FX Modelling in Collateralized Markets: Foreign Measures, Basis Curves, and Pricing Formulae

Abstract

We present a general derivation of the arbitrage-free pricing framework for multiplecurrency collateralized products. We include the impact on option pricing of the policy adopted to fund in foreing 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. JEL classification code: G13.

Pricing of Counterparty Risk and Funding With CSA Discounting, Portfolio Effects and Initial Margin

“…Piterbarg (2010). • The (clean) value of a derivative collateralized in a foreign currency is discounted on the market at a rate depending on cross currency bases, see the formulas and derivations in Table 1 in Moreni and Pallavicini (2017).…”