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Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR


  • Marco Bianchetti
  • Mattia Carlicchi


We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects. We also review the new modern pricing approach prevailing among practitioners, based on multiple yield curves reflecting the different credit and liquidity risk of Libor rates with different tenors and the overnight discounting of cash flows originated by derivative transactions under collateral with daily margination. We report the classical and modern no-arbitrage pricing formulas for plain vanilla interest rate derivatives, and the multiple-curve generalization of the market standard SABR model with stochastic volatility. We then report the results of an empirical analysis on recent market data comparing pre- and post-credit crunch pricing methodologies and showing the transition of the market practice from the classical to the modern framework. In particular, we prove that the market of Interest Rate Swaps has abandoned since March 2010 the classical Single-Curve pricing approach, typical of the pre-credit crunch interest rate world, and has adopted the modern Multiple-Curve CSA approach, thus incorporating credit and liquidity effects into market prices. The same analysis is applied to European Caps/Floors, finding that the full transition to the modern Multiple-Curve CSA approach has retarded up to August 2010. Finally, we show the robustness of the SABR model to calibrate the market volatility smile coherently with the new market evidences.

Suggested Citation

  • Marco Bianchetti & Mattia Carlicchi, 2011. "Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR," Papers 1103.2567,, revised Apr 2012.
  • Handle: RePEc:arx:papers:1103.2567

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    Cited by:

    1. Jaroslav Baran & Jiří Witzany, 2014. "Konstrukce výnosových křivek v pokrizovém období [Yield Curve Construction after Crisis]," Politická ekonomie, Prague University of Economics and Business, vol. 2014(1), pages 67-99.
    2. Marcin Dec, 2019. "Markovian and multi-curve friendly parametrisation of a HJM model used in valuation adjustment of interest rate derivatives," Bank i Kredyt, Narodowy Bank Polski, vol. 50(2), pages 107-148.
    3. Yangfan Zhong, 2018. "LIBOR market model with multiplicative basis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-38, June.
    4. Chiara Sabelli & Michele Pioppi & Luca Sitzia & Giacomo Bormetti, 2014. "Multi-curve HJM modelling for risk management," Papers 1411.3977,, revised Oct 2015.
    5. Mesias Alfeus, 2019. "Stochastic Modelling of New Phenomena in Financial Markets," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2019.
    6. Gola, Carlo & Ilari, Antonio, 2015. "Financial innovation oversight: a policy framework," Journal of Financial Perspectives, EY Global FS Institute, vol. 3(1), pages 59-100.
    7. Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.
    8. repec:uts:finphd:41 is not listed on IDEAS
    9. Jaroslav Baran & Jiří Witzany, 2017. "Analysing Cross-Currency Basis Spreads," Working Papers 25, European Stability Mechanism.
    10. Dušan Staniek, . "Cross-Currency Basis Spread and Its Impact on Corporate Lending Rates in the Czech Banking Sector," Prague Economic Papers, Prague University of Economics and Business, vol. 0.
    11. Eric Jondeau & Benoit Mojon & Jean-Guillaume Sahuc, 2020. "Bank Funding Cost and Liquidity Supply Regimes," BIS Working Papers 854, Bank for International Settlements.

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