Improving Swaption Calibration in Factor HJM Stochastic Volatility Models: A First-Order Correction to Frozen Swap-Rate Loadings

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Highly relevant for quantitative trading desks dealing with interest rate derivatives (swaptions, SOFR options). The paper addresses a fundamental calibration bias in stochastic volatility term structure models that directly affects parameter interpretation and pricing accuracy. The correction improves parameter recovery (especially rate-volatility correlation beta) without adding calibration parameters, which is practically valuable for model risk management and hedging. However, it is primarily a pricing/calibration methodology paper rather than a trading strategy paper. The improvements are most relevant for desks using factor HJM models for swaption pricing and calibration.

The first-order correction adds no new calibration parameters but requires computing the Jacobian J(t) of the swap-rate loading along the deterministic centering path. The E1 finite ODE system adds 21 complex ODE coefficients (for N=6) to the existing 3 baseline coefficients in a block-triangular structure. The log-volatility PDE/spectral alternative requires Chebyshev collocation. The Fourier pricing framework remains the same. Implementation requires careful handling of time-reversed coefficient paths, complex contour integration, and numerical stability checks. The paper provides a reference implementation and detailed algorithmic specifications.

Code and numerical outputs are available at https://github.com/quaere-verum/FHJM-SV-Calibration. The paper builds on a public reference implementation by Sepp (2026) at https://github.com/ArturSepp/StochVolModels. Detailed numerical specifications including parameter grids, random seeds methodology (scrambled Sobol), time discretization, and accuracy criteria are fully documented. Symbolic verification of PDE residuals is described. Multiple independent validation methods (PDE, E1 ODE, pathwise QMC) are cross-checked.