Signature-based validation of real-world economic scenarios

TL;DR

This paper introduces a signature-based statistical test for validating real-world economic scenarios, particularly useful in insurance and finance, by comparing stochastic process samples with different properties.

Contribution

It applies a novel signature-based test to diverse stochastic processes relevant for financial and actuarial modeling, expanding its practical validation scope.

Findings

Effective in distinguishing different stochastic process distributions

Applicable to processes with various pathwise properties

Useful for validating economic scenarios in finance and insurance

Abstract

Motivated by insurance applications, we propose a new approach for the validation of real-world economic scenarios. This approach is based on the statistical test developed by Chevyrev and Oberhauser (2022) and relies on the notions of signature and maximum mean distance. This test allows to check whether two samples of stochastic processes paths come from the same distribution. Our contribution is to apply this test to a variety of stochastic processes exhibiting different pathwise properties (H{\"o}lder regularity, autocorrelation, regime switches) and which are relevant for the modelling of stock prices and stock volatility as well as of inflation in view of actuarial applications.