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


  • Nicola Moreni
  • Andrea Pallavicini


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.

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  • Nicola Moreni & Andrea Pallavicini, 2015. "FX Modelling in Collateralized Markets: foreign measures, basis curves, and pricing formulae," Papers 1508.04321,, revised Sep 2015.
  • Handle: RePEc:arx:papers:1508.04321

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    References listed on IDEAS

    1. Baba, Naohiko & Packer, Frank, 2009. "From turmoil to crisis: Dislocations in the FX swap market before and after the failure of Lehman Brothers," Journal of International Money and Finance, Elsevier, vol. 28(8), pages 1350-1374, December.
    2. Naohiko Baba & Frank Packer & Teppei Nagano, 2008. "The spillover of money market turbulence to FX swap and cross-currency swap markets," BIS Quarterly Review, Bank for International Settlements, March.
    3. Damiano Brigo & Marco Francischello & Andrea Pallavicini, 2015. "Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs," Papers 1506.00686,, revised Nov 2015.
    4. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2012. "Funding, Collateral and Hedging: uncovering the mechanics and the subtleties of funding valuation adjustments," Papers 1210.3811,, revised Dec 2012.
    5. Niall Coffey & Warren B. Hrung & Asani Sarkar, 2009. "Capital constraints, counterparty risk, and deviations from covered interest rate parity," Staff Reports 393, Federal Reserve Bank of New York.
    6. Masaaki Fujii & Akihiko Takahashi, 2015. "A General Framework for the Benchmark pricing in a Fully Collateralized Market," Papers 1508.06339,, revised Sep 2015.
    7. Fabio Filipozzi & Karsten Staehr, 2013. "Covered Interest Parity and the Global Financial Crisis in Four Central and Eastern European Countries," Eastern European Economics, Taylor & Francis Journals, vol. 51(1), pages 21-35, January.
    8. Andrea Pallavicini & Damiano Brigo, 2013. "Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPs," Papers 1304.1397,
    9. Crystal Ossolinski & Andrew Zurawski, 2010. "The Financial Crisis through the Lens of Foreign Exchange Swap Markets," RBA Bulletin (Print copy discontinued), Reserve Bank of Australia, pages 47-53, June.
    10. Eduard Gim'enez & Alberto Elices & Giovanna Villani, 2014. "A heuristic pricing and hedging framework for multi-currency fixed income desks," Papers 1406.1811,, revised Jan 2017.
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    1. Nicola Moreni & Andrea Pallavicini, 2017. "Derivative Pricing With Collateralization And Fx Market Dislocations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-27, September.

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