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Modelling the implied probability of stock market movements

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  • Glatzer, Ernst
  • Scheicher, Martin

Abstract

In this paper we study risk-neutral densities (RNDs) for the German stock market. The use of option prices allows us to quantify the risk-neutral probabilities of various levels of the DAX index. For the period from December 1995 to November 2001, we implement the mixture of log-normals model and a volatility-smoothing method. We discuss the time series behaviour of the implied PDFs and we examine the relations between the moments and observable factors such as macroeconomic variables, the US stock markets and credit risk. We find that the risk-neutral densities exhibit pronounced negative skewness. Our second main observation is a significant spillover of volatility, as the implied volatility and kurtosis of the DAX RND are mostly driven by the volatility of US stock prices. JEL Classification: C22, C51, G13, G15

Suggested Citation

  • Glatzer, Ernst & Scheicher, Martin, 2003. "Modelling the implied probability of stock market movements," Working Paper Series 212, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:2003212
    Note: 152802
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    References listed on IDEAS

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    Cited by:

    1. Vahamaa, Sami, 2005. "Option-implied asymmetries in bond market expectations around monetary policy actions of the ECB," Journal of Economics and Business, Elsevier, vol. 57(1), pages 23-38.
    2. Martin Scheicher, 2003. "What drives investor risk aversion? Daily evidence from the German equity market," BIS Quarterly Review, Bank for International Settlements, June.
    3. Ascari, Guido & Rankin, Neil, 2007. "Perpetual youth and endogenous labor supply: A problem and a possible solution," Journal of Macroeconomics, Elsevier, vol. 29(4), pages 708-723, December.
    4. Salazar Celis, Oliver & Liang, Lingzhi & Lemmens, Damiaan & Tempère, Jacques & Cuyt, Annie, 2015. "Determining and benchmarking risk neutral distributions implied from option prices," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 372-387.

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    More about this item

    Keywords

    Option prices; risk-neutral density; spillover; volatility;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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