FX Double Touch Option

ORE defines the product as follows:

This product has two continuously monitored barriers with a Cash-or-Nothing digital underlying.

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

ORE states the payoff condition as follows:

A FX Double Touch option pays either a fixed predetermined payoff amount or zero (Cash-or-Nothing) depending upon an FX spot rate reaching one of the pre-set barrier levels.

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

ORE also states the two forms. A knock-in, or double one-touch, has a fixed payout if one of the barriers is breached, and no payout otherwise. A knock-out, or double no-touch, has no payout if one of the barriers is breached, and a fixed payout otherwise. The buyer pays a premium to the seller.

An FX double touch option is a bet on a corridor. One side bets that the rate touches either wall before expiry. The other side bets that it never does. The payout is fixed. There is no middle ground.

The FxDoubleTouchOptionData node includes one OptionData node and one BarrierData node. The barrier Type is KnockOut or KnockIn. Levels holds the two levels. The OptionType can be omitted. PayOffAtExpiry selects the payout timing. Only payout at expiry is currently supported, for both knock-out and knock-in barriers. PayoffAmount and PayoffCurrency set the fixed payout. ForeignCurrency and DomesticCurrency name the rate. StartDate sets the monitoring start, with the Calendar and FXIndex naming the fixing source.

ORE notes that the current implementation supports FX double touch options with payout at expiry only. No rebates are supported.

The value is the probability of the touch condition, discounted, times the fixed payout. A knock-in pays when the rate breaches either level at any time before expiry. A knock-out pays when it breaches neither. The probability of touching either level rises with volatility and with time. With payout at expiry, the timing of the touch does not change the payout date.

• The FX spot rate. Its position inside the corridor sets the state.
• The volatility of the pair. It drives the touch probability.
• The interest rates in the two currencies.
• The two barrier levels and the fixed payout.
• The payoff currency and the fixing source.

A double no-touch loses value as spot approaches either level. A double one-touch gains. Near the levels the delta and vega change direction.

The two levels are monitored continuously. A one-touch can be decided at any moment, though the payout waits for expiry. A no-touch stays alive while spot stays inside the corridor. As expiry approaches, the remaining time to touch shrinks. At expiry the payout settles and the trade stops.

A customer who expects the rate to stay in a range sells a double no-touch and collects the premium. A customer who expects a breakout buys a double one-touch. In ORE Studio a customer books FX double touch options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long double no-touch:

<FxDoubleTouchOptionData>
  <OptionData>
    <LongShort>Long</LongShort>
    <PayOffAtExpiry>true</PayOffAtExpiry>
    <ExerciseDates>
      <ExerciseDate>2021-12-14</ExerciseDate>
    </ExerciseDates>
    ...
  </OptionData>
  <BarrierData>
    <Type>KnockOut</Type>
    <Levels>
      <Level>1.1</Level>
      <Level>1.2</Level>
    </Levels>
  </BarrierData>
  <ForeignCurrency>EUR</ForeignCurrency>
  <DomesticCurrency>USD</DomesticCurrency>
  <PayoffCurrency>USD</PayoffCurrency>
  <PayoffAmount>100000</PayoffAmount>
  <StartDate>2019-01-25</StartDate>
  <FXIndex>FX-ECB-EUR-USD</FXIndex>
  <Calendar>TARGET</Calendar>
</FxDoubleTouchOptionData>

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

The single-level form is the FX Touch Option.