Extracting Correlations from the Market: New Correlation Parameterizations and the Calibration of a Stochastic Volatility LMM to CMS Spread Options

30 Pages Posted: 5 Jun 2010 Last revised: 16 Jun 2010

Matthias Lutz

Barclays

Date Written: June 16, 2010

Abstract

We present a new generic method for constructing correlation parameterizations that are always positive definite, and derive new flexible parametric forms.

Furthermore, we use the CMS spread option pricing formula from Kiesel & Lutz to calibrate a stochastic volatility LMM to caplets, swaptions and CMS spread options, and in this way extract the implied correlation information available from the market.

We investigate the performance of several correlation parameterizations and compare the implied correlation matrices with the corresponding empirical correlation matrices.

Keywords: Libor Market Model, Stochastic Volatility, CMS Spread Options, Correlation Calibration, Correlation Parameterization, Historical Foward Rate Correlations

JEL Classification: C13, C14, G12, G13

Suggested Citation

Lutz, Matthias, Extracting Correlations from the Market: New Correlation Parameterizations and the Calibration of a Stochastic Volatility LMM to CMS Spread Options (June 16, 2010). Available at SSRN: https://ssrn.com/abstract=1620356 or http://dx.doi.org/10.2139/ssrn.1620356

Matthias Lutz (Contact Author)

Barclays ( email )

London EC3P 3AH
United Kingdom

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