TY - JOUR
T1 - Prices and Asymptotics for Discrete Variance Swaps
AU - Bernard, Carole
AU - Cui, Zhenyu
PY - 2014/3
Y1 - 2014/3
N2 - 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).
AB - 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).
KW - Discrete variance swap
KW - Heston model
KW - Hull-White model
KW - Schöbel-Zhu model
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U2 - 10.1080/1350486X.2013.820524
DO - 10.1080/1350486X.2013.820524
M3 - Article
AN - SCOPUS:84892983298
SN - 1350-486X
VL - 21
SP - 140
EP - 173
JO - Applied Mathematical Finance
JF - Applied Mathematical Finance
IS - 2
ER -