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Convergence of the discrete variance swap in time-homogeneous diffusion models

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  • Carole Bernard
  • Zhenyu Cui
  • Don McLeish

Abstract

In stochastic volatility models based on time-homogeneous diffusions, we provide a simple necessary and sufficient condition for the discretely sampled fair strike of a variance swap to converge to the continuously sampled fair strike. It extends Theorem 3.8 of Jarrow, Kchia, Larsson and Protter (2013) and gives an affirmative answer to a problem posed in this paper in the case of 3/2 stochastic volatility model. We also give precise conditions (not based on asymptotics) when the discrete fair strike of the variance swap is higher than the continuous one and discuss the convex order conjecture proposed by Keller-Ressel and Griessler (2012) in this context.

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  • Carole Bernard & Zhenyu Cui & Don McLeish, 2013. "Convergence of the discrete variance swap in time-homogeneous diffusion models," Papers 1310.0099, arXiv.org.
    • Handle: RePEc:arx:papers:1310.0099
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    References listed on IDEAS

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    1. Martin Keller-Ressel & Claus Griessler, 2011. "Convex order of discrete, continuous and predictable quadratic variation & applications to options on variance," Papers 1103.2310, arXiv.org, revised Oct 2012.
    2. Carole Bernard & Zhenyu Cui, 2013. "Prices and Asymptotics for Discrete Variance Swaps," Papers 1305.7092, arXiv.org.
    3. Robert Jarrow & Younes Kchia & Martin Larsson & Philip Protter, 2013. "Discretely sampled variance and volatility swaps versus their continuous approximations," Finance and Stochastics, Springer, vol. 17(2), pages 305-324, April.
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