FX European Barrier Option

ORE defines the product as follows:

A FX European Barrier option gives the buyer the right, but not the obligation, to exchange a set amount of one currency for another, at a predetermined exchange rate, at one predetermined time in the future.

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

ORE states that this right may be withdrawn depending upon an FX spot rate reaching a predetermined barrier level at the predetermined time. The underlying is monitored only at expiry, with a single barrier. For this right the buyer pays a premium to the seller. Settlement can be either cash or physical delivery.

ORE defines the two life modes at expiry 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 expiry.

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

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

An FX European barrier option is a vanilla option with an expiry-day condition. The barrier matters only at the end. If the rate sits past the level at expiry, the option switches on or off. During the life of the option, the barrier does not react.

The FxEuropeanBarrierOptionData 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 on inactive expiry. The bought and sold currencies and amounts set the underlying exchange.

A European barrier option prices against the terminal spot distribution, not the path. The barrier event and the expiry fixing are the same observation. The value is the vanilla option adjusted by the probability that the terminal rate sits past the barrier. A cash rebate applies when the option expires inactive.

• The FX spot rate. Its position against the barrier at expiry sets the state.
• The volatility of the pair. It spreads the terminal rate around the forward.
• The interest rates in both currencies.
• The strike, the barrier level, and the rebate.

The absence of continuous monitoring removes the intraday touch risk. The barrier exposure lives at the expiry date. A knock-out loses value as the forward rate sits closer to the barrier at expiry.

The option ages like a vanilla option for most of its life. The barrier sleeps until expiry. At expiry the fixing decides both the moneyness and the barrier state. The option settles in cash or by delivery, or expires with the rebate.

A customer who wants a cheaper vanilla hedge buys a European barrier option. The barrier check at expiry only suits a view on the terminal rate. In ORE Studio a customer books FX European 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 and a rebate:

<FxEuropeanBarrierOptionData>
  <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>100000</Rebate>
  </BarrierData>
  <BoughtCurrency>EUR</BoughtCurrency>
  <BoughtAmount>1000000</BoughtAmount>
  <SoldCurrency>USD</SoldCurrency>
  <SoldAmount>1100000</SoldAmount>
</FxEuropeanBarrierOptionData>

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

The continuously monitored form is the FX Barrier Option.