English

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

Statistical Finance 2014-09-09 v1

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.

Keywords

Cite

@article{arxiv.1409.2214,
  title  = {Approximation of eigenvalues of spot cross volatility matrix with a view toward principal component analysis},
  author = {Nien-Lin Liu and Hoang-Long Ngo},
  journal= {arXiv preprint arXiv:1409.2214},
  year   = {2014}
}