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A CLOSED-FORM PRICING FORMULA FOR VARIANCE SWAPS WITH MEAN-REVERTING GAUSSIAN VOLATILITY

Part of: Mathematical finance

Published online by Cambridge University Press:  10 September 2014

LI-WEI ZHANG
LI-WEI ZHANG*
Affiliation:
School of Mathematics, Jilin University, Changchun, 130012, China email [email protected]
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Abstract

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Although variance swaps have become an important financial derivative to hedge against volatility risks, closed-form formulae have been developed only recently, when the realized variance is defined on discrete sample points and no continuous approximation is adopted to alleviate the mathematical difficulties associated with dealing with the discreteness of the sample data. In this paper, a new closed-form pricing formula for the value of a discretely sampled variance swap is presented under the assumption that the underlying asset prices can be described by a mean-reverting Gaussian volatility model. With the newly found analytical formula, not only can all the hedging ratios of a variance swap be analytically derived, the numerical values of the swap price can be efficiently computed as well.

Keywords

variance swapsmean-reverting Gaussian volatility modelclosed-form solutiondiscrete sampling

MSC classification

Secondary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 4 , April 2014 , pp. 362 - 382
Copyright
Copyright © 2014 Australian Mathematical Society 

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