Prices and Asymptotics for Discrete Variance Swaps

Carole Bernard, Zhenyu Cui

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

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 Schöbel-Zhu stochastic volatility models, we give simple explicit expressions (improving Broadie and Jain (2008a). The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11(8), 761-797) 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. The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11(8), 761-797), Jarrow et al. (2013. Discretely sampled variance and volatility swaps versus their continuous approximations. Finance and Stochastics, 17(2), 305-324) and Keller-Ressel and Griessler (2012. Convex order of discrete, continuous and predictable quadratic variation and applications to options on variance. Working paper. Retrieved from http://arxiv.org/abs/1103.2310).

Original languageEnglish
Pages (from-to)140-173
Number of pages34
JournalApplied Mathematical Finance
Volume21
Issue number2
DOIs
StatePublished - Mar 2014

Keywords

  • Discrete variance swap
  • Heston model
  • Hull-White model
  • Schöbel-Zhu model

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