FX Asian Option

ORE defines the product as follows:

For an FX Asian option, the payoff is determined by the averaged foreign exchange rate over a pre-set period of time. At the expiration date, this product gives the buyer the right, but not the obligation, to obtain a cash amount of averaged rate in return for a predetermined strike rate. For this right the buyer pays a premium to the seller.

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

ORE adds that an FX Asian option is a path-dependent option whose payoff depends upon the averaged foreign exchange rate over a pre-set period of time.

An FX Asian option is a bet on an average. The exchange rate is measured many times over a period. The average decides the payoff, not any single day. The average smooths the swings of the rate.

The FxAsianOptionData node carries one OptionData node plus elements specific to the option. The Currency is the payoff currency. The Quantity scales the payoff. The Strike is the strike rate. The Underlying names the FX pair, with Type FX. The OptionData sets the direction and the payoff type. PayoffType Asian or AverageStrike identifies a fixed or floating strike. PayoffType2 selects Arithmetic or Geometric averaging, with arithmetic the default. The ObservationDates node builds the averaging schedule, rules-based or date-based, like a ScheduleData node. Settlement defaults to the exercise date.

ORE states the payoff as follows:

Quantity x max(w x (A(0,T) - K), 0)

A(0,T) is the arithmetic average FX rate over the observation period, as amount of CCY2 per one unit of CCY1. K is the strike rate, in the same terms. w is 1 for a call, which receives the averaged FX and pays the strike, and -1 for a put. In the average-strike form, the strike is the average itself.

• The FX forward curve at each observation date. It drives the expected average.
• The volatility of the rate over the window. The average damps it.
• The strike and the quantity.
• The observation schedule and the averaging convention.
• The discount rate of the payoff currency.

A call gains when the average rises above the strike. A put gains when the average falls below it.

Each observation turns part of the average from unknown to known. The remaining observations keep their market exposure. The averaging window closes as the period end approaches. Near the end the average is largely determined. At expiry the option settles on the final average.

A customer with a stream of FX conversions over time wants protection on the average rate, not on one date. The average makes the hedge cheaper than a single-date option. In ORE Studio a customer books FX Asian options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long arithmetic Asian call:

<Trade id="FxAsianOption">
  <TradeType>FxAsianOption</TradeType>
  <Envelope>
    <CounterParty>CPTY_A</CounterParty>
    <NettingSetId>CPTY_A</NettingSetId>
    <AdditionalFields />
  </Envelope>
  <FxAsianOptionData>
    <Currency>USD</Currency>
    <Quantity>100</Quantity>
    <Strike>1.05</Strike>
    <Underlying>
      <Type>FX</Type>
      <Name>ECB-EUR-USD</Name>
    </Underlying>
    <OptionData>
      <LongShort>Long</LongShort>
      <OptionType>Call</OptionType>
      <PayoffType>Asian</PayoffType>
      <PayoffType2>Arithmetic</PayoffType2>
      <ExerciseDates>
        <ExerciseDate>2020-07-15</ExerciseDate>
      </ExerciseDates>
    </OptionData>
    <Settlement>2020-07-20</Settlement>
    <ObservationDates>
      <Rules>
        <StartDate>2019-12-27</StartDate>
        <EndDate>2020-07-06</EndDate>
        <Tenor>1D</Tenor>
        <Calendar>US</Calendar>
        <Convention>F</Convention>
        <TermConvention>F</TermConvention>
        <Rule>Forward</Rule>
      </Rules>
    </ObservationDates>
  </FxAsianOptionData>
</Trade>

Source: ORE User Guide, Products catalogue, fx_asianoption.tex, listing FX Asian Option data.