🤖 AI Summary
This study addresses the limitations of traditional multifactor interest rate model calibration, which often neglects the influence of market data and parameter uncertainty, thereby hindering reliable assessment of calibration quality. The authors formulate calibration within a nonlinear regression framework, demonstrating that minimizing the root mean squared relative error (RMSRE) is equivalent to weighted least squares. They introduce, for the first time, an influence diagnostic framework tailored to stochastic interest rate models, enabling local sensitivity analysis with boundary constraints and confidence interval estimation. Their approach integrates weighted hat matrices, influence functions, the functional delta method, and an efficient Jacobian decomposition leveraging analytical gradients from at-the-money (ATM) cap prices. Empirical analysis using euro ATM cap data from 2016–2025 reveals pronounced leverage effects near parameter boundaries, effective dimensionality reduction, and a marked shift in parameter stability after 2022, indicating that low RMSRE alone does not guarantee trustworthy calibration.
📝 Abstract
The accurate calibration of interest rate models is central to market-consistent valuation and Economic Scenario Generators (ESGs). Traditional calibration methods for multi-factor models such as the G2++ model often rely on point estimates, neglecting the influence of specific market data and the quantification of estimation uncertainty. This paper develops a diagnostic framework embedding the calibration problem into non-linear regression theory. It shows that the common industry practice of minimizing the Root Mean Squared Relative Error (RMSRE) is equivalent to a Weighted Least Squares (WLS) problem. This equivalence yields the corresponding formulations for diagnostic tools, including the Weighted Hat Matrix for leverage analysis, Influence Functions for local sensitivity diagnostics, and the Functional Delta Method for local, boundary-respecting confidence intervals. The implementation uses an efficient Jacobian factorization that exploits the analytical tractability of At-The-Money (ATM) caps. The framework is applied to a dataset of Euro ATM caps covering the period 2016--2025. Our empirical analysis reveals a boundary-dominated leverage profile, repeated losses of effective dimensionality due to active parameter constraints, and a diagnostic regime shift in local parameter stability around the post-2022 market transition. The resulting message for actuarial model governance is that low RMSRE is not sufficient for calibration validation. We conclude by discussing the framework's applicability to general least-squares problems while highlighting the computational challenges for instruments lacking closed-form gradients, such as swaptions.