Asymptotic and Exact Pricing of Options on Variance
Dresden University of Technology - Department of Mathematics
ETH Zürich; Swiss Finance Institute; University of Michigan at Ann Arbor
November 19, 2010
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.
Number of Pages in PDF File: 22
Keywords: Realized Variance, Quadratic Variation, Option Pricing, Small-Time Asymptotics, Fourier-Laplace Methods
JEL Classification: C63, G19
Date posted: November 20, 2010 ; Last revised: December 15, 2010
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