Abstract
The popular replication formula to price variance swaps assumes continuity of traded option strikes. In practice, however, there is only a discrete set of option strikes traded on the market. We present here different discrete replication strategies and explain why the continuous replication price is more relevant.
Highlights
Variance swaps contracts allow a buyer to receive the future realized variance of the price changes until a specific maturity date against a fixed strike price, paid at maturity
This paper stays in the Carr and Madan framework, but analyzes other possible simple discrete replications for the variance swap that can be better in terms of direct hedge than the solution from Leung and Lorig, which is optimal only in terms of quadratic hedging error
We show that the effect is not necessarily so small on one-year variance swaps and look comparatively at the effect of jumps on the volatility swap replication
Summary
Variance swaps contracts allow a buyer to receive the future realized variance of the price changes until a specific maturity date against a fixed strike price, paid at maturity. In Fukasawa et al (2011), Fukasawa et al describe a practical continuous replication for the variance swap based on market quotes While their technique is elegant and their interpolation methodology is sound, they do not explore the issue of discrete replication or truncation. Their idea is to propose an alternative standard methodology to the CBOE VIXindex calculation Their method produces prices very close to the one obtained by the direct implementation of the Carr–Madan continuous replication formula as described in this paper. Truncation and discretization play a more important role, especially on assets that are less liquid than the SPX500 index It focuses on discrete hedging, with a close look at Demeterfi et al.’s methodology, often considered a standard in the industry. We show that the effect is not necessarily so small on one-year variance swaps and look comparatively at the effect of jumps on the volatility swap replication
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