Performance Option Type 01

The performance option of type 01 is characterised by its data: a notional amount, a participation rate, one valuation date and one settlement date, a number of underlyings with weights, initial strike prices for the underlyings, and an option strike. On the valuation date the average performance of the underlying basket is computed. The option holder receives the notional times the participation rate times the computed performance on the settlement date. The underlyings can be equity, FX or commodity underlyings.

ORE distinguishes the two strike treatments as follows:

The above payoff includes the strike in the performance calculation. There is another variant with excluded strike and payoff:

Source: ORE User Guide, Products catalogue, performanceoption_01.tex.

A performance option is a call on the average performance of a basket. Each asset in the basket is measured from its own initial strike price. The weighted average of these performances is compared with an option strike. The buyer receives a share of the positive part of the result, scaled by a participation rate. The structure pays only when the basket as a whole beats the option strike. The choice of strike treatment changes where the option strike enters the calculation.

The catalogue shows the trade data container PerformanceOption01Data for the PerformanceOption_01 trade type. NotionalAmount is the notional amount of the option. ParticipationRate is the participation rate:

The participation rate. Allowable values are non-negative numbers. Usually the value will be between 0 and 1.

Source: ORE User Guide, Products catalogue, performanceoption_01.tex.

ValuationDate is the valuation date and SettlementDate the settlement date. Underlyings holds the underlyings of the option, each with its Weight. StrikePrices holds the initial strike price of each underlying. For an FX underlying it is the number of units of CCY2 per unit of CCY1; for an equity underlying it is the equity price in the equity currency; for a commodity underlying it is the commodity price as quoted for the commodity.

Strike is the option strike, expressed in terms of the performance of the underlying basket. ORE describes it as follows:

The option strike. This is expressed in terms of the performance of the underlying basket (see the product description for more details). Allowable values are numbers.

Source: ORE User Guide, Products catalogue, performanceoption_01.tex.

StrikeIncluded is optional. When true, the strike is included in the performance calculation of each underlying; this is also the default when the flag is not given. When false, the strike is excluded and applies to the basket performance as a whole. Position takes Long or Short. PayCcy is the payment currency of the option.

ORE computes the performance P on the valuation date from the weighted sum of the underlying performances. In the included form the option strike enters each underlying's term:

P = max( sum over i of w-i x (U-i(V) / s-i - K), 0 ).

In the excluded form the option strike applies once, after the weighted sum:

P = max( [ sum over i of w-i x U-i(V) / s-i ] - K, 0 ).

The performance is floored at zero in both forms. The option holder receives the notional N times the participation rate q times P on the settlement date S.

• The levels of the basket underlyings on the valuation date. They drive the basket performance.
• The initial strike prices, which anchor each underlying's return.
• The weights of the underlyings.
• The option strike, and the choice of strike treatment.
• The participation rate.
• The volatility of each underlying and the correlation between them. They set the dispersion of the basket performance.
• The interest rates that discount the payout from the settlement date.

The trade has one valuation date. Until then the basket underlyings diffuse and the option value tracks the expected floored basket performance. On the valuation date the underlyings fix and the performance is computed under the selected strike treatment. The payout settles shortly after on the settlement date.

A performance option buys participation in the average performance of a basket, with a floor at zero. The buyer keeps the upside of a collection of assets while the option strike sets the performance hurdle. Banks use it to give clients diversified participation in a basket of currencies or markets. In ORE Studio a customer books performance options of type 01 to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long performance option on a basket of Scandinavian and Swiss currencies against the euro. The basket lists CHF-EUR at 34%, NOK-EUR at 32%, and SEK-EUR twice, at 24% and 10%. The option strike of 1.15 is included in the performance calculation:

<PerformanceOption01Data>
  <NotionalAmount>12500000</NotionalAmount>
  <ParticipationRate>0.9</ParticipationRate>
  <ValuationDate>2022-05-03</ValuationDate>
  <SettlementDate>2022-05-05</SettlementDate>
  <Underlyings>
    <Underlying>
      <Type>FX</Type>
      <Name>ECB-CHF-EUR</Name>
      <Weight>0.34</Weight>
    </Underlying>
    <Underlying>
      <Type>FX</Type>
      <Name>ECB-NOK-EUR</Name>
      <Weight>0.32</Weight>
    </Underlying>
    <Underlying>
      <Type>FX</Type>
      <Name>ECB-SEK-EUR</Name>
      <Weight>0.24</Weight>
    </Underlying>
    <Underlying>
      <Type>FX</Type>
      <Name>ECB-SEK-EUR</Name>
      <Weight>0.10</Weight>
    </Underlying>
  </Underlyings>
  <StrikePrices>
    <StrikePrice>0.910002</StrikePrice>
    <StrikePrice>0.097192</StrikePrice>
    <StrikePrice>0.096085</StrikePrice>
    <StrikePrice>0.035032</StrikePrice>
  </StrikePrices>
  <Strike>1.15</Strike>
  <StrikeIncluded>true</StrikeIncluded>
  <Position>Long</Position>
  <PayCcy>EUR</PayCcy>
</PerformanceOption01Data>

Source: ORE User Guide, Products catalogue, performanceoption_01.tex, listing Performance Option Type 01 data.