Prices and Asymptotics for Discrete Variance Swaps

44 Pages Posted: 23 Jul 2012 Last revised: 19 Jun 2013

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Zhenyu Cui

Stevens Institute of Technology - School of Business

Date Written: May 30, 2013

Abstract

We study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull-White and Schoebel-Zhu stochastic volatility models we give simple explicit expressions (improving Broadie and Jain (2008a) in the case of the Heston model). We give conditions on parameters under which the fair strike of a discrete variance swap is higher or lower than that of the continuous variance swap. The interest rate and the correlation between the underlying price and its volatility are key elements in this analysis. We derive asymptotics for the discrete variance swaps and compare our results with those of Broadie and Jain (2008a), Jarrow et al. (2013) and Keller-Ressel and Griessler (2012).

Keywords: Discrete variance swaps, Heston model, Hull-White model, Schoebel-Zhu model

JEL Classification: G12, G13

Suggested Citation

Bernard, Carole and Cui, Zhenyu, Prices and Asymptotics for Discrete Variance Swaps (May 30, 2013). Applied Mathematical Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2115881 or http://dx.doi.org/10.2139/ssrn.2115881

Carole Bernard

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Zhenyu Cui (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://sites.google.com/site/zhenyucui86/publications

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