2025/03/03 by Eduardo Abi Jaber, Jaber, Eduardo Abi, Donatien Hainaut +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #Mathematical Dynamics and Fractals #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2503.01716
openalex publication_date 2025/03/03 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
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.