Journal of Computational Finance

Christoph Reisinger
University of Oxford

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

The three papers in this issue all apply new methodologies or use existing metrics in a novel way to solve some classical computational problems encountered in finance.

The issue’s first paper, “Clustering market regimes using theWasserstein distance” by Blanka Horvath, Zacharia Issa and Aitor Muguruza, introduces us to the application of clustering algorithms to identify market regimes from time series data. The authors’ novel idea consists in the use of the Wasserstein metric as a way to measure the distance between sample distributions. After an in-depth discussion of their motivation and a description of their approach, Horvath et al show that their Wasserstein k-means algorithm greatly outperforms two alternative benchmark approaches.

In our second paper, “An iterative copula method for probability density estimation”, Michael Roitman proposes a new method for solving the classical problem of estimating a probability density from a sample. His algorithm consists of a sequence of transformations to a normal distribution, for which convergence is guaranteed. Roitman considers a couple of examples, and provides a theoretical justification for why this method should work. The findings of his numerical tests with two examples are encouraging and show that, at least in some cases, the method is superior to some standard methods for density estimation.

Lastly, in the third paper in the issue, “Pricing high-dimensional Bermudan options using deep learning and higher-order weak approximation”, Riu Naito and Toshihiro Yamada propose a new deep-learning-based algorithm that utilizes a higherorder weak approximation scheme to approximate the value function of Bermudan options by neural networks, permitting the conditional expectations appearing in Bermudan option pricing to be estimated quickly even if the dimension is high. Numerical examples demonstrate that accurate solutions can be obtained even in high-dimensional settings.

I hope you will find these papers and the novel methodologies therein inspiring.