A non-parametric calibration of the HJM geometry: an application of Ito calculus to financial statistics

We show that the geometry of the Heath-Jarrow-Morton interest rates market dynamics can be non-parametrically calibrated by the observation of a single trajectory of the market evolution. Then the hypoellipticity of the infinitesimal generator can be exactly measured. On a data set of actual interest rates we show the prevalence of the hypoelliptic effect together with a sharp change of regime. Volatilities are computed by applying the Fourier cross-volatility estimation methodology.