FX Barrier Option

ORE defines the product as follows:

An FX Barrier option is a path-dependent option whose existence depends upon an FX spot rate reaching a pre-set barrier level. Exercise is European.

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

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

ORE defines the two life modes as follows:

A knock-in option is a barrier option that only comes into existence/becomes active when the FX spot rate reaches the barrier level at any point in the option's life. Once a barrier is knocked-in, the option will not cease to exist until the option expires and effectively it becomes a Vanilla FX Option.

A knock-out option starts its life active, but ceases to exist/becomes inactive, if the barrier is reached during the life of the option.

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

An FX barrier option is a vanilla option with a condition. The condition is a rate level. If the rate touches the level, the option switches on or off. The four types pair the level above or below with the switching direction.

The FxBarrierOptionData node includes one OptionData node and one BarrierData node. The barrier level is quoted as the amount in SoldCurrency per unit BoughtCurrency. The barrier Type selects one of the four main types. Levels holds the level, and Rebate the cash rebate paid on inactive expiry. StartDate sets the start of the barrier monitoring, with the associated Calendar and FXIndex. The bought and sold currencies and amounts set the underlying exchange.

A barrier option prices as a vanilla option plus a correction for the barrier. The knock-in form is a vanilla option that becomes active. The knock-out form is a vanilla option that can disappear. When the option expires inactive, the payoff is zero or the rebate, a fraction of the original premium. The value depends on the distance of spot from the barrier and on the volatility.

• The FX spot rate. Its distance from the barrier sets the state.
• The volatility of the pair. It drives the probability of touching the barrier.
• The interest rates in both currencies.
• The strike, the barrier level, and the rebate.
• The time to expiry.

Near the barrier the exposure to spot and volatility changes direction. This is the classic barrier skew. A knock-out loses value as spot approaches the barrier. A knock-in gains.

The barrier is monitored continuously through the option's life. A knock-out can end at any moment. A knock-in waits to activate. After a knock-out the trade ends with the rebate or nothing. After a knock-in the trade becomes a vanilla FX option and ages like one. At expiry the option settles in the money or expires.

A customer who holds a view on a rate range buys a barrier option at a lower premium than the vanilla. An exporter who expects the rate to stay in a band sells a knock-out. Barrier options shape the cost of hedging. In ORE Studio a customer books FX barrier options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long European call with an up-and-in barrier:

<FxBarrierOptionData>
  <OptionData>
    <LongShort>Long</LongShort>
    <OptionType>Call</OptionType>
    <Style>European</Style>
    <Settlement>Cash</Settlement>
    <ExerciseDates>
      <ExerciseDate>2021-12-14</ExerciseDate>
    </ExerciseDates>
    ...
  </OptionData>
  <BarrierData>
    <Type>UpAndIn</Type>
    <Levels>
      <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>
</FxBarrierOptionData>

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

The family includes the FX Double Barrier Option, the FX European Barrier Option, and the FX KIKO Barrier Option.