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Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves

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  • Marco Bianchetti

Abstract

We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations are no longer valid, and can be recovered by taking properly into account the forward basis bootstrapped from market basis swaps. Numerical results show that the resulting forward basis curves may display a richer micro-term structure that may induce appreciable effects on the price of interest rate instruments. By recurring to the foreign-currency analogy we also derive generalised no-arbitrage double-curve market-like formulas for basic plain vanilla interest rate derivatives, FRAs, swaps, caps/floors and swaptions in particular. These expressions include a quanto adjustment typical of cross-currency derivatives, naturally originated by the change between the numeraires associated to the two yield curves, that carries on a volatility and correlation dependence. Numerical scenarios confirm that such correction can be non negligible, thus making unadjusted double-curve prices, in principle, not arbitrage free. Both the forward basis and the quanto adjustment find a natural financial explanation in terms of counterparty risk.

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  • Marco Bianchetti, 2009. "Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves," Papers 0905.2770, arXiv.org, revised Jul 2012.
    • Handle: RePEc:arx:papers:0905.2770
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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. Guillermo Andrés Cangrejo Jiménez, 2014. "La Estructura a Plazos del Riesgo Interbancario," Documentos de Trabajo 12172, Universidad del Rosario.
    4. N. Moreni & A. Pallavicini, 2014. "Parsimonious HJM modelling for multiple yield curve dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 199-210, February.
    5. 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," CARF F-Series CARF-F-196, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Apr 2011.
    6. Jacob Gyntelberg & Peter Hördahl & Kristyna Ters & Jörg Urban, 2013. "Intraday dynamics of euro area sovereign CDS and bonds," BIS Working Papers 423, Bank for International Settlements.
    7. Jan Šedivý, 2019. "Optimální způsob sjednání derivátu za přítomnosti rizika protistrany [Optimal Method of Entering a Derivative Contract in the Presence of Counterparty Risk]," Politická ekonomie, Prague University of Economics and Business, vol. 2019(1), pages 65-81.
    8. Anna Maria Gambaro & Riccardo Casalini & Gianluca Fusai & Alessandro Ghilarducci, 2019. "A market-consistent framework for the fair evaluation of insurance contracts under Solvency II," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 157-187, June.
    9. V. Brousseau & Alexandre Chailloux & Alain Durré, 2013. "Fixing the Fixings: What Road to a More Representative Money Market Benchmark?," IMF Working Papers 2013/131, International Monetary Fund.
    10. Laura Morino & Wolfgang J. Ruggaldier, 2014. "On multicurve models for the term structure," Papers 1401.5431, arXiv.org.
    11. Masaaki Fujii & Akihiko Takahashi, 2009. "A Survey on Modeling and Analysis of Basis Spreads," CARF F-Series CARF-F-195, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. Masaaki Fujii & Akihiko Takahashi, 2009. "A Survey on Modeling and Analysis of Basis Spreads," CIRJE F-Series CIRJE-F-697, CIRJE, Faculty of Economics, University of Tokyo.
    13. Piotr Mielus, 2016. "Dylematy reformy indeksów rynku finansowego," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 4, pages 91-114.
    14. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    15. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Risks, MDPI, vol. 6(1), pages 1-39, March.
    16. Filipović, Damir & Trolle, Anders B., 2013. "The term structure of interbank risk," Journal of Financial Economics, Elsevier, vol. 109(3), pages 707-733.
    17. Eric Jondeau & Benoit Mojon & Jean-Guillaume Sahuc, 2020. "Bank Funding Cost and Liquidity Supply Regimes," BIS Working Papers 854, Bank for International Settlements.
    18. Eduard Gim'enez & Alberto Elices & Giovanna Villani, 2014. "A heuristic pricing and hedging framework for multi-currency fixed income desks," Papers 1406.1811, arXiv.org, revised Jan 2017.
    19. Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.
    20. 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.

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