Interest Rates After the Credit Crunch: Multiple Curve Vanilla Derivatives and SABR

26 Pages Posted: 14 Mar 2011 Last revised: 3 Apr 2012

Marco Bianchetti

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

Mattia Carlicchi

Intesa Sanpaolo - Market Risk Management

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Date Written: March 11, 2011

Abstract

We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects.

We also review the new modern pricing approach prevailing among practitioners, based on multiple yield curves reflecting the different credit and liquidity risk of Libor rates with different tenors and the overnight discounting of cash flows originated by derivative transactions under collateral with daily margination. We report the classical and modern no-arbitrage pricing formulas for plain vanilla interest rate derivatives, and the multiple-curve generalization of the market standard SABR model with stochastic volatility.

We then report the results of an empirical analysis on recent market data comparing pre- and post-credit crunch pricing methodologies and showing the transition of the market practice from the classical to the modern framework. In particular, we prove that the market of Interest Rate Swaps has abandoned since March 2010 the classical Single-Curve pricing approach, typical of the pre-credit crunch interest rate world, and has adopted the modern Multiple-Curve CSA approach, thus incorporating credit and liquidity effects into market prices. The same analysis is applied to European Caps/Floors, finding that the full transition to the modern Multiple-Curve CSA approach has retarded up to August 2010. Finally, we show the robustness of the SABR model to calibrate the market volatility smile coherently with the new market evidences.

Keywords: crisis, liquidity, credit, counterparty, risk, fixed income, Libor, Euribor, Eonia, yield curve, forward curve, discount curve, single curve, multiple curve, volatility surface, collateral, CSA discounting, no arbitrage, pricing, interest rate derivative

JEL Classification: E43, G12, G13

Suggested Citation

Bianchetti, Marco and Carlicchi, Mattia, Interest Rates After the Credit Crunch: Multiple Curve Vanilla Derivatives and SABR (March 11, 2011). Available at SSRN: https://ssrn.com/abstract=1783070 or http://dx.doi.org/10.2139/ssrn.1783070

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

Mattia Carlicchi

Intesa Sanpaolo - Market Risk Management ( email )

Piazza P. Ferrari 10
Milan, 20121
Italy

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