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

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  • Marco, Bianchetti
  • Mattia, Carlicchi
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    Abstract

    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.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 42248.

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    Date of creation: 28 Mar 2012
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    Handle: RePEc:pra:mprapa:42248

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    Keywords: crisis; liquidity; credit; counterparty; risk; fixed income; Libor; Euribor; Eonia; yield curve; forward curve; discount curve; single curve; multiple curve; volatility surface; collateral; CSA discounting; no arbitrage; pricing; interest rate derivatives; FRAs; swaps; OIS; basis swaps; caps; floors; SABR;

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    References

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    1. Fran├žois-Louis Michaud & Christian Upper, 2008. "What drives interbank rates? Evidence from the Libor panel," BIS Quarterly Review, Bank for International Settlements, Bank for International Settlements, March.
    2. Andrea Pallavicini & Marco Tarenghi, 2010. "Interest-Rate Modeling with Multiple Yield Curves," Papers 1006.4767, arXiv.org.
    3. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
    4. Nicola Moreni & Andrea Pallavicini, 2010. "Parsimonious HJM Modelling for Multiple Yield-Curve Dynamics," Papers 1011.0828, arXiv.org.
    5. Fries, Christian P., 2010. "Discounting Revisited. Valuations under Funding Costs, Counterparty Risk and Collateralization," MPRA Paper 23082, University Library of Munich, Germany, revised 30 May 2010.
    6. Carlo Acerbi & Giacomo Scandolo, 2008. "Liquidity risk theory and coherent measures of risk," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(7), pages 681-692.
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