MODELING THE VOLATILITY AND EXPECTED VALUE OF A DIVERSIFIED WORLD INDEX

Eckhard Platen ()

International Journal of Theoretical and Applied Finance (IJTAF), 2004, vol. 07, issue 04, 511-529

Abstract: This paper considers a diversified world stock index in a continuous financial market with the growth optimal portfolio (GOP) as reference unit or benchmark. Diversified broadly based indices and portfolios, which include major world stock market indices, are shown to approximate the GOP. It is demonstrated that a key financial quantity is the trend of a world index. It turns out that it can be directly observed since the expected increments of the index equal four times those of the quadratic variation of its square root. Using a world stock index as approximation of the discounted GOP it is shown that, in reality, the trend of the discounted GOP does not vary greatly in the long term. This leads for a diversified world index to a natural model, where the index is a transformed square root process of dimension four. The squared index volatility appears then as the inverse of the square root process. This feature explains most of the properties of an index and its volatility.

Keywords: Diversified world stock index; stochastic volatility; benchmark model; growth optimal portfolio; square root process; market activity; JEL classification code G10; JEL classification code G13; primary 90A12; secondary 60G30; secondary 62P20 (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (20)

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Working Paper: Modeling the Volatility and Expected Value of a Diversified World Index (2003)
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DOI: 10.1142/S0219024904002499

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