Prices and Asymptotics for Discrete Variance Swaps

TL;DR

This paper derives explicit formulas and asymptotic behaviors for the fair strike of discrete variance swaps across various stochastic volatility models, highlighting the influence of interest rates and correlation.

Contribution

It provides simplified explicit expressions for discrete variance swap fair strikes in key models and analyzes their asymptotic properties, improving prior results.

Findings

Explicit formulas for Heston, Hull-White, Schobel-Zhu models

Conditions for higher or lower discrete vs. continuous variance swap strikes

Asymptotic behaviors and comparison with previous studies

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 Schobel-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).