Journal of Computational Finance

I am delighted to introduce the latest issue of The Journal of Computational Finance.

Its three papers showcase the remarkable spread and depth of computational methodology for state-of-the-art financial models. The techniques employed range from novel, improved applications of Fourier schemes over modern developments of gradient methods to the training of generative time series models.

The issue’s first paper, “High-performance applications of the nonuniform fast Fourier transform to option pricing” by Leif Andersen and Mark Lake, combines the nonuniform fast Fourier transform with adaptive integration techniques to produce a robust and highly efficient pricing framework. Numerical tests on the pricing of European options in a variance gamma Lévy-jump model with a singular density and in a constant elasticity of variance model extended with stochastic volatility demonstrate high accuracy (with errors of around 10^-13 to 10^-16 while pricing tens of thousands – and sometimes even millions – of options per second on a single processor core.

In our second paper, “Optimality, sparsity and regularization parameter analysis for a risk diversification portfolio selection model”, Qian Li, Aining Kou and Hao Lin introduce the risk diversification mean–variance model: a convergent numerical algorithm for portfolio optimization in a model that mitigates against the risk of drastic market downturns while controlling transaction costs. Theoretical results on the relationship between the regularization parameter and sparsity indicate that the model exhibits a certain degree of sparsity in portfolio weights without explicit sparse regularization terms. The authors’ empirical analysis demonstrates that their risk diversification mean–variance model outperforms classical mean–variance, sparse portfolio and risk-diversified portfolio models in terms of sparsity, stability and net profit for a data period that includes the 2007–9 global financial crisis and the 2020–23 Covid-19 pandemic.

In “The log-signature-based time series Wasserstein generative adversarial network”, the third and final contribution to this issue, David Hirnschall, Paul Krühner and Kurt Hornik propose a modification to the signature Wasserstein generative adversarial network (a purely data-driven model) and use neural networks to minimize the Wasserstein distance between log signatures to reduce the target dimension of the generator and increase performance. Using adapted loss functions, generators and discriminators, the authors validate their proposed model on synthetic and real-world data across several performance evaluation metrics, showcasing its effectiveness for financial time series generation.

I trust you will find the papers inspiring and useful.