Real world economic scenarios are widely used by insurance companies for applications requiring the simulation of realistic asset and liability cash-flows in the future. These applications cover the calculation of the Solvency Capital Requirement, strategic asset allocation analysis, or profitability studies, among others.
An important process for insurers is the validation of those scenarios, that is the assessment of their consistency with respect to historical data and any additional expectation of future behavior. While current validation methods essentially consist in basic analyses of marginal distributions of the forecasts for a limited number of points in time, we propose a more general approach to validation by assessing the relevance of the pathwise properties of the generated scenarios, including core stylized facts such as autocorrelation, smoothness or clustering, that are often neglected in practice. The tool we rely on was originally introduced [2] to test whether two samples of stochastic processes paths come from the same distribution. It relies on a statistical test which is based on the concept of signature [4] and maximum mean distance [3]. The signature of a path, defined as the iterated integrals of the trajectory against itself, is essential in this method as it provides a way to represent paths in a parsimonious, hierarchical and accurate manner, that has proven to be successful in a variety of learning problems [1].
Our contribution is to apply this method as a validation tool to assess the appropriateness of a given model over another, and so for a collection of use cases that are relevant to the insurance industry. We will present in particular the statistical power of this approach for stochastic models used for forecasting risk drivers such as indices, volatility, inflation or spread, among others. We will also discuss several challenges related to the numerical implementation of this approach, and highlight its domain of validity in terms of distance between models and the volume of historical data at hand.
References: [1] Hans Buehler, Blanka Horvath, Terry Lyons, Imanol Perez Arribas, and Ben Wood. Generating financial markets with signatures. Available at SSRN 3657366, 2020. [2] Ilya Chevyrev and Harald Oberhauser. Signature moments to characterize laws of stochastic processes. arXiv preprint arXiv:1810.10971, 2018. [3] Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola. A kernel two-sample test. The Journal of Machine Learning Research, 13(1):723-773, 2012. [4] Terry J Lyons, Michael Caruana, and Thierry Lévy. Differential equations driven by rough paths. Springer, 2007.
 
Find the Q&A here: Q&A on 'Modelling for Our Future World'