Signature-based validation of real-world economic scenarios
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We propose a new approach for the validation of real-world economic scenario motivated by insurance applications. This approach is based on the statistical test developed by Chevyrev and Oberhauser [6] 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 two stochastic processes, namely the fractional Brownian motion and the Black-Scholes dynamics. We analyze its statistical power based on numerical experiments under two constraints: 1. we work in an asymetric setting in which we compare a large sample that represents simulated real-world scenarios and a small sample that mimics information from historical data, both with a monthly time step as often considered in practice and 2. we make the two samples identical from the perspective of validation methods used in practice, i.e. we impose that the marginal distributions of the two samples are the same at a given one-year horizon. By performing specic transformations of the signature, we obtain high statistical powers and demonstrate the potential of this validation approach for real-world economic scenarios. We 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 data at hand.
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