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

被引：5

作者：

Malliavin, Paul

Mancino, Maria Elvira ^{[1
]}

Recchioni, Maria Cristina ^{[2
]}

机构：

[1] Dipartimento Matemat Decis, I-50134 Florence, Italy

[2] Univ Politecn Marche, Dipartimento Sci Sociali D Serrani, I-60121 Ancona, Italy

来源：

JAPANESE JOURNAL OF MATHEMATICS | 2007年 / 2卷 / 01期

关键词：

non-parametric estimation; stochastic volatility; Fourier analysis; high frequency data; HJM equation; hypoellipticity; Lie brackets; finite dimensional realizations; FINITE-DIMENSIONAL REALIZATIONS; CONTINGENT CLAIMS; EQUATIONS; VOLATILITY; EXISTENCE;

D O I：

10.1007/s11537-007-0666-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：55 / 77

页数：23

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