Estimating the diffusion coefficient function for a diversified world stock index

2012 ◽  
Vol 56 (6) ◽  
pp. 1333-1349 ◽  
Author(s):  
Katja Ignatieva ◽  
Eckhard Platen
Keyword(s):  
Diffusion Coefficient ◽  
Stock Index ◽  
Coefficient Function ◽  
World Stock Index ◽  
Diversified World Stock Index

MODELING THE VOLATILITY AND EXPECTED VALUE OF A DIVERSIFIED WORLD INDEX

2004 ◽  
Vol 07 (04) ◽  
pp. 511-529 ◽  
Author(s):  
ECKHARD PLATEN
Keyword(s):  
Stock Market ◽  
Financial Market ◽  
Expected Value ◽  
Quadratic Variation ◽  
Stock Index ◽  
Square Root ◽  
Growth Optimal Portfolio ◽  
World Stock Index ◽  
Diversified World Stock Index

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.

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