Pré-Publication, Document De Travail Année : 2025

The Volterra Stein-Stein model with stochastic interest rates

Résumé

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 wellknown 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 loglog 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.

Fichier principal
Vignette du fichier
Volterra_Stein_Stein_stochastic_rates (4).pdf (3.57 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04981004 , version 1 (06-03-2025)

Licence

Identifiants

  • HAL Id : hal-04981004 , version 1

Citer

Eduardo Abi Jaber, Donatien Hainaut, Edouard Motte. The Volterra Stein-Stein model with stochastic interest rates. 2025. ⟨hal-04981004⟩
65 Consultations
162 Téléchargements

Partager

  • More