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.
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页码：55 / 77
页数：23
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