Calibration of Local-Stochastic Volatility Models by Optimal Transport
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 optimise our cost function given the prices of a finite number of European options. We formulate the problem as a convex optimisation 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2019
- DOI:
- 10.48550/arXiv.1906.06478
- arXiv:
- arXiv:1906.06478
- Bibcode:
- 2019arXiv190606478G
- Keywords:
-
- Quantitative Finance - Mathematical Finance;
- Mathematics - Optimization and Control