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

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  • Bram Brongers

Abstract

The factor HJM stochastic volatility model introduced by Sepp and Rakhmonov (2025) obtains tractable swaption pricing by freezing the nonlinear swap-rate loading along a deterministic expected-state path. This removes the dependence of conditional swap-rate variance on the current yield-curve state. We introduce a first-order Taylor correction to the loading that adds no calibration parameters. Conditional on retaining the frozen annuity-measure drift, we show that the first variation of the swap-rate transform is affine in the centered rate states and reduces to one-dimensional equations in volatility. For quadratic-drift lognormal stochastic volatility, these equations yield a finite-dimensional ODE representation and a direct log-volatility formulation. Calibrations to independently generated nonlinear-model prices show substantially lower stochastic volatility parameter bias and held-out pricing error, with only modest changes in local calibration identifiability.

Suggested Citation

  • Bram Brongers, 2026. "Improving Swaption Calibration in Factor HJM Stochastic Volatility Models: A First-Order Correction to Frozen Swap-Rate Loadings," Papers 2608.29423, arXiv.org.
    • Handle: RePEc:arx:papers:2608.29423
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    1. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    2. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    3. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv.
    4. Abdelkoddousse Ahdida & Aurélien Alfonsi & Ernesto Palidda, 2017. "Smile with the Gaussian term structure model," Post-Print hal-01098554, HAL.
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