Streamlining Variance Swaps Trading: Standardizing Documentation In The Interdealer Market

As part of its goal to streamline the process supporting over-the-counter equity derivatives trading by standardizing documentation, the International Swaps and Derivatives Association has published the Index Variance Swap Annex and the Share Variance Swap Annex (the Variance Annexes) for the interdealer market.

  • 27 Aug 2004
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As part of its goal to streamline the process supporting over-the-counter equity derivatives trading by standardizing documentation, the International Swaps and Derivatives Association has published the Index Variance Swap Annex and the Share Variance Swap Annex (the Variance Annexes) for the interdealer market. These annexes are for use with ISDA's 2004 Americas Interdealer Master Equity Derivatives Confirmation Agreement (the Interdealer Master Confirmation).

The Interdealer Master Confirmation, which dealers enter into bilaterally, incorporates the 2002 Equity Derivatives Definitions (the 2002 Definitions) and is subject to the applicable ISDA Master Agreement. With the publication of the Variance Annexes, dealers now have the ability to trade index and share variance swaps under the Interdealer Master Confirmation, in addition to Index Options, Index Swaps, Index Basket Swaps, Share Options, Share Swaps and Share Basket Swaps on U.S. underlyings. The Master Confirmation has separate annexes for each product with agreed upon elections under the 2002 Definitions and is supplemented with a related Transaction Supplement including trade details.


Overview Of Variance Swaps

The publication of the Variance Annexes moves forward the work of ISDA's Equity Derivatives Committee into an area of increasing importance for market participants. Variance swaps are an efficient tool to express a long or short view on future volatility that can be used for hedging or yield-enhancing trading strategies. Standardizing the terms on which institutions transact will help facilitate continued growth of the product.

Variance swaps have become commonplace in the equity derivatives market over the past few years because traders are able to use this contract to take a pure view on the future realized volatility of a given stock or index. They provide constant exposure to volatility with a fixed gamma and time decay that is not dependent on stock prices and index levels, as distinct from options on stocks or indices.

Pursuant to the terms of a variance swap, the parties agree to make cash payments based on whether the realized variance (i.e., volatility2) of a stock or index over a specified period is more or less than an agreed level. The variance buyer receives a payment if the realized variance is higher and makes a payment if it is lower than the agreed level.

A variance swap can essentially be replicated by using a strip of options, each option being held in inverse proportion to the square of its strike. Once the initial hedge to the variance swap is established, the dealer will delta hedge this static set of options until their expiration.

In light of this, the provisions of the Variance Annexes closely match the terms of listed options with respect to consequences of Merger Events & Index Adjustment Events/Potential Adjustment Events. For example, the acquisition of a U.S. company by another U.S. company for a combination of New Shares and cash will often result in the listed options being adjusted to become a basket of the New Shares and cash. Correspondingly, the variance swap will be adjusted to have the same underlying basket of New Shares and cash. Furthermore, if there is an Index Modification and the Index is a Specified Index (i.e., there are U.S. listed option contracts based on the Index), then the variance swap will continue if the Primary Options Exchange adjusts the related options contracts in a manner that the Calculation Agent determines is economically equivalent in methodology to the modification announced by the Index Sponsor. In such cases the variance swap will be priced using the new index formula from that time on.

Additional evidence of the linkage to listed options is found in the new valuation provision called "Options Price Valuation", which states that the Index level or stock price used on the final Observation Date is the level or price used by the specified options exchange in settling its listed contracts.


Final Realized Volatility

The Variance Buyer receives a payment if the Final Realized Volatility2 is higher than the agreed level and makes a payment if it is lower. The Equity Amount payable is equal to (Variance Amount x [Final Realized Volatility2 ­ Variance Strike Price]). For example, if the Final Realized Volatility2 is five points higher than the agreed level and the Variance Amount is USD1 million then the Equity Amount payable to the Variance Buyer is USD5 million.

The Final Realized Volatility formula for an index variance swap is:





"t" means the relevant Observation Day;

"N" means the actual number of Observation Days;

"Expected N" means the number of days that, as of the Trade Date, are expected to be Scheduled Trading Days for the period from, but excluding, the Trade Date to, and including, the Scheduled Valuation Date;

"Ln" means the natural logarithm;

"Pt" means, in respect of any Observation Day, the official level of the Index at the Valuation Time on such Observation Day; provided that, if "Futures Price Valuation" or "Options Price Valuation" is specified as applicable in the relevant Transaction Supplement, in respect of the Observation End Date, "Pt" means the Official Settlement Price of the Exchange-traded Contract on the Observation End Date; and

"Pt-1" means, in respect of: (a) the first Observation Day, the Initial Index Level specified in the relevant Transaction Supplement and (b) any subsequent Observation Day, the official level of the Index at the Valuation Time on the Observation Day immediately preceding such Observation Day.

A similar formula exists for share variance swaps with two important differences. First, certain dividends, determined by the election of the parties, will result in an adjustment to Pt-1 where the closing share price on the day prior to the ex-date will be reduced by the Relevant Dividend Amount. The second difference is that there is a cap on the Final Realized Volatility equal to [2.52 x Variance Strike Price].


Disrupted Days

In the Variance Annexes, Scheduled Trading Days during the term of the variance swap that turn out to be Disrupted Days (either because of the occurrence of a Market Disruption Event or because the Exchange does not open and therefore are not Exchange Business Days) are included in the "Expected N" denominator. Such Disrupted Days, however, are not included in the "N" numerator. This result is due to the fact that listed option contracts are generally used to hedge variance swaps. Listed options are priced based on the number of Scheduled Trading Days during their term (i.e., the same methodology as in "Expected N"). On the other hand, "N" is used in the denominator to determine the Final Realized Volatility because we need to compare actual price changes from one Observation Day to the next.


Cancellation & Payment

The Variance Annexes also give guidance on how the Cancellation & Payment calculation is to be performed if there is an early termination of the variance swap. The provision is best illustrated by an example. If there is an early termination four months into a six-month variance swap, then the amount payable will be determined as follows:

Calculate the realized volatility for the four months that have elapsed;

Assume that the volatility for the remaining two months is the mid-market implied volatility for such time period that is present in the listed options market. To determine such amount, the trader in this example would look at the most comparable listed option contracts on the Primary Options Exchange and then calculate the mid-market implied volatility by interpolating or extrapolating from such contracts;

Once the Final Realized Volatility is determined by weighting one and two above, the Equity Amount calculation is performed; and

This amount, which would have been payable on the originally scheduled Cash Settlement Payment date, is then present valued to the date that the amount is payable pursuant to the early termination, using a mid-market zero-coupon swap rate.



ISDA and its membership continue to explore ways in which to enhance the documentation infrastructure that supports the ongoing sound growth and development of this important market sector. ISDA is currently consulting with its members to prepare a master confirmation template for share and index variance swaps based on the Variance Annexes for use outside of the interdealer market. Copies of the Variance Annexes are available on ISDA's website at


This week's Learning Curve was written byGlen Rae, v.p. and assistant general counsel atGoldman Sachsin New York and chairman of ISDA's equity derivatives committee for North America. He also served as chairman of the working groups that drafted the Variance Annexes, the Interdealer Master Confirmation and the 2002 Definitions.

  • 27 Aug 2004

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