Calibration of local‐stochastic volatility models by optimal transport
研究半鞅最优输运问题，通过有限数量的欧式期权价格约束来校准局部随机波动率模型，提出凸优化问题的PDE形式和对偶形式，并用Heston类LSV模型在模拟数据和外汇市场数据上测试。
Abstract In this paper, we study a semi‐martingale optimal transport problem and its application to the calibration of local‐stochastic volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial and final time, we optimize our cost function given the prices of a finite number of European options. We formulate the problem as a convex optimization problem, for which we provide a PDE formulation along with its dual counterpart. Then we solve numerically the dual problem, which involves a fully non‐linear Hamilton–Jacobi–Bellman equation. The method is tested by calibrating a Heston‐like LSV model with simulated data and foreign exchange market data.