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Everything You Always Wanted to Know About Multiple Interest Rate Curve Bootstrapping but Were Afraid to Ask

82 Pages Posted: 18 Feb 2013 Last revised: 3 Apr 2013

Ferdinando M. Ametrano

Milan Bicocca University - Department of Statistics and Quantitative Methods; QuantLib; Intesa Sanpaolo Bank; Banca IMI - Intesa Sanpaolo Group

Marco Bianchetti

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

Date Written: April 2, 2013

Abstract

After the credit and liquidity crisis started in summer 2007 the market has recognized that multiple yield curves are required for estimation of both discount and FRA rates with dfferent tenors (e.g. Overnight, Libor 3 months, etc.), consistently with the large basis spreads and the wide diffusion of bilateral collateral agreements and central counterparties for derivatives transactions observed on the market.

This paper recovers and extends our previous work to the modern multiple-curve bootstrapping of both discounting and FRA yield curves, consistently with the funding of market instruments. The theoretical pricing framework is introduced and modern pricing formulas for plain vanilla interest rate derivatives, such as Deposits, Forward Rate Agreements (FRA), Futures, Swaps, OIS, and Basis Swaps, are derived from scratch.

The concrete EUR market case is worked out, and many details are discussed regarding the selection of market instruments, synthetic market quotes, smooth interpolation, effect of OIS discounting, possible negative rates, turn of year effect, local vs non local delta sensitivities, performance and yield curve sanity checks.

The implementation of the proposed algorithms is available open source within the QuantLib framework.

Keywords: crisis, crunch, liquidity, funding, credit, counterparty risk, collateral, CSA, Libor, Euribor, Eonia, yield curve, discount curve, bootstrapping, no-arbitrage, pricing, hedging, derivatives, Deposit, FRA, Future, Swap, IRS, OIS, Basis Swap, turn of year, spline, Greeks, sensitivity, QuantLib

JEL Classification: E43, G12, G13

Suggested Citation

Ametrano, Ferdinando M. and Bianchetti, Marco, Everything You Always Wanted to Know About Multiple Interest Rate Curve Bootstrapping but Were Afraid to Ask (April 2, 2013). Available at SSRN: https://ssrn.com/abstract=2219548 or http://dx.doi.org/10.2139/ssrn.2219548

Ferdinando M. Ametrano

Milan Bicocca University - Department of Statistics and Quantitative Methods ( email )

Milano, 20126
Italy

QuantLib ( email )

HOME PAGE: http://quantlib.org

Intesa Sanpaolo Bank ( email )

Italy

Banca IMI - Intesa Sanpaolo Group ( email )

Largo Mattioli 3
Milano, 20121
Italy

Marco Bianchetti (Contact Author)

Intesa Sanpaolo - Financial and Market Risk Management ( email )

Piazza P. Ferrari 10
Milan, 20121
Italy

University of Bologna ( email )

Piazza Scaravilli 2
Bologna, 40100
Italy

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