Model Risk Measurement under Wasserstein Distance

TL;DR

This paper introduces a Wasserstein distance-based method for measuring model risk that accounts for both equivalent and non-equivalent probability measures, enhancing robustness in financial risk management.

Contribution

It develops a novel Wasserstein distance framework for model risk measurement that overcomes limitations of existing methods by including non-equivalent measures and addressing complex financial problems.

Findings

Provides a practically feasible approach for model risk assessment.

Enables analysis of correlation risk in capital market models.

Applicable to various financial risk management scenarios.

Abstract

The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust risk management. The proposed approach accounts for equivalent and non-equivalent probability measures and incorporates the economic reality of the fictitious adversary. It provides practically feasible results that overcome the restriction of considering only models implying probability measures equivalent to the reference model. The Wasserstein approach suits for various types of model risk problems, ranging from the single-asset hedging risk problem to the multi-asset allocation problem. The robust capital market line, accounting for the correlation risk, is not achievable with other non-parametric approaches.