Article Detail

Interest Rates After the Credit Crunch: Markets and Models Evolution

Journal 32: Applied Finance

Marco Bianchetti, Mattia Carlicchi

We present a quantitative study of the evolution of markets and models during the recent crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidence regarding the divergence 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 been deferred until August 2010. Finally, we show the robustness of the SABR model to calibrate the market volatility smile coherently with the new market evidences.

The financial crisis that began in the second half of 2007 has triggered, among its many other implications, a deep evolution phase of the classical framework adopted for trading derivatives. In particular, credit and liquidity issues were found to have macroscopical impacts on the prices of financial instruments, both plain vanillas and exotics. These are clearly visible in the market quotes of plain vanilla interest rate derivatives, such as deposits, forward rate agreements (FRA), swaps (IRS), and options (caps, floors, and swaptions). Since August 2007 the primary interest rates of the interbank market, such as Libor, Euribor, Eonia, and Federal Funds rate2, display large basis spreads that have reached up to 200 basis points. Similar divergences are also found between FRA rates and the forward rates implied by two consecutive deposits, and similarly, among swap rates with different floating leg tenors. Recently, the market has also included the effect of collateral agreements widely diffused among derivatives counterparties in the interbank market.

After the market evolution the standard no-arbitrage framework adapted to price derivatives, developed over forty years following the Copernican revolution of Black and Scholes (1973) and Merton (1973), became obsolete. Familiar relations described in standard textbooks [see, for example, Brigo and Mercurio (2006), Hull (2010)], such as the basic definition of forward interest rates, or the swap pricing formula, had to be abandoned. Also the fundamental idea of the construction of a single risk free yield curve, reflecting at the same time the present cost of funding of future cash flows and the level of forward rates, has been ruled out. The financial community has thus been forced to start the development of a new theoretical framework, including a larger set of relevant risk factors, and to review from scratch the no-arbitrage models used on the market for derivatives pricing and risk analysis. We refer to such old and new frameworks as “classical” and “modern,” respectively, to remark the shift of paradigm induced by the crisis.

The topics discussed in this paper sit at the heart of the present derivative’s market, with many consequences for trading, financial control, risk management, and IT, and are attracting a growing attention in the financial literature. To our knowledge, they have been approached by Kijima et al. (2008), Chibane and Sheldon (2009), Ametrano and Bianchetti (2009), Ametrano (2011), Fujii et al. (2009a, 2010a, 2011) in terms of multiplecurves; by Henrard (2007, 2009) and Fries (2010) using a first-principles approach; by Bianchetti (2010) using a foreign currency approach; by Fujii et al. (2009b), Mercurio (2009, 2010a, 2010b) and Amin (2010) within the Libor Market Model; by Pallavicini and Tarenghi (2010) and Moreni and Pallavicini (2010) within the HJM model; by Kenyon (2010) using a short rate model; by Morini (2009) in terms of counterparty risk; by Burghard and Kjaer (2010), Piterbarg (2010a, 2010b), Fujii et al. (2010b), Morini and Prampolini (2010) in terms of cost of funding.

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