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The Price‐Volatility Feedback Rate: An Implementable Mathematical Indicator of Market Stability

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  • Emilio Barucci
  • Paul Malliavin
  • Maria Elvira Mancino
  • Roberto Renò
  • Anton Thalmaier

Abstract

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.

Suggested Citation

  • Emilio Barucci & Paul Malliavin & Maria Elvira Mancino & Roberto Renò & Anton Thalmaier, 2003. "The Price‐Volatility Feedback Rate: An Implementable Mathematical Indicator of Market Stability," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 17-35, January.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:1:p:17-35
    DOI: 10.1111/1467-9965.t01-1-00003
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    References listed on IDEAS

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    1. David S. Bates, "undated". "Testing Option Pricing Models," Rodney L. White Center for Financial Research Working Papers 14-95, Wharton School Rodney L. White Center for Financial Research.
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    9. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    10. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Andrea Pascucci & Marco Di Francesco, 2005. "On the complete model with stochastic volatility by Hobson and Rogers," Finance 0503013, University Library of Munich, Germany.
    2. Allaj, Erindi & Sanfelici, Simona, 2023. "Early Warning Systems for identifying financial instability," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1777-1803.

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