Japanese Journal of Mathematics

, Volume 2, Issue 1, pp 55–77 | Cite as

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

  • Paul Malliavin
  • Maria Elvira Mancino
  • Maria Cristina Recchioni
Special Feature: Award of the 1st Gauss Prize to K. Ito

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.

Keywords and phrases:

non-parametric estimation stochastic volatility Fourier analysis high frequency data HJM equation hypoellipticity Lie brackets finite dimensional realizations 

Mathematics Subject Classification (2000):

35H10 42B05 62H12 62P05 

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Copyright information

© The Mathematical Society of Japan and Springer 2007

Authors and Affiliations

  • Paul Malliavin
    • 1
  • Maria Elvira Mancino
    • 2
  • Maria Cristina Recchioni
    • 3
  1. 1.ParisFrance
  2. 2.Dipartimento di Matematica per le DecisioniFirenzeItaly
  3. 3.Dipartimento di Scienze Sociali “D. Serrani”Università Politecnica delle MarcheAnconaItaly

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