The Zeeman Effect in Finance: Libor Spectroscopy and Basis Risk Management

Marco, Bianchetti (2011): The Zeeman Effect in Finance: Libor Spectroscopy and Basis Risk Management.

Abstract

Once upon a time there was a classical financial world in which all the Libors were equal. Standard textbooks taught that simple relations held, such that, for example, a 6 months Libor Deposit was replicable with a 3 months Libor Deposits plus a 3x6 months Forward Rate Agreement (FRA), and that Libor was a good proxy of the risk free rate required as basic building block of no-arbitrage pricing theory. Nowadays, in the modern financial world after the credit crunch, some Libors are more equal than others, depending on their rate tenor, and classical formulas are history. Banks are not anymore “too big to fail”, Libors are fixed by panels of risky banks, and they are risky rates themselves. These simple empirical facts carry very important consequences in derivative’s trading and risk management, such as, for example, basis risk, collateralization and regulatory pressure in favour of Central Counterparties. Something that should be carefully considered by anyone managing even a single plain vanilla Swap. In this qualitative note we review the problem trying to shed some light on this modern animal farm, recurring to an analogy with quantum physics, the Zeeman effect.

• Item Type: MPRA Paper
• Language: English
• Keywords: crisis; liquidity; credit; counterparty; risk; fixed income; Libor; Euribor; Eonia; yield curve; forward curve; discount curve; single curve; multiple curve; collateral; CSA-discounting; liquidity; funding; no arbitrage; pricing; interest rate derivatives; Deposit; FRA; Swap; OIS; Basis Swap; Zeeman; Lorentz; quantum mechanics; atomic physics
• 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

References

[1] See Zeeman’s biography at the Nobel Prize website http://nobelprize.org and Wikipedia at http://en.wikipedia.org/wiki/Pieter_Zeeman.

[2] See P. Zeeman, "The Effect of Magnetisation on the Nature of Light Emitted by a Substance", Nature 55, p. 347, 11 February 1897; R. P. Feynman, R. Leighton, M. Sands, “The Feynman Lectures on Physics”, vol. 3, ch. 12-4; Wikipedia at http://en.wikipedia.org/wiki/Zeeman_effect.

[3] D. Wood, “Libor fix”, Risk Magazine, 1 Jul. 2011.

[4] C. Snider, T. Youle, “Does the Libor reflect banks’ borrowing costs ?”, 2 Apr. 2010, SSRN working paper, http://ssrn.com/abstract=1569603

[5] M. Morini, ”Solving the Puzzle in the Interest Rate Market”, Oct. 2009, SSRN working paper, http://ssrn.com/abstract=1506046.

[6] B. Tuckman and P. Porfirio, “Interest Rate Parity, Money Market Basis Swap, and Cross-Currency Basis Swap”, Lehman Brothers Fixed Income Liquid Markets Research – LMR Quarterly , 2004, Q2.

[7] ISDA, “ISDA Margin survey 2011”, 14 Apr. 2011, http://www.isda.org.

[8] V. Piterbarg, “Funding beyond discounting: collateral agreements and derivatives pricing“, Risk, Feb. 2010.

[9] M. Morini, A. Prampolini, ”Risky Funding with counterparty and liquidity charges”, Risk, Mar. 2011.

[10] C. Burgard, M. Kjaer, “In the Balance”, 14 Mar. 2011, SSRN working paper, http://ssrn.com/abstract=1785262

[11] C. Fries, “Discounting Revisited – Valuations under Funding Costs, Counterparty Risk and Collateralization”, 15 May 2010, SSRN working paper, http://ssrn.com/abstract=1609587.

[12] A. Castagna, “”Funding, Liquidity, Credit and Counterparty Risk: Links and Implications”, DefaultRisk.com working paper, http://www.defaultrisk.com/pp_liqty_53.htm.

[13] M. Fujii and A. Takahashi, “Choice of Collateral Currency”, Risk, Jan. 2011.

[14] F. Ametrano, M. Bianchetti, “Bootstrapping the Illiquidity: Multiple Yield Curves Construction For Market Coherent Forward Rates Estimation”, in “Modeling Interest Rates: Latest Advances for Derivatives Pricing”, edited by F. Mercurio, Risk Books, 2009.

[15] H. Lipman, F. Mercurio, “The New Swap Math”, Bloomberg Markets, Feb. 2010.

[16] M. Bianchetti, “Two Curves, One Price”, Risk, August 2010.

[17] M. Bianchetti, M. Carlicchi “Interest Rates after the Credit Crunch: Multiple Curve Vanilla Derivatives and SABR”, SSRN working paper, http://ssrn.com/abstract=1783070.

[18] N. Sawyer, “ISDA working group to draw up new, standardised CSA”, Risk, 15 Feb. 2011.

[19] D. Brigo, A. Capponi, A. Pallavicini, V. Papatheodorou, “Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment including Re-Hypotecation and Netting”, SSRN working paper, http://ssrn.com/abstract=1744101.

[20] F. Mercurio, “Modern LIBOR Market Models: Using Different Curves for Projecting Rates and for Discounting”, International Journal of Theoretical and Applied Finance, Vol. 13, No. 1, 2010, pp. 113-137.

[21] D. Brigo and F. Mercurio, “Interest Rate Models: Theory and Practice”, 2nd edition, 2006, Springer.

[22] Leif B.G. Andersen and Vladimir V. Piterbarg, “Interest Rate Modeling”, 1st edition, 2010, Atlantic Financial Press.