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首页> 外文期刊>Selected Topics in Signal Processing, IEEE Journal of >Covariance Matrix Estimation for Interest-Rate Risk Modeling via Smooth and Monotone Regularization
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Covariance Matrix Estimation for Interest-Rate Risk Modeling via Smooth and Monotone Regularization

机译：通过平滑和单调正则化的利率风险模型的协方差矩阵估计

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摘要

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.
机译：在高维环境中估计协方差矩阵是现代金融的核心难题。众所周知，样本协方差矩阵无法在高维度上提供足够的样本，而样本不足，可能会导致Markowitz框架中优化组合的严重风险低估。为了在这种情况下提供有用的估计，已经开发了利用数据中附加结构的各种改进的协方差矩阵估计。流行的方法包括低秩（主要成分和因子分析）模型，带状结构，稀疏逆协方差和参数模型。我们针对具有空间顺序的随机向量研究了一种新颖的非参数先验：我们假设协方差相对于这种顺序是单调且平滑的。这自然适用于诸如利率风险建模之类的问题，在这些问题中，到期日更远的合同的相关性会衰减。我们针对此估计问题提出了凸优化（半定规划）公式，并开发了有效的算法。我们将我们的框架用于欧洲美元期货的风险衡量和预测，研究有限，缺失和异步的数据，并表明与现有方法相比，它提供了更准确的有效（正定）协方差估计。

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