We consider the pricing of derivatives written on the discrete realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the short-time limits of call options on both objects. We find that the difference  strongly depends on whether or not the stock price process has jumps. 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. To illustrate our results , we also present some numerical examples.
We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic 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 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 . We compare the methods and illustrate our results by some numerical examples.
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short-time limits of call
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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
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to price European-style options efficiently. To
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