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.

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

MANCINO, MARIA ELVIRA;
2007-01-01

Abstract

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.
2007
non-parametric estimation - stochastic volatility - Fourier analysis - high frequency data - HJM equation - hypoellipticity - Lie brackets - finite dimensional realizations
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/79775
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