Approximation of eigenvalues of spot cross volatility matrix with a view toward principal component analysis

Nien-Lin Liu and Hoang-Long Ngo

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Abstract: In order to study the geometry of interest rates market dynamics, Malliavin, Mancino and Recchioni [A non-parametric calibration of the HJM geometry: an application of It\^o calculus to financial statistics, {\it Japanese Journal of Mathematics}, 2, pp.55--77, 2007] introduced a scheme, which is based on the Fourier Series method, to estimate eigenvalues of a spot cross volatility matrix. In this paper, we present another estimation scheme based on the Quadratic Variation method. We first establish limit theorems for each scheme and then we use a stochastic volatility model of Heston's type to compare the effectiveness of these two schemes.

Date: 2014-09
New Economics Papers: this item is included in nep-ecm and nep-ger
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