Geodesic
On the approximate calculation of the coefficient of correlation between two functions of dependent random variates
Matematičeskie zametki, Tome 7 (1970) no. 5, pp. 617-625.

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A general formula is derived for the calculation of the coefficient of correlation between functions of random variates. A formula is presented for the approximate calculation of the correlation coefficient with error estimation. The case of the calculation of the coefficient of correlation between $\ln\xi$ and $\ln\eta$ with $\xi$ and $\eta$ connected by gamma correlation is considered in detail. 
@article{MZM_1970_7_5_a9,
     author = {I. O. Sarmanov},
     title = {On the approximate calculation of the coefficient of correlation between two functions of dependent random variates},
     journal = {Matemati\v{c}eskie zametki},
     pages = {617--625},
     publisher = {mathdoc},
     volume = {7},
     number = {5},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_5_a9/}
}
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I. O. Sarmanov. On the approximate calculation of the coefficient of correlation between two functions of dependent random variates. Matematičeskie zametki, Tome 7 (1970) no. 5, pp. 617-625. http://geodesic.mathdoc.fr/item/MZM_1970_7_5_a9/