Local Volatility Pricing Models for Long-dated FX Derivatives

TL;DR

This paper develops local volatility models for long-dated FX derivatives considering stochastic interest rates, providing derivations and calibration methods for practical application in FX markets.

Contribution

It introduces a local volatility framework for FX options with stochastic interest rates and proposes calibration techniques for these models.

Findings

Derived local volatility functions for FX with stochastic rates

Proposed calibration methods for market data

Extended models for more general volatility dynamics

Abstract

We study the local volatility function in the Foreign Exchange market where both domestic and foreign interest rates are stochastic. This model is suitable to price long-dated FX derivatives. We derive the local volatility function and obtain several results that can be used for the calibration of this local volatility on the FX option's market. Then, we study an extension to obtain a more general volatility model and propose a calibration method for the local volatility associated to this model.