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The Whys of the LOIS: Credit Skew and Funding Spread Volatility


  • Stéphane Crépey

    () (LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - UEVE - Université d'Évry-Val-d'Essonne - ENSIIE - CNRS - Centre National de la Recherche Scientifique)

  • Raphaël Douady

    (Riskdata - Financial Risk Management Software, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)


The 2007 subprime crisis has induced a persistent disconnection between the Libor derivative markets of different tenors and the OIS market. Commonly proposed explanations for the corresponding spreads are a combination of credit risk and liquidity risk. However in the literature the meaning of liquidity is either not precisely stated, or it is simply defined as a residual spread after removal of a credit component. In this paper we propose a stylized equilibrium model in which a Libor-OIS spread (LOIS) emerges as a consequence of a credit component determined by the skew of the CDS curve of a representative Libor panelist (playing the role of the “borrower” in an interbank loan) and a liquidity component corresponding to a volatility of the spread between the refinancing (or funding) rate of a representative Libor panelist (playing the role of the “lender”) and the overnight interbank rate. The credit component is thus in fact a credit skew component, whilst the relevant notion of liquidity appears as the optionality, valued by the aforementioned volatility, of dynamically adjusting through time the amount of a rolling overnight loan, as opposed to lending a fixed amount up to the tenor horizon on Libor. “At-the-money” when the funding rate of the lender and the overnight interbank rate match on average, this results, under diffusive features, in a square root term structure of the LOIS, with a square root coefficient given by the above-mentioned volatility. Empirical observations reveal a square root term structure of the LOIS consistent with this theoretical analysis, with, on the EUR market studied in this paper on the period half-2007 half-2012, LOIS explained in a balanced way by credit and liquidity until the beginning of 2009 and dominantly explained by liquidity since then.

Suggested Citation

  • Stéphane Crépey & Raphaël Douady, 2014. "The Whys of the LOIS: Credit Skew and Funding Spread Volatility," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01151315, HAL.
  • Handle: RePEc:hal:cesptp:hal-01151315
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    References listed on IDEAS

    1. Markus K. Brunnermeier & Lasse Heje Pedersen, 2009. "Market Liquidity and Funding Liquidity," Review of Financial Studies, Society for Financial Studies, vol. 22(6), pages 2201-2238, June.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    3. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2011. "Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation," Papers 1112.1521,, revised Dec 2011.
    4. Tapking, Jens & Eisenschmidt, Jens, 2009. "Liquidity risk premia in unsecured interbank money markets," Working Paper Series 1025, European Central Bank.
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    Cited by:

    1. St'ephane Cr'epey & R'emi Gerboud & Zorana Grbac & Nathalie Ngor, 2012. "Counterparty Risk and Funding: The Four Wings of the TVA," Papers 1210.5046,

    More about this item


    Libor; OIS; funding; credit; liquidity;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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