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

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
Settore SECS-P/06 - Economia Applicata
Finite dimensional realizations; Fourier analysis; high frequency data; HJM equation; hypo ellipticity; Lie brackets; non-parametric estimation; stochastic volatility
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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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