Before revision:  To study the exact valuation of options on the discrete realized varianceitself, we then propose a novel approach that allows to apply Fourier-Laplace techniques to price European-style options efficiently.
After revision:  To study the exact valuation of options on the discretely sampled realized variance. One of the methods is approximative; it is based on correcting prices of options on quadratic variation by our asymptotic results. The other method is exact; it uses a novel randomization approach and applies Fourier-Laplace techniques to price European-style options efficiently.