FX Modelling in Collateralized Markets: foreign measures, basis curves, and pricing formulae

TL;DR

This paper develops an arbitrage-free framework for pricing collateralized multi-currency products, incorporating foreign funding costs and FX market dislocations, with practical applications to cross-currency swaps and curve bootstrapping.

Contribution

It introduces a comprehensive arbitrage-free pricing model for multi-currency collateralized products, including foreign funding costs and FX market effects, with practical implementation guidance.

Findings

Pricing formulas for multi-currency collateralized products derived.

Practical issues in curve bootstrapping discussed and addressed.

Numerical examples based on real market data provided.

Abstract

We present a general derivation of the arbitrage-free pricing framework for multiple-currency collateralized products. We include the impact on option pricing of the policy adopted to fund in foreign currency, so that we are able to price contracts with cash flows and/or collateral accounts expressed in foreign currencies inclusive of funding costs originating from dislocations in the FX market. Then, we apply these results to price cross-currency swaps under different market situations, to understand how to implement a feasible curve bootstrap procedure. We present the main practical problems arising from the way the market is quoting liquid instruments: uncertainties about collateral currencies and renotioning features. We discuss the theoretical requirements to implement curve bootstrapping and the approximations usually taken to practically implement the procedure. We also provide numerical examples based on real market data.