V, and V, Bivariate NormalConditional on the value of Vi, V, is normal withmeanV,-μi+po2a201and standard deviation , /1-p? where μ1, μ2, 1,and o, are the unconditional means and SDs ofVi and V, and p is the coefficient of correlationbetween V, and V2RiskManagementandFinancialInstitutions3e,Chapter11,CopyrightJohnC.Hull201211
V1 and V2 Bivariate Normal ⚫ Conditional on the value of V1 , V2 is normal with mean and standard deviation where m1, , m2 , s1 , and s2 are the unconditional means and SDs of V1 and V2 and r is the coefficient of correlation between V1 and V2 Risk Management and Financial Institutions 3e, Chapter 11, Copyright © John C. Hull 2012 11 1 1 1 2 2 s − m m + rs V 2 2 s 1− r
Multivariate NormalDistributionFairly easyto handleA yariance-covariancematrix definesthe variances of and correlationsbetween variables To be internally consistent a variance-covariance matrix must be positivesemidefinite12RiskManagementandFinancialInstitutions3e,Chapter11,CopyrightJohnC.Hull2012
Multivariate Normal Distribution ⚫ Fairly easy to handle ⚫ A variance-covariance matrix defines the variances of and correlations between variables ⚫ To be internally consistent a variancecovariance matrix must be positive semidefinite Risk Management and Financial Institutions 3e, Chapter 11, Copyright © John C. Hull 2012 12