FX Variance Swap

ORE defines the product as follows:

An FX Variance Swap has a payoff, similar to an Equity Variance Swap's payoff, that depends on the volatility of an underlying FX rate. 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, fxvarianceswap.tex.

ORE notes that the strike is typically set at ATM so the swap initially has zero value. If the subsequent realised volatility is above the strike level, the buyer of a variance swap, who is long volatility, has a positive NPV. The seller, who is short volatility, has a negative NPV.

An FX variance swap is a bet on movement, not direction. One side pays the realised variance of an exchange rate over the life of the swap. The other side pays a fixed variance agreed at trade time. If the rate moves more than expected, the variance buyer gains.

The FxVarianceSwapData node carries the swap terms. StartDate and EndDate frame the observation period. Currency is the bought currency. Name, or the Underlying node, names the currency pair. LongShort sets the direction. 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, the notional in volatility units. Calendar joins the calendars of the two currencies. MomentType distinguishes a volatility or variance payoff. Volatility or Variance, with variance the default.

ORE notes that only vanilla variance swaps are supported by this trade type. Exotic variance swaps are supported by the scripted trade mechanism. FX variance and volatility swaps also cover precious metals, with currencies XAU, XAG, XPT, and XPD, and cryptocurrencies.

ORE states the variance payoff as follows:

Payoff = N x (RealisedVol^2 - K^2)

N is the variance notional, determined as the vega notional divided by 2K. The realised volatility is annualised from the squared daily log returns over the observation period. The volatility swap payoff is closely related:

Payoff = N x (RealisedVol - K)

• The implied volatility of the FX pair. It prices the variance strike.
• The realised path of daily returns. It settles the payoff.
• The vega notional and the strike.
• The observation schedule and the annualisation convention.
• The discount rate of the settlement currency.

A long variance position gains when realised movement exceeds the strike. It gains from jumps in either direction. Direction of the rate itself does not drive the payoff.

Each day adds one return to the realised variance. Early in life the realised part is small and the trade behaves like a forward on implied variance. Late in life the realised variance dominates and the payoff locks in. At maturity the final variance settles and the swap stops.

A customer with FX exposure wants protection on the volatility of the rate. A trader takes a view that FX volatility is cheap or rich. Variance swaps isolate that view from direction. In ORE Studio a customer books FX variance swaps to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long variance swap on euro-yen:

<FxVarianceSwapData>
  <StartDate>2018-05-10</StartDate>
  <EndDate>2018-11-12</EndDate>
  <Currency>EUR</Currency>
  <Underlying>
    <Type>FX</Type>
    <Name>ECB-EUR-JPY</Name>
  </Underlying>
  <LongShort>Long</LongShort>
  <Strike>0.05</Strike>
  <Notional>200000</Notional>
  <Calendar>EUR</Calendar>
  <MomentType>Variance</MomentType>
</FxVarianceSwapData>

Source: ORE User Guide, Products catalogue, fxvarianceswap.tex, listing Variance Swap data.