Modeling the volatility and expected value of a diversified world index

Publisher:
World Scientific
Publication Type:
Journal Article
Citation:
International Journal of Theoretical and Applied Finance, 2004, 7 (4), pp. 511 - 529
Issue Date:
2004-01
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This paper considers a diversified world tock index in a continuous financial market with the growth optimal portfolio (GOP) as reference unit or benchmark. Diversified boradly based indices and portfolios, which include major world stock market indices, are shown to approximate the GOP. It is demonstated that a key financial quantity is the trend of a world index. It turns out tat 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 atock index as approximation of the discounted GTOP 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 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 te properties of an index and its volatility
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