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

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  • Bianchetti, Marco
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    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 dierent 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by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations are no longer valid, and can be recovered by taking properly into account the forward basis bootstrapped from market basis swaps.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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    File URL: http://mpra.ub.uni-muenchen.de/22022/
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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22022.

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    Date of creation: 14 Nov 2008
    Date of revision: 24 Jan 2010
    Handle: RePEc:pra:mprapa:22022

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    Related research

    Keywords: liquidity; crisis; counterparty risk; yield curve; forward curve; discount curve; pricing; hedging; interest rate derivatives; FRAs; swaps; basis swaps; caps; floors; swaptions; basis adjustment; quanto adjustment; measure changes; no arbitrage; QuantLib;

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    1. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
    2. Uri Ron, 2000. "A Practical Guide to Swap Curve Construction," Working Papers 00-17, Bank of Canada.
    3. Leif Andersen, 2007. "Discount curve construction with tension splines," Review of Derivatives Research, Springer, vol. 10(3), pages 227-267, December.
    4. Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
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