标题： 带有随机利率的Volterra Stein-Stein模型 显示英文标题

标题： The Volterra Stein-Stein model with stochastic interest rates

摘要： 我们引入了具有随机利率的Volterra Stein-Stein模型，其中波动率和利率均由相关高斯Volterra过程驱动。 该框架统一了各种著名的马尔可夫和非马尔可夫模型，同时保持了对金融衍生品定价和对冲的解析可处理性。 我们推导了零息债券和利率上限或下限的显式定价公式，并利用Fredholm预解算子和行列式得到了对数远期指数特征函数的半显式表达式。 这使得可以通过傅里叶方法快速有效地进行衍生品定价和校准。 我们将模型校准到市场数据，观察到我们的框架足够灵活，能够捕捉关键的经验特征，例如针对利率上限期权的ATM隐含波动率的驼峰状期限结构，以及标普500期权的ATM隐含波动率偏斜期限结构（在双对数尺度上）。 最后，我们将我们的特征函数公式与依赖于无限维Riccati方程的表达式建立了联系，从而与传统的线性二次模型建立了联系。 显示英文摘要

摘要： 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.