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In this paper, we develop a theory of common decomposition for two correlatedBrownian motions, in which, by using change of time method, the correlatedBrownian motions are represented by a triplet of processes, $(X,Y,T)$, where$X$ and $Y$ are independent Brownian motions. We show the equivalent conditionsfor the triplet being independent. We discuss the connection and difference ofthe common decomposition with the local correlation model. Indicated by thediscussion, we propose a new method for constructing correlated Brownianmotions which performs very well in simulation. For applications, we use thesevery general results for pricing two-factor financial derivatives whose payoffsrely very much on the correlations of underlyings. And in addition, with thehelp of numerical method, we also make a discussion of the pricing deviationwhen substituting a constant correlation model for a general one.

Common Decomposition of Correlated Brownian Motions and its Financial Applications