Abstract
In order to test whether scaling exists in finance at the world level, we test whether the average growth rates and volatility of market capitalization ( MC ) depend on the level of MC .W e analyze the MC for 54 worldwide stock indices and 48 worldwide bond indices. We find that (i) the average growth raterof the MC and (ii) the standard deviation σ(r )o f growth ratesr decrease both with MC as power laws, with exponents αw =0 .28 ± 0.09 and βw =0 .12 ± 0.04. We define a stochastic process in order to model the scaling results we find for worldwide stock and bond indices. We establish a power-law relationship between the MC of a country's financial market and the gross domestic product (GDP) of the same country.
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