Window Barrier Option

ORE defines the product as follows:

Window Barrier Options pay a (European) vanilla call / put. An American Knock-In or Knock-Out barrier condition can be defined that are monitored continuously between a start and end date.

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

ORE lists the barrier types:

The different barrier types are "UpAndIn", "UpAndOut", "DownAndIn", "DownAndOut".

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

A window barrier option is a normal European option with a timed barrier. The barrier is not watched for the whole life of the trade. It is watched only inside a window, between a start date and an end date. If the underlying touches the barrier level inside that window, the option knocks in or out. After the window closes, the barrier can no longer fire. The vanilla payoff is decided at expiry, much later in the typical structure.

The trade containers are FxWindowBarrierOptionData, EquityWindowBarrierOptionData and CommodityWindowBarrierOptionData, for the FxWindowBarrierOption, EquityWindowBarrierOption and CommodityWindowBarrierOption trade types. Currency is the payout currency. ORE describes the fixing amount per asset class as follows:

For FxWindowBarrierOptions: The FixingAmount is expressed in the foreign currency (CCY1). For EquityWindowBarrierOptions: The FixingAmount is expressed as number of shares/units of the underlying equity or equity index. For CommodityWindowBarrierOptions: The FixingAmount is expressed as number of units of the underlying commodity.

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

Underlying names the underlying of the instrument. For an FX underlying the name has the form SOURCE-CCY1-CCY2, with CCY1 the foreign currency and CCY2 the domestic currency. Strike is the strike: for FX, the amount in domestic currency per unit of foreign currency. StrikeData is an optional node for the equity form only; it holds the strike in Value together with the Currency in which the underlying and the strike are quoted.

StartDate and EndDate bound the continuous observation window. OptionData carries the option terms: LongShort, OptionType, the single ExerciseDate, an optional Premiums node, and an optional PaymentData node with the pay date of the exercise. BarrierData specifies the barrier type and level. ORE describes the monitoring:

The barrier is continuously monitored between the StartDate and EndDate.

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

The barrier types are UpAndOut, DownAndOut, UpAndIn and DownAndIn, with exactly one level given as a positive real number.

ORE also provides a scripted representation:

Window Barrier Options can be alternatively represented as scripted trades, refer to ore/Docs/ScriptedTrade for an introduction.

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

In the scripted form the trade type is ScriptedTrade and the data node is WindowBarrierOptionData. The node carries the same terms as typed event, number, option-type, barrier-type, long-short, index and currency fields, with Quantity as the number of option contracts.

The payoff script expresses the pricing. The raw payoff is the quantity times the call-put sign times the underlying at expiry minus the strike. A trigger probability is computed over the window: the probability that the underlying is below the barrier level for some barrier types, and above it for the others. For the knock-in types the payoff is scaled by the trigger probability; for the knock-out types it is scaled by one minus the trigger probability. The option is the long-short signed difference between the discounted scaled payoff and the discounted premium. The current notional of the trade is the quantity times the strike.

• The underlying spot at expiry. It drives the vanilla payoff.
• The volatility of the underlying, over both the window and the remaining life.
• The barrier level, and the length and placement of the window relative to the expiry date.
• The strike.
• The interest rates that discount the payoff and the premium.

The barrier lives only inside the window. Before the start date, and after the end date, the barrier is dormant. Inside the window the trade behaves like an American-barrier option. A knock-out inside the window kills the payoff; a knock-in inside the window grants it. After the window the trade becomes a plain European option until the exercise date, where the vanilla payoff is decided and settled.

A window barrier option prices a barrier view with a time limit. The buyer is protected from barrier events outside the window, which makes the structure cheaper than a whole-life barrier for the seller, or safer for the buyer. The structure suits views that say a market will, or will not, reach a level within a specific period. In ORE Studio a customer books window barrier options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long FX window barrier call on EUR-USD with a 1.1 strike and an up-and-out barrier at 1.3, monitored during 2023 and expiring in 2026:

<Trade id="FX_Window_BarrierOption">
  <TradeType>FxWindowBarrierOption</TradeType>
  <Envelope>
   ...
  </Envelope>
  <FxWindowBarrierOptionData>
    <Currency>USD</Currency>
    <FixingAmount>1000000</FixingAmount>
    <Underlying>
      <Type>FX</Type>
      <Name>ECB-EUR-USD</Name>
    </Underlying>
    <Strike>1.1</Strike>
    <StartDate>2023-03-01</StartDate>
    <EndDate>2024-03-01</EndDate>
    <OptionData>
      <LongShort>Long</LongShort>
      <OptionType>Call</OptionType>
      <ExerciseDates>
        <ExerciseDate>2026-03-01</ExerciseDate>
      </ExerciseDates>
      <Premiums>
        <Premium>
          <Amount>10900</Amount>
          <Currency>EUR</Currency>
          <PayDate>2018-03-01</PayDate>
        </Premium>
      </Premiums>
      <PaymentData>
        <Dates>
          <Date>2026-03-01</Date>
        </Dates>
      </PaymentData>
    </OptionData>
    <BarrierData>
      <Type>UpAndOut</Type>
      <Levels>
        <Level>1.3</Level>
      </Levels>
    </BarrierData>
  </FxWindowBarrierOptionData>
</Trade>

Source: ORE User Guide, Products catalogue, window_barrieroption.tex, the example FX window barrier option trade. The catalogue shows the same trade again as a scripted trade with the WindowBarrierOptionData node, and lists the payoff script that prices it.