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The Volterra Stein-Stein model with stochastic interest rates

Author

Listed:
  • Abi Jaber, Eduardo

    (Ecole Polytechnique)

  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Motte, Edouard

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

We introduce the Volterra Stein-Stein model with stochastic interest rates, where both volatility and interest rates are driven by correlated Gaussian Volterra processes. This framework unifies various well-known Markovian and non-Markovian models while preserving analytical tractability for pricing and hedging financial derivatives. We derive explicit formulas for pricing zero-coupon bond and interest rate cap or floor, along with a semi-explicit expression for the characteristic function of the log-forward index using Fredholm resolvents and determinants. This allows for fast and efficient derivative pricing and calibration via Fourier methods. We calibrate our model to market data and observe that our framework is flexible enough to capture key empirical features, such as the humped-shaped term structure of ATM implied volatilities for cap options and the concave ATM implied volatility skew term structure (in log-log scale) of the S&P 500 options. Finally, we establish connections between our characteristic function formula and expressions that depend on infinite-dimensional Riccati equations, thereby making the link with conventional linear-quadratic models.

Suggested Citation

  • Abi Jaber, Eduardo & Hainaut, Donatien & Motte, Edouard, 2025. "The Volterra Stein-Stein model with stochastic interest rates," LIDAM Discussion Papers ISBA 2025003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2025003
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    References listed on IDEAS

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    1. Aur'elien Alfonsi & Ahmed Kebaier, 2026. "Weak error approximation for rough and Gaussian mean-reverting stochastic volatility models," Papers 2602.18234, arXiv.org.

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