FX Double Barrier Option

ORE defines the product as follows:

An FX Double Barrier option is a path-dependent option whose existence depends upon an FX spot rate reaching one of the two pre-set barrier levels. Exercise is European.

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

ORE adds that the product has two continuously monitored barriers with a vanilla European FX option underlying.

ORE notes that the current implementation does not support options with knock-in knock-out (KIKO) or knock-out knock-in (KOKI) barrier combinations. The former is covered by the separate FX KIKO Barrier Option instrument.

An FX double barrier option is a vanilla option inside a corridor. The corridor has a floor and a ceiling. A knock-in option comes alive when the rate touches either level. A knock-out option dies when the rate touches either level.

The FxDoubleBarrierOptionData node includes one OptionData node and one BarrierData node. The barrier levels are quoted as the amount in SoldCurrency per unit BoughtCurrency. The barrier Type is KnockOut or KnockIn for the pair of levels. Levels holds the two levels, and Rebate the cash rebate on inactive expiry. The bought and sold currencies and amounts set the underlying exchange.

A double barrier option prices as a vanilla option plus a two-sided corridor correction. The value depends on the distance of spot from both levels. The probability of touching either level rises with volatility and with time. When the option expires inactive, the payoff is zero or the rebate.

• The FX spot rate. Its position inside the corridor sets the state.
• The volatility of the pair. It drives the touch probability of either level.
• The interest rates in both currencies.
• The strike, the two barrier levels, and the rebate.
• The time to expiry.

A knock-out loses value as spot approaches either barrier. A knock-in gains. Near the barriers the exposure to spot and volatility changes direction.

The two barriers are monitored continuously. A knock-out can end at any moment. A knock-in waits for its first touch. After a knock-out the trade ends with the rebate or nothing. After a knock-in the trade becomes a vanilla FX option. At expiry the option settles in the money or expires.

A customer who expects the rate to stay inside a range buys a double knock-out at a lower premium than a single barrier. A customer who expects a breakout buys a double knock-in. In ORE Studio a customer books FX double barrier options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long European call inside two knock-out levels:

<FxDoubleBarrierOptionData>
  <OptionData>
    <LongShort>Long</LongShort>
    <OptionType>Call</OptionType>
    <Style>European</Style>
    <ExerciseDates>
      <ExerciseDate>2021-12-14</ExerciseDate>
    </ExerciseDates>
    ...
  </OptionData>
  <BarrierData>
    <Type>KnockOut</Type>
    <Levels>
      <Level>1.1</Level>
      <Level>1.2</Level>
    </Levels>
    <Rebate>0.0</Rebate>
  </BarrierData>
  <StartDate>2019-01-25</StartDate>
  <Calendar>TARGET</Calendar>
  <FXIndex>FX-ECB-EUR-USD</FXIndex>
  <BoughtCurrency>EUR</BoughtCurrency>
  <BoughtAmount>1000000</BoughtAmount>
  <SoldCurrency>USD</SoldCurrency>
  <SoldAmount>1100000</SoldAmount>
</FxDoubleBarrierOptionData>

Source: ORE User Guide, Products catalogue, fx_doublebarrieroption.tex, listing FX Double Barrier Option data (optional elements omitted).

The single-level form is the FX Barrier Option. The FX KIKO Barrier Option pairs one knock-in with one knock-out.