Calibration of local volatility models with stochastic interest rates using optimal transport
提出一种非参数半鞅最优传输方法，用于校准具有随机利率的局部波动率模型，通过求解全非线性Hamilton-Jacobi-Bellman方程找到最接近参考模型的校准模型，并应用于Vašíček利率模型下的股票局部波动率校准。
Abstract We develop a nonparametric, semimartingale optimal transport, calibration methodology for local volatility models with stochastic interest rates. The method finds a fully calibrated model which is closest, in a way defined by a general cost function, to a given reference model. We establish a general duality result which allows to solve the problem by optimising over solutions to a second-order fully nonlinear Hamilton–Jacobi–Bellman equation. Our methodology is analogous to Guo et al. (SIAM J. Financ. Math. 13:1–31, 2022; Math. Finance 32:46–77, 2022), but features a novel element of solving for discounted densities, or sub-probability measures. As an example, we apply the method to a sequential calibration problem, where a Vašíček model is already given for the interest rates and we seek to calibrate a stock price’s local volatility model with a volatility coefficient depending on time, the underlying and the short rate process, and the two processes driven by possibly correlated Brownian motions. The equity model is calibrated to any number of European option prices.