A closed-form exact solution for pricing variance swaps with stochastic volatility
Files
Date
Authors
Supervisor
Item type
Journal Article
Degree name
Journal Title
Journal ISSN
Volume Title
Publisher
Wiley-Blackwell
Abstract
In this paper, we present a highly efficient approach to price variance swaps with discrete sampling times. We have found a closed-form exact solution for the partial differential equation (PDE) system based on the Heston’s two-factor stochastic volatility model embedded in the framework proposed by Little and Pant. In comparison with the previous approximation models based on the assumption of continuous sampling time, the current research of working out a closed-form exact solution for variance swaps with discrete sampling times at least serves for two major purposes: (i) to verify the degree of validity of using a continuous-sampling-time approximation for variance swaps of relatively short sampling period; (ii) to demonstrate that significant errors can result from still adopting such an assumption for a variance swap with small sampling frequencies or long tenor. Other key features of our new solution approach include the following: (1) with the newly found analytic solution, all the hedging ratios of a variance swap can also be analytically derived; (2) numerical values can be very efficiently computed from the newly found analytic formula.Description
Source
Mathematical Finance, vol.21(2), pp.233–256
Publisher's version
Rights statement
© 2010 Wiley Periodicals, Inc. John Wiley & Sons. All rights reserved. Authors retain the right to place his/her pre-publication version of the work on a personal website or institutional repository. This article may not exactly replicate the final version published in (please see citation) as it is not a copy of this record. An electronic version of this article can be found online at: (Please see Publisher’s Version)