalized risk budgeting approach to portfolio construction” written by Martin Haugh, Garud Iyengar and Irene Song is the issue’s second paper. In a generalized budgeting approach to portfolio construction, assets are bundled into overlapping subsets, and a risk budget is allocated to each bundle. The aim is to find an optimal risk–return front. Two solution approaches are proposed, one based on semidefinite programming and another based on the Markov chain Monte Carlo method. The generality of the second approach is emphasized.
J. Lars Kirkby is the author of the third contribution to this issue: “Robust option pricing with characteristic functions and the B-spline order of density projection”. As in the first paper, the characteristic function of the asset price process is known and, based on this, the so-called PROJ method is defined. This is a wavelets-based technique, based on B-splines. The method’s applicability extends to discretely monitored exotic options under exponential Lévy dynamics. Three different implementations are compared: one is a Hilbert transform-based technique, which particularly offers control over errors.
The issue’s final paper is “European option pricing under geometric Lévy processes with proportional transaction costs” by Haipeng Xing,Yang Yu and Tiong Wee Lim. The authors propose a computational algorithm for the European option pricing problem under transaction costs, where the asset dynamics follow a geometric Lévy process. The approach adopted is based on maximization of the expected utility of terminal wealth, where the option-pricing problem is transformed into a stochastic optimal control problem. A coupled backward induction algorithm is developed to solve the resulting formulation.
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
This paper proposes an efficient algorithm to value two popular crediting formulas found in equity-indexed annuities – APP and MPP – under general Lévy-process-based index returns.
This paper proposes a generalized risk budgeting approach to portfolio construction.
This paper extends and refines the method of option pricing by frame projection of risk-neutral densities to incorporate B-splines.
This paper considers the problem of European option pricing in the presence of a proportional transaction cost when the price of the underlying follows a jump–diffusion process.