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Asymptotic and Exact Pricing of Options on Variance

Martin Keller-Ressel

Dresden University of Technology - Department of Mathematics

Johannes Muhle-Karbe

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

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Date posted: November 20, 2010 ; Last revised: December 15, 2010

Suggested Citation

Keller-Ressel, Martin and Muhle-Karbe, Johannes, Asymptotic and Exact Pricing of Options on Variance (November 19, 2010). Available at SSRN: http://ssrn.com/abstract=1711774 or http://dx.doi.org/10.2139/ssrn.1711774

Contact Information

Martin Keller-Ressel (Contact Author)
Dresden University of Technology - Department of Mathematics ( email )
Zellescher Weg 12-14
Willers-Bau C 112
Dresden, 01062
Johannes Muhle-Karbe
ETH Zürich ( email )
Rämistrasse 101
CH-8092 Zürich
+41 44 632 3087 (Phone)
HOME PAGE: http://www.math.ethz.ch/~jmuhleka/
Swiss Finance Institute ( email )
c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
University of Michigan at Ann Arbor ( email )
500 S. State Street
Ann Arbor, MI 48109
United States
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