Modelling the Implied Probability of Stock Market Movements

39 Pages Posted: 6 Feb 2003

See all articles by Ernst Glatzer

Ernst Glatzer

Austrian National Bank - Economic Studies Division

Martin Scheicher

European Central Bank (ECB)

Date Written: January 2003

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.

Keywords: Option prices, risk-neutral density, volatility, spillover

JEL Classification: C22, C51, G13, G15

Suggested Citation

Glatzer, Ernst and Scheicher, Martin, Modelling the Implied Probability of Stock Market Movements (January 2003). ECB Working Paper No. 212. Available at SSRN: https://ssrn.com/abstract=376242

Ernst Glatzer (Contact Author)

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

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
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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