Intraday Empirical Analysis and Modeling of Diversified World Stock Indices

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.