Intraday Empirical Analysis and Modeling of Diversified World Stock Indices |
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| Authors: | Wolfgang Breymann Leah Kelly Eckhard Platen |
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| Affiliation: | 1.Eidgen?ssische Technische Hochschule Zürich,Risk Lab,Zürich,Switzerland;2.School of Finance & Economics and Department of Mathematical Sciences,University of Technology Sydney,Broadway,Australia;3.Institute for Data Analysis and Process Design,Zurich University of Applied Science Winterthur,Winterthur,Switzerland |
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| Abstract: | This paper proposes an approach to the intraday analysis of diversified world stock accumulation indices. The growth optimal portfolio (GOP) is used as reference unit or benchmark in a continuous financial market model. Diversified portfolios, covering the world stock market, are constructed and shown to approximate the GOP, providing the basis for a range of financial applications. The normalized GOP is modeled as a time transformed square root process of dimension four. Its dynamics are empirically verified for several world stock indices. Furthermore, the evolution of the transformed time is modeled as the integral over a rapidly evolving mean-reverting market activity process with deterministic volatility. The empirical findings suggest a rather simple and robust model for a world stock index that reflects the historical evolution, by using only a few readily observable parameters. Mathematics Subject Classification: (1991) primary 90A12, secondary 60G30,62P20 JEL Classification: G10, G13 |
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| Keywords: | world stock index intraday analysis growth optimal portfolio diversified portfolio market activity deseasonalization square root process |
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