New York. 7th December 2011
The Numerical Algorithms Group (NAG) and the finance publication Wilmott hosted a city seminar for finance industry professionals on 7th December 2011. It was a free seminar, with speakers from industry and academia, and was open to those working within the finance industry.
Normal linear factor models provide an intuitive and common first step in the modeling of strongly correlated assets, but the assumption of normality is unrealistic for most financial market distributions, which typically display fat tails and skew. In order to improve their distributional accuracy while retaining their simplicity, we have generalized a class of factor models by permitting multiple regimes, thereby adding the parametric flexibility to capture fat tails and skew, while keeping the useful concept of factor loadings. Using maximum likelihood inference, we have estimated our multi-regime factor model with USD interest rate swap data. The regime-dependent factor loadings are consistent with an intuitive picture of multi-regime market dynamics. In addition, the posterior probabilities provide estimates of the time-series of regime residency. I will discuss these results and our general observations concerning the choice of the number of regimes, the influence of the regime-switching assumptions on the estimates, and the application of the model to risk management.
Nicholas J Higham – The University of Manchester
Functions of Matrices and Nearest Correlation Matrices
Functions of matrices, which date back to the 1858 paper by Cayley that introduced matrix algebra, are of growing interest in many application areas due to the succinct and insightful way they allow problems to be formulated and solutions to be expressed. They are a valuable part of the problem solver's toolbox, as I will illustrate with practical examples relevant to finance. I will outline the main matrix functions of interest and indicate the state of the art in methods for computing them. I will also describe the University of Manchester's collaboration with NAG, through a Knowledge Transfer Partnership, to extend the repertoire of matrix function codes in the NAG Library.
In many practical applications involving statistical modeling it is required to adjust an approximate, empirically obtained correlation matrix so that it has the three required properties of symmetry, positive semidefiniteness, and unit diagonal. I will give an overview of existing methods for computing the nearest correlation matrix to a given matrix and discuss an extension of the problem that incorporates factor structure, also indicating available software.
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Venue: 7city Learning, 55 Broad Street, 3rd Floor, New York, NY 10004