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AN ANALYTICAL APPROACH FOR VARIANCE SWAPS WITH AN ORNSTEIN–UHLENBECK PROCESS

Part of: Mathematical economics

Published online by Cambridge University Press:  19 July 2017

JIAN-PENG CAO Open the ORCID record for JIAN-PENG CAO [Opens in a new window]  and
YAN-BING FANG
JIAN-PENG CAO
Affiliation:
School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China email caoxiaojian0524@gmail.com, nxfangzi@163.com
YAN-BING FANG*
Affiliation:
School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China email caoxiaojian0524@gmail.com, nxfangzi@163.com
*
✉nxfangzi@163.com
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Abstract

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Pricing variance swaps have become a popular subject recently, and most research of this type come under Heston’s two-factor model. This paper is an extension of some recent research which used the dimension-reduction technique based on the Heston model. A new closed-form pricing formula focusing on a log-return variance swap is presented here, under the assumption that the underlying asset prices can be described by a mean-reverting Gaussian volatility model (Ornstein–Uhlenbeck process). Numerical tests in two respects using the Monte Carlo (MC) simulation are included. Moreover, we discuss a procedure of solving a quadratic differential equation with one variable. Our method can avoid the previously encountered limitations, but requires more time for calculation than other recent analytical discrete models.

Keywords

variance swapsOrnstein–Uhlenbeck processclosed-form solutionstochastic volatility

MSC classification

Primary: 91B70: Stochastic models
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 1 , July 2017 , pp. 83 - 102
Copyright
© 2017 Australian Mathematical Society 

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