Equity Outperformance Option

ORE introduces the product as follows:

An Equity Outperformance option has a payoff that depends on the `outperformance' of two equity indices (i.e. the difference between their returns) against a strike return. The buyer has the right but not the obligation to receive the outperformance in exchange for the strike rate at a predetermined time in the future.

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

ORE describes the barrier condition as follows:

A knockIn and knockOut price may be provided. The payoff is then only paid if on the exercise date the price of Index2 is above the knockIn price and below the knockOut price.

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

An outperformance option is a bet on relative performance. The buyer is long the return of index one and short the return of index two, through one option. The buyer profits when index one beats index two by more than the strike return. A call expects index one to win; a put expects index two to win. The barrier condition ties the payout to the level of index two on the exercise date.

The data node EquityOutperformanceOptionData is the trade data container for the EquityOutperformanceOption trade type:

The EquityOutperformanceOptionData node includes one OptionData trade component sub-node plus elements specific to the Equity Outperformance Option.

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

OptionData holds the option terms. LongShort takes Long or Short. OptionType takes Call or Put. A call gives the holder the right, but not the obligation, to receive the outperformance and pay the strike return; a put gives the holder the right to pay the outperformance and receive the strike return. Style takes European only, the sole style the trade type allows. Settlement takes Cash or Physical. The ExerciseDates node must carry exactly one ExerciseDate. A Premiums node is optional and holds the premium amounts paid by the option buyer to the seller.

Currency is the currency of the option. Underlying1 and Underlying2 name the two equity underlyings and the equity curves used for pricing. ORE notes a constraint on them:

Also note that the equities in Underlying1 and Underlying2 must be quoted in the same currency.

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

InitialPrice1 and InitialPrice2 hold the initial prices of the two underlyings. StrikeReturn is the strike return of the option. Notional is the notional amount of the trade. All three take any positive real number. The optional KnockInPrice and KnockOutPrice bound the second index on the settlement date: the payoff pays only when the price of underlying two is above the knock-in value and below the knock-out value.

The optional InitialPriceCurrency1 and InitialPriceCurrency2 apply when an initial price is given in a currency other than its underlying's currency. Each then requires its InitialPriceFXTerms node, which carries the FXIndex for the conversion.

ORE states the payoff of the option as the notional N times the positive part of the return of index one minus the return of index two, minus the strike return:

N x max(0, R1 - R2 - K).

R1 and R2 are the returns of Underlying1 and Underlying2, and K is the StrikeReturn. The payoff is zero when the second index's return closes the gap to the first by K or more. The knock-in and knock-out prices add a binary condition on the price of index two at the exercise date. ORE states that the pricing methodology was generalised from Brigo and Mercurio 2006, section 13.16.2.

• The level of each index at expiry. The return spread decides the payoff.
• The volatility of each index. Higher volatility widens the distribution of the return spread.
• The correlation between the two indices. It sets the volatility of the spread: the spread is less volatile than either index.
• The strike return.
• The knock-in and knock-out prices, which filter the payoff binarily.
• The interest rates that discount the payoff.

The payoff is a call on the return spread. The barrier condition makes the trade sensitive to the joint level of index two at expiry.

The trade holds until its single exercise date. Each index return is measured from its initial price. At expiry the payoff is the positive part of the spread minus the strike return, scaled by the notional. The barrier condition checks the price of index two on the same date. Cash settlement follows on the settlement date.

An outperformance option prices a view on relative performance directly. It lets an investor benefit when one market beats another, without taking a position in either market alone. Banks and asset managers use it to trade pairs of indices. In ORE Studio a customer books equity outperformance options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a European cash-settled call on the outperformance of the S&P 500 over the NASDAQ 100, with a strike return of 1% and a knock-in and knock-out window on the second index:

<EquityOutperformanceOptionData>
  <OptionData>
    <LongShort>Long</LongShort>
    <OptionType>Call</OptionType>
    <Style>European</Style>
    <Settlement>Cash</Settlement>
    <ExerciseDates>
      <ExerciseDate>2022-09-21</ExerciseDate>
    </ExerciseDates>
    ...
  </OptionData>
  <Currency>USD</Currency>
  <Notional>500000</Notional>
  <Underlying1>
    <Type>Equity</Type>
    <Name>RIC:.SPX</Name>
  </Underlying1>
  <Underlying2>
    <Type>Equity</Type>
    <Name>RIC:.NDX</Name>
  </Underlying2>
  <InitialPrice1>2140</InitialPrice1>
  <InitialPrice2>13000</InitialPrice2>
  <StrikeReturn>0.01</StrikeReturn>
  <KnockInPrice>12500</KnockInPrice>
  <KnockOutPrice>14000</KnockOutPrice>
</EquityOutperformanceOptionData>

Source: ORE User Guide, Products catalogue, eq_outperformance.tex, listing Equity Outperformance Option Data.