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Multi-underlying stochastic volatility
Hi folks,I heard there is a method called "alpha-parameterization" to define vol/vol and stock/vol. correlations for mulit underlying Heston model.Let S = stock, V= volatilityCorr( S(i) V(j) ) = Corr( S(j) V(j) ) * Corr( S(i) S(j) ) ******************************** (1)Corr( V(i) V(j) ) = Corr( S(i) V(i) ) * Corr( S(j) V(j) ) * Corr( S(i) S(j) ) + sqrt ( 1 - Corr( S(i) V(i) ) ^ 2) * sqrt ( 1 - Corr( S(j) V(j) ) ^ 2) ************************************* (2)May I know how to derive these 2 equations above ? Any good ref. papers appreciated as well.thx,