FX KIKO Barrier Option

ORE defines the product as follows:

An FX KIKO Barrier option is an option with both a knock-out and a knock-in barrier. The knock-out barrier can happen at any time, and once the knock-in barrier is hit the trade becomes a single barrier knock-out trade.

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

ORE states the exercise condition as follows:

The KIKO option can only be exercised if the knock-out barrier is never touched and the knock-in barrier is touched at least once.

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

ORE notes that the barriers can be any of the four main barrier types. One of the barriers must be a knock-in and the other a knock-out.

An FX KIKO option needs both a touch and a miss. The rate must touch one level to arm the option. The rate must never touch the other level, or the option dies. Two conditions, one payout.

The FxKIKOBarrierOptionData node includes one OptionData node and two BarrierData nodes, wrapped in a Barriers node. One barrier data node names the knock-in, the other the knock-out. The strike rate and the barrier levels are expressed as the amount in SoldCurrency per unit BoughtCurrency. The bought and sold currencies and amounts set the underlying exchange.

The value is the vanilla payoff conditioned on two path events. The knock-in must occur at least once. The knock-out must never occur. Both barriers are continuously monitored. The joint probability of the two events prices the option.

• The FX spot rate. Its position between the two barriers sets the state.
• The volatility of the pair. It drives both touch probabilities.
• The interest rates in both currencies.
• The strike and the two barrier levels.

A spot move toward the knock-out level destroys value. A move toward the knock-in level creates it. Near either level the exposure to spot and volatility changes direction.

The knock-out barrier is monitored continuously. The knock-in barrier waits for its first touch. Once the knock-in fires, the trade becomes a single-barrier knock-out trade. If the knock-out fires first, the trade dies. At expiry the survivor settles in the money or expires.

A customer sells a KIKO to fund a cheap hedge with a tight range view. The knock-in lowers the premium; the knock-out caps the payout. KIKO structures are common in corporate FX. In ORE Studio a customer books FX KIKO 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 and a down-and-out barrier:

<FxKIKOBarrierOptionData>
  <OptionData>
    <LongShort>Long</LongShort>
    <OptionType>Call</OptionType>
    <Style>European</Style>
    <Settlement>Cash</Settlement>
    <ExerciseDates>
      <ExerciseDate>2021-12-14</ExerciseDate>
    </ExerciseDates>
    ...
  </OptionData>
  <Barriers>
    <BarrierData>
      <Type>UpAndIn</Type>
      <Levels>
        <Level>1.2</Level>
      </Levels>
    </BarrierData>
    <BarrierData>
      <Type>DownAndOut</Type>
      <Levels>
        <Level>1.2</Level>
      </Levels>
    </BarrierData>
  </Barriers>
  <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>
</FxKIKOBarrierOptionData>

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

The two-level form without mixed types is the FX Double Barrier Option.