Joint Calibration of Local Volatility Models with Stochastic Interest Rates using Semimartingale Optimal Transport

TL;DR

This paper introduces a non-parametric joint calibration method for local volatility and stochastic interest rate models using semimartingale optimal transport, enabling more accurate modeling of equity-rate dynamics.

Contribution

It presents a novel iterative approach for joint calibration based on semimartingale optimal transport, improving over sequential calibration methods.

Findings

Successfully calibrates models to market data for SPX options and interest rate options.

Demonstrates improved accuracy over sequential calibration.

Provides a practical implementation of the theoretical duality results.

Abstract

We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results established in Joseph, Loeper, and Obloj, 2023 and jointly calibrates the whole equity-rate dynamics. It uses an iterative approach which starts with a parametric model and tries to stay close to it, until a perfect calibration is obtained. We demonstrate the performance of our approach on market data using European SPX options and European cap interest rate options. Finally, we compare the joint calibration approach with the sequential calibration, in which the short rate model is calibrated first and frozen.