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A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies


  • Masaaki Fujii

    (Graduate School of Economics, University of Tokyo)

  • Yasufumi Shimada

    (Capital Markets Division, Shinsei Bank, Limited)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)


The recent financial crisis caused dramatic widening and elevated volatilities among basis spreads in cross currency as well as domestic interest rate markets. Furthermore, the wide spread use of cash collateral, especially in fixed income contracts, has made the effective funding cost of financial institutions for the trades significantly different from the Libor of the corresponding payment currency. Because of these market developments, the text-book style application of a market model of interest rates has now become inappropriate for financial firms; It cannot even reflect the exposures to these basis spreads in pricing, to say nothing of proper delta and vega (or kappa) hedges against their movements. This paper presents a new framework of the market model to address all these issues.

Suggested Citation

  • Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies," CIRJE F-Series CIRJE-F-698, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2009cf698

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    References listed on IDEAS

    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
    3. Robert Jarrow & Yildiray Yildirim, 2008. "Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 16, pages 349-370 World Scientific Publishing Co. Pte. Ltd..
    4. Marco Bianchetti, 2009. "Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves," Papers 0905.2770,, revised Jul 2012.
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    Cited by:

    1. Jean-Paul Laurent & Philippe Amzelek & Joe Bonnaud, 2014. "An overview of the valuation of collateralized derivative contracts," Review of Derivatives Research, Springer, vol. 17(3), pages 261-286, October.
    2. Guillermo Andrés Cangrejo Jiménez, 2014. "La Estructura a Plazos del Riesgo Interbancario," DOCUMENTOS DE TRABAJO 012172, UNIVERSIDAD DEL ROSARIO.
    3. Calice, Giovanni, 2011. "The Impact of Collateral Policies on Sovereign CDS Spreads," ECMI Papers 12234, Centre for European Policy Studies.

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