Extrapolation and generative algorithms for three applications in finance

TL;DR

This paper introduces RKHS-based numerical algorithms for three key financial applications: pricing, reverse stress testing, and time series analysis, demonstrating their accuracy and efficiency in practical scenarios.

Contribution

The paper presents novel RKHS-based algorithms tailored for financial applications, enhancing extrapolation, inverse problem solving, and model extension capabilities.

Findings

Accurate pricing from few examples using RKHS algorithms.

Effective reverse stress testing via optimal transport and kernel methods.

Enhanced time series analysis allowing model extension and non-Gaussian analysis.

Abstract

For three applications of central interest in finance, we demonstrate the relevance of numerical algorithms based on reproducing kernel Hilbert space (RKHS) techniques. Three use cases are investigated. First, we show that extrapolating from few pricer examples leads to sufficiently accurate and computationally efficient results so that our algorithm can serve as a pricing framework. The second use case concerns reverse stress testing, which is formulated as an inversion function problem and is treated here via an optimal transport technique in combination with the notions of kernel-based encoders, decoders, and generators. Third, we show that standard techniques for time series analysis can be enhanced by using the proposed generative algorithms. Namely, we use our algorithm in order to extend the validity of any given quantitative model. Our approach allows for conditional analysis as well as for escaping the `Gaussian world'. This latter property is illustrated here with a portfolio investment strategy.