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P. Carr and L. Wu, “Variance Risk Premia,” (Working seminar paper, Bloomberg LP, Courant Institute, and Baruch College, 21 March 2005).

P. Carr and L. Wu, “Variance Risk Premia,” (Working seminar paper, Bloomberg LP, Courant Institute, and Baruch College, 21 March 2005).

Abstract: We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. Ignoring the small approximation error, the difference between the realized variance and this synthetic variance swap rate quantifies the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premium on five stock indexes and 35 individual stocks.