Equity Variance Swap

ORE defines the product as follows:

An Equity Variance Swap has a payoff that depends on the volatility of an underlying equity instrument. Underlying individual stocks and indices are supported. The swap counterparties agree to exchange a pre-agreed variance level (the strike) for the actual amount of variance realized over an observation period.

Source: ORE User Guide, Products catalogue, equityvarianceswap.tex.

ORE limits the product as follows:

Only vanilla variance swaps are supported.

Source: ORE User Guide, Products catalogue, equityvarianceswap.tex.

A variance swap is a bet on how much a share bounces around. The parties agree a volatility level at trade time. If the share then moves more than that level, the buyer of variance receives the difference. If it moves less, the buyer pays it. Direction does not matter: only the size of the daily moves counts.

The EquityVarianceSwapData node is the trade data container for the EquityVarianceSwap trade type. ORE's guide spells the container node name as EqutiyVarianceSwapData, without the second i, in its prose and listings. StartDate and EndDate bound the observation period. Underlying or Name names the equity or index. LongShort names the side. A long variance swap has positive value if the realised variance exceeds the variance strike. Strike is the volatility strike quoted absolutely, not as a percent. If the swap was struck in terms of variance, the square root of that variance is used here. Notional is the vega notional, that is the notional in volatility units. Calendar sets the fixing dates. The calendar of the equity curve configuration combines with it. MomentType distinguishes a swap struck in terms of volatility from one struck in terms of variance. It defaults to Variance. The strike is always quoted as a volatility. AddPastDividends adds past dividend payments to the fixings when calculating accrued variance. It defaults to false.

The payoff is N x (RealisedVol squared minus K squared). Here N is the variance notional, determined as the vega notional divided by twice the strike. K is the strike volatility. RealisedVol is the annualised volatility of the daily log returns over the observation period. Each daily log return ln(P_t / P_t-1) is squared and summed. The sum is scaled by 252 over the expected number of scheduled trading days and the square root is taken. P_0 is the official closing price at the observation start date. P_t is the official closing price at each observation date.

• The implied volatility of the underlying. It sets the fair strike.
• The realised volatility from the observation start date onward.
• The dividend treatment of the underlying, through the fixing adjustment flag.
• The expected number of trading days and the calendar.
• The discount rate over the observation period.

A swap struck at the market level of variance starts near zero value. A long position gains as realised volatility runs above the strike.

Variance accrues day by day from the observation start date. The realised part becomes fixed as fixings land. The remaining uncertainty shrinks with the remaining trading days. Close to the end date the realised variance is almost known, so the swap value moves toward its final payoff. A long swap near expiry behaves like a fixed claim.

A variance swap trades volatility directly, without a directional view on the share. Option desks use it to hedge the vega of their books. A customer can also express the view that implied volatility is too high or too low against realised. The payoff is linear in variance, unlike an option position. In ORE Studio a customer books equity variance swaps to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long USD variance swap on the S&P 500 index, struck at 20 percent volatility:

<EquityVarianceSwapData>
    <StartDate>2016-01-29</StartDate>
    <EndDate>2016-05-05</EndDate>
    <Currency>USD</Currency>
    <Underlying>
      <Type>Equity</Type>
      <Name>.SPX</Name>
      <IdentifierType>RIC</IdentifierType>
    </Underlying>
    <LongShort>Long</LongShort>
    <Strike>0.20</Strike>
    <Notional>50000</Notional>
    <Calendar>US</Calendar>
    <MomentType>Variance</MomentType>
    <AddPastDividends>true</AddPastDividends>
</EquityVarianceSwapData>

Source: ORE User Guide, Products catalogue, equityvarianceswap.tex, listing Variance Swap data. The source spells the container node name as EqutiyVarianceSwapData; it is reproduced verbatim here.