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Models of Financial Return With Time-Varying Zero Probability

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  • Sucarrat, Genaro
  • Grønneberg, Steffen

Abstract

The probability of an observed financial return being equal to zero is not necessarily zero. This can be due to price discreteness or rounding error, liquidity issues (e.g. low trading volume), market closures, data issues (e.g. data imputation due to missing values), characteristics specific to the market, and so on. Moreover, the zero probability may change and depend on market conditions. In standard models of return volatility, however, e.g. ARCH, SV and continuous time models, the zero probability is zero, constant or both. We propose a new class of models that allows for a time-varying zero probability, and which can be combined with standard models of return volatility: They are nested and obtained as special cases when the zero probability is constant and equal to zero. Another attraction is that the return properties of the new class (e.g. volatility, skewness, kurtosis, Value-at-Risk, Expected Shortfall) are obtained as functions of the underlying volatility model. The new class allows for autoregressive conditional dynamics in both the zero probability and volatility specifications, and for additional covariates. Simulations show parameter and risk estimates are biased if zeros are not appropriately handled, and an application illustrates that risk-estimates can be substantially biased in practice if the time-varying zero probability is not accommodated.

Suggested Citation

  • Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:68931
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    References listed on IDEAS

    as
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    Cited by:

    1. Francq, Christian & Sucarrat, Genaro, 2017. "An equation-by-equation estimator of a multivariate log-GARCH-X model of financial returns," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 16-32.
    2. Escribano, Alvaro & Sucarrat, Genaro, 2016. "Equation-by-Equation Estimation of Multivariate Periodic Electricity Price Volatility," MPRA Paper 72736, University Library of Munich, Germany.
    3. Francq, Christian & Sucarrat, Genaro, 2015. "Equation-by-Equation Estimation of a Multivariate Log-GARCH-X Model of Financial Returns," MPRA Paper 67140, University Library of Munich, Germany.

    More about this item

    Keywords

    Financial return; volatility; zero-inflated return; GARCH; log-GARCH; ACL;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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