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

Marco Bianchetti

Intesa Sanpaolo - Financial and Market Risk Management; University of Bologna

November 14, 2008

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by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations are no longer valid, and can be recovered by taking properly into account the forward basis bootstrapped from market basis swaps.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.

Number of Pages in PDF File: 29

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

JEL Classification: E43, G12, G13

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Date posted: January 29, 2009 ; Last revised: June 22, 2016

Suggested Citation

Bianchetti, Marco, Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves (November 14, 2008). Available at SSRN: https://ssrn.com/abstract=1334356 or http://dx.doi.org/10.2139/ssrn.1334356

Contact Information

Marco Bianchetti (Contact Author)
Intesa Sanpaolo - Financial and Market Risk Management ( email )
Piazza P. Ferrari 10
Milan, 20121
University of Bologna ( email )
Piazza Scaravilli 2
Bologna, 40100
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