Modelling the Implied Probability of Stock Market Declines

27 Pages Posted: 16 Feb 2002

See all articles by Ernst Glatzer

Ernst Glatzer

Austrian National Bank - Economic Studies Division

Martin Scheicher

European Central Bank (ECB)

Date Written: June 2002

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 and a volatility-smoothing method. We discuss the time series behaviour of the moments of the two models and we examine linkages of the moments to macroeconomic variables, the US stock markets and credit risk. We find that the risk-neutral densities exhibit pronounced negative skewness. The spline and mixture models produce a similar shape for the entire density, but their pricing performance differs. Finally, we observe a significant volatility spillover effect, 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 and Scheicher, Martin, Modelling the Implied Probability of Stock Market Declines (June 2002). Available at SSRN: https://ssrn.com/abstract=300199 or http://dx.doi.org/10.2139/ssrn.300199

Ernst Glatzer

Austrian National Bank - Economic Studies Division ( email )

POB 61
Otto Wagner Platz 3
A-1011 Vienna
Austria
+43+1 40420 7423 (Phone)
+43+1 40420 7499 (Fax)

Martin Scheicher (Contact Author)

European Central Bank (ECB) ( email )

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Frankfurt am Main, 60314
Germany
+49 69 1344 (Phone)
+49 69 1344 7949 (Fax)

HOME PAGE: http://www.ecb.europa.eu

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