The generalized Stein/Rubinstein covariance formula and its application to estimate real systematic risk

This paper generalizes Stein’s, Rubinstein’s and Losq and Chateau’s covariance formula to the case where both variables are functions of multivariate normal random variables. The resulting formula is extremely useful for either implicit functions of, or nonpolynomials of, multivariate normal random variables, such as exponential functions. An application of the use of the generalized Stein/Rubinstein covariance formula to the estimation of real systemic risk is provided to illustrate the results.