  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.
