Abstract

http://ssrn.com/abstract=1711774
 
 

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Citations (7)



 


 



Asymptotic and Exact Pricing of Options on Variance


Martin Keller-Ressel


TU Berlin

Johannes Muhle-Karbe


ETH Zürich; Swiss Finance Institute

November 19, 2010


Abstract:     
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)
TU Berlin ( email )
Strasse des 17
Juni 135
Berlin, 10623
Germany
Johannes Muhle-Karbe
ETH Zürich ( email )
Rämistrasse 101
CH-8092 Zürich
Switzerland
+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
Switzerland
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