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. We analyze the MC for 54 worldwide stock indices and 48 worldwide bond indices. We find that (i) the average growth rate (r) of the MC and (ii) the standard deviation sigma(r) of growth rates r decrease both with MC as power laws, with exponents alpha(w) = 0.28 +/- 0.09 and beta(w) = 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.