A JOINT EMPIRICAL AND THEORETICAL INVESTIGATION OF THE MODES OF DEFORMATION OF SWAPTION MATRICES: IMPLICATIONS FOR MODEL CHOICE

Riccardo Rebonato () and Mark Joshi ()
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Riccardo Rebonato: Quantitative Research Centre, Group Risk, Royal Bank of Scotland, 2nd Floor, Waterhouse Square, 138–142, Holborn, London, EC1N 2TH, UK;
Mark Joshi: Quantitative Research Centre, Group Risk, Royal Bank of Scotland, 2nd Floor, Waterhouse Square, 138–142, Holborn, London, EC1N 2TH, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2002, vol. 05, issue 07, 667-694

Abstract: We present a joint empirical/theoretical analysis of the changes in the implied volatility swaption matrix for two currencies (USD and DEM/EUR). We recognize the existence of a small number of recognizable shape patterns, and comment about the speed of transition between them. By Principal/Component/Analyzing the associated correlation and covariance matrices we highlight a non/trivial interpretation for the leading eigenvectors. We also compare the empirically obtained eigenvectors and eigenvalues with the corresponding quantities produced by the stochastic/volatility LIBOR market model of Joshi and Rebonato[10]. This allows us to perform a measure-independent comparison that is of intrinsic interest, and that can also provide a general blueprint for analyzing the realism of and choosing among similarly-fitting stochastic models. We find that mean reversion of the instantaneous volatility is a necessary condition in order to obatin the market-observed shape of the first eigenvector associated with the covariance matrix.

Keywords: LIBOR market model; stochastic volatility; swaption matrix (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1142/S0219024902001651

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