Variance Swap Replication: Option Expiry and Dynamic Hedging

Summary

The document addresses which option maturities to use when replicating a variance swap whose observation period runs from the next day through a later end date. It says the option strip used for static replication should expire on the same date as the variance swap. The calculations should use business time, with the response noting a common convention for annualizing trading days.

Static option replication does not remove the need to manage the underlying exposure: futures may need to be traded dynamically through the period. An alternative is to adjust the option strip between puts and calls as the forward changes, using put-call parity to keep options out of the money. The response is a brief practical explanation and points to references for derivation; it does not provide the replication formula or discuss market frictions, discrete hedging error, or contract-specific conventions.

Key ideas

• The static option strip should expire on the variance swap’s observation end date.
• Use business time consistently when calculating variance swap analytics.
• The underlying futures exposure may require dynamic trading during the observation period.
• Put-call parity supports switching between puts and calls as the forward moves.
• The response omits detailed derivation and does not address replication frictions.

Tags

# Question regarding the purchase of a Variance Swap


# Question regarding the purchase of a Variance Swap












Imagine I price a Variance Swap for an investor and the observation date starts tomorrow and ends in 30 days. If I use dynamic replication with options to price my variance swap do I use options with a maturity of 1 month?

## Answer by FinanceGuyThatCantCode (score 4)

https://quant.stackexchange.com/a/34016

The options will form a static replication - and yes - they should expire on the same day as the variance swap. You should be sure to do all of your analytics in business time. Also, typically a year is considered 252 business days by default - even in FX where there are no holidays (though there are no WMR fixings on New Years, Christmas, Good Friday). You will still need to trade the underlying futures for the expiration date dynamically (or alternatively flip puts to calls or vice versa in your option strip as the forward moves to keep all options out of the money - a put call parity argument will explain that). The details are in Derman's famous paper about variance swaps. Skimmed wikipedia and this is probably ok too (though I didn't look carefully):

http://www.emanuelderman.com/writing/entry/more-than-you-ever-wanted-to-know-about-volatility-swaps-the-journal-of-der

https://en.wikipedia.org/wiki/Variance_swap

The wikipedia link has some good references at the bottom also.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.