Correlating Market Models

10 Pages Posted: 24 May 2003

See all articles by Bruce Choy

Bruce Choy

Commonwealth Bank of Australia

Tim Dun

ANZ Investment Bank

Erik Schlögl

University of Technology Sydney (UTS), Quantitative Finance Research Centre; University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management; Faculty of Science, Department of Statistics, University of Johannesburg; Financial Research Network (FIRN)

Date Written: April 8, 2003

Abstract

One of the key features differentiating methods of calibrating the lognormal LIBOR Market Model (LMM) to observed at-the-money option prices is the way in which these methods handle correlation between forward rates of different maturities. On the basis of the Pedersen (1998) calibration algorithm, we pursue the question of whether there is sufficient information contained in swaption prices to calibrate correlation, and what this means for the pricing of exotic derivatives off a calibrated LMM.

After briefly summarising the calibration method, we review the different concepts of correlation relevant to the LMM. The potential inconsistency between historical and implied correlation is found not to be an issue. We analyse the sensitivity of swaption prices and the calibrated volatility levels to correlations, and also study the trade-off between fitting correlations and fitting a calendar-time dependence of volatility. Subsequently, we discuss the effects of calibration ambiguity on derivatives priced off the calibrated model.

Keywords: LIBOR Market Models, interest rate term structure, model calibration, swaptions, correlation, implied volatility

JEL Classification: G13, E43

Suggested Citation

Choy, Bruce and Dun, Tim and Schloegl, Erik, Correlating Market Models (April 8, 2003). Available at SSRN: https://ssrn.com/abstract=395640 or http://dx.doi.org/10.2139/ssrn.395640

Bruce Choy

Commonwealth Bank of Australia ( email )

Melbourne
Australia

Tim Dun

ANZ Investment Bank ( email )

Erik Schloegl (Contact Author)

University of Technology Sydney (UTS), Quantitative Finance Research Centre ( email )

Ultimo
PO Box 123
Sydney, NSW 2007
Australia
+61 2 9514 2535 (Phone)

HOME PAGE: http://www.schlogl.com

University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management ( email )

Leslie Commerce Building
Rondebosch
Cape Town, Western Cape 7700
South Africa

Faculty of Science, Department of Statistics, University of Johannesburg ( email )

Auckland Park, 2006
South Africa

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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