2012): “Asymptotic and exact pricing of options on variance,”Finance and Stochastics, forthcoming

Abstract. We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the re-alized variance is usually approximated by its continuous-time limit, the qua-dratic variation of the underlying log-price. Here, we characterize the small-time limits of options on both objects. We find that the difference between them strongly depends on whether or not the stock price process has jumps. Subsequently, we propose two new methods to evaluate the price of options on the discretely sampled realized variance. One of the methods is approxima-tive; 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. We compare the methods and illustrate our results by some numerical examples. 1