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The Price‐Volatility Feedback Rate: An Implementable Mathematical Indicator of Market Stability
Author(s) -
Barucci Emilio,
Malliavin Paul,
Mancino Maria Elvira,
Renò Roberto,
Thalmaier Anton
Publication year - 2003
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.t01-1-00003
Subject(s) - volatility (finance) , infinitesimal , stability (learning theory) , econometrics , economics , mathematics , measure (data warehouse) , ordinary differential equation , asset (computer security) , series (stratigraphy) , mathematical economics , differential equation , computer science , mathematical analysis , paleontology , computer security , database , machine learning , biology
Geometric analysis of iterated cross‐volatilities of asset prices is adopted to assess the stability of the (risk‐free) measure under infinitesimal perturbations. Perturbations of asset prices evolve through time according to an ordinary linear differential equation (hedged transfer). The decay (feedback) rate is explicitly computed through a Fourier series method implemented on high frequency time series.