Equity Asian Option

ORE defines the product as follows:

An Equity Asian Option is a path-dependent option whose payoff depends upon the averaged price of an Equity underlying over a pre-set period of time.

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

An Asian option looks at the average price instead of the final price. Daily fixings over the observation period build the average. A customer who fears a price spike on one day prefers the average. The payoff is harder to manipulate and cheaper than a vanilla option.

The EquityAsianOptionData node is the trade data container for the EquityAsianOption trade type. It has one OptionData trade component sub-node plus elements specific to the equity Asian option. StrikeData holds the strike in Value and the currency of the underlying and the strike in Currency. Quantity is the number of underlying equities. The node takes one Underlying element with Type set to Equity. The OptionData fields set LongShort, OptionType, PayoffType and the exercise date. PayoffType must be Asian or AverageStrike. The first identifies a fixed-strike Asian payoff and the second a floating-strike payoff. PayoffType2 is optional and takes Arithmetic or Geometric. It defaults to Arithmetic. Exactly one ExerciseDate must be given. Premiums can represent deterministic option premia. Settlement is optional and defaults to the exercise date. ObservationDates holds the Asian observation period as a rules-based or dates-based schedule.

The payoff is Payoff = Quantity x MAX(omega x (A(0,T) - K), 0). A(0,T) is the arithmetic average of the underlying equity spot price over the Asian observation period from start 0 to end T. K is the equity strike price. Omega is 1 for a call option and -1 for a put option. A geometric average is available through PayoffType2. The averaging reduces the volatility that reaches the payoff.

• The spot price of the underlying equity.
• The implied volatility of the underlying.
• The strike and the exercise date.
• The observation schedule and its remaining fixings.
• The interest rates and dividends of the underlying.

The average lags the spot. A move near the end of the period moves the average more than a move near the start.

Each observation date adds a fixing to the average. Early fixings become fixed parts of the average. As the period fills, the average stiffens and the option's effective delta falls. Near the final observation the average is almost known and the option value approaches its settlement value.

A customer who receives or pays a periodic equity price, such as an average-priced buyback, wants an option on that average. The Asian payoff matches the exposure and costs less than a vanilla option of the same expiry. In ORE Studio a customer books equity Asian options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long call on the average of the S&P 500 index over daily observations:

<Trade id="EquityAsianOption">
  <TradeType>EquityAsianOption</TradeType>
  <Envelope>
    <CounterParty>CPTY_A</CounterParty>
    <NettingSetId>CPTY_A</NettingSetId>
    <AdditionalFields />
  </Envelope>
  <EquityAsianOptionData>
    <Quantity>100</Quantity>
    <Currency>USD</Currency>
    <StrikeData>
      <Value>3100</Value>
      <Currency>USD</Currency>
    </StrikeData>
    <Underlying>
      <Type>Equity</Type>
      <Name>RIC:.SPX</Name>
      <Currency>USD</Currency>
    </Underlying>
    <OptionData>
      <LongShort>Long</LongShort>
      <OptionType>Call</OptionType>
      <PayoffType>Asian</PayoffType>
      <PayoffType2>Arithmetic</PayoffType2>
      <ExerciseDates>
        <ExerciseDate>2020-07-15</ExerciseDate>
      </ExerciseDates>
      <Premiums> ... </Premiums>
    </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>
  </EquityAsianOptionData>
</Trade>

Source: ORE User Guide, Products catalogue, eq_asianoption.tex, listing Equity Asian Option data.