Bianchetti, Marco (2008): Two Curves, One Price :Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves.

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Abstract
We revisit the problem of pricing and hedging plain vanilla singlecurrency 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 doublecurvesinglecurrency framework, adopted by the market after the creditcrunch crisis started in summer 2007, standard singlecurve noarbitrage relations are no longer valid, and can be recovered by taking properly into account the forward basis bootstrapped from market basis swaps.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 microterm structure that may induce appreciable effects on the price of interest rate instruments. By recurring to the foreigncurrency analogy we also derive generalised noarbitrage doublecurve marketlike formulas for basic plain vanilla interest rate derivatives, FRAs, swaps, caps/floors and swaptions in particular. These expressions include a quanto adjustment typical of crosscurrency 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 doublecurve prices, in principle, not arbitrage free. Both the forward basis and the quanto adjustment find a natural financial explanation in terms of counterparty risk.
Item Type:  MPRA Paper 

Original Title:  Two Curves, One Price :Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves 
Language:  English 
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 
Subjects:  E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates > E43  Interest Rates: Determination, Term Structure, and Effects G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing ; Futures Pricing 
Item ID:  22022 
Depositing User:  Marco Bianchetti 
Date Deposited:  10. Apr 2010 23:59 
Last Modified:  21. Feb 2015 22:04 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/22022 