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Covariance matrix estimation for interest-rate risk modeling via smooth and monotone regularization

Malioutov, Dmitry M. and Çorum, Aycan Adrian and Çetin, Müjdat (2016) Covariance matrix estimation for interest-rate risk modeling via smooth and monotone regularization. IEEE Journal of Selected Topics in Signal Processing, 10 (6). pp. 1006-1014. ISSN 1932-4553 (Print) 1941-0484 (Online)

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Official URL: http://dx.doi.org/10.1109/JSTSP.2016.2555285

Abstract

Estimating covariance matrices in high-dimensional settings is a challenging problem central to modern finance. The sample covariance matrix is well-known to give poor estimates in high dimensions with insufficient samples, and may cause severe risk underestimates of optimized portfolios in the Markowitz framework. In order to provide useful estimates in this regime, a variety of improved covariance matrix estimates have been developed that exploit additional structure in the data. Popular approaches include low-rank (principal component and factor analysis) models, banded structure, sparse inverse covariances, and parametric models. We investigate a novel nonparametric prior for random vectors which have a spatial ordering: we assume that the covariance is monotone and smooth with respect to this ordering. This applies naturally to problems such as interest-rate risk modeling, where correlations decay for contracts that are further apart in terms of expiration dates. We propose a convex optimization (semi-definite programming) formulation for this estimation problem, and develop efficient algorithms. We apply our framework for risk measurement and forecasting with Eurodollar futures, investigate limited, missing and asynchronous data, and show that it provides valid (positive-definite) covariance estimates more accurate than existing methods.

Item Type:Article
Uncontrolled Keywords:High-dimensional covariance estimation; Smooth-monotone regularization; Semi-definite programming
Subjects:T Technology > TK Electrical engineering. Electronics Nuclear engineering
H Social Sciences > HG Finance
ID Code:29699
Deposited By:Müjdat Çetin
Deposited On:06 Oct 2016 15:39
Last Modified:14 Nov 2016 14:25

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