Equity Double Touch Option

ORE defines the product as follows:

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

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

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

ORE describes the two forms as follows:

A Knock-In or Double One-Touch option has a fixed payout if one of the barriers is breached, and no payout otherwise.

A Knock-Out or Double No-Touch option has no payout if one of the barriers is breached, and fixed payout otherwise.

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

ORE notes that the current implementation supports equity double touch options with payout at expiry only.

A double touch option is a bet on a corridor. Two levels sit above and below the current price. The double one-touch form pays when the price touches either level. The double no-touch form pays when the price stays inside the corridor for the whole life. Either way the payout is a fixed cash amount or nothing.

The EquityDoubleTouchOptionData node is the trade data container for the EquityDoubleTouchOption trade type. It has one OptionData sub- node and one BarrierData sub-node. The OptionType can be omitted. LongShort names the side. PayOffAtExpiry takes true for payoff at expiry and false for payoff at hit. Only payoff at expiry is currently supported, for both knock-out and knock-in barriers. It defaults to true. Exactly one ExerciseDate must be given. Premiums is optional. BarrierData holds two levels in Levels in ascending order. Type takes KnockOut or KnockIn. StrictComparison is optional: it selects <= and >= or the strict < and > for the barrier check. It defaults to the non-strict comparison. The barrier levels are quoted in the same currency as the underlying equity spot. PayoffCurrency must be consistent with that currency. PayoffAmount is the fixed payoff amount. The underlying comes from Name or an Underlying node. StartDate, Calendar and EQIndex support a check for a barrier breach before today's date. The equity index format is EQ-RIC:Code.

The product is a digital claim on a corridor event. The double one- touch form pays the payoff amount if the spot touches either barrier at any time during the life. The double no-touch form pays if the spot stays between the two barriers for the whole life. No rebates are supported. The value is the discounted probability of the event times the payoff amount.

• The spot price of the underlying equity and its distance to each barrier.
• The implied volatility of the underlying. It drives the chance of a touch.
• The width of the corridor between the two levels.
• The time to expiry and the payoff amount.

Close to a barrier the chance of a touch rises quickly. The no-touch form loses value as the spot nears either level.

Both barriers are monitored continuously. A double one-touch option that touches a barrier has its event decided, and pays at expiry. A double no-touch option that touches a barrier is dead from that moment. A no-touch option that survives ages toward a more certain payout, while its survival probability falls with every day that passes without a touch.

A double no-touch pays when the market stays calm inside a range. It suits a customer who expects the index to trade sideways. The double one-touch pays when the range breaks, which suits a view of a large move in either direction. In ORE Studio a customer books equity double touch options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a double one-touch on the S&P 500 index that pays one million when the spot touches 3000 or 4500:

<EquityDoubleTouchOptionData>
    <OptionData>
        <LongShort>Long</LongShort>
        <PayOffAtExpiry>true</PayOffAtExpiry>
        <ExerciseDates>
          <ExerciseDate>2021-12-14</ExerciseDate>
        </ExerciseDates>
        ...
    </OptionData>
    <BarrierData>
        ...
        <Type>KnockIn</Type> <!-- KnockOut or KnockIn -->
        <Levels>
            <Level>3000</Level>
            <Level>4500</Level>
        </Levels>
        ...
    </BarrierData>
    <PayoffCurrency>USD</PayoffCurrency>
    <PayoffAmount>1000000</PayoffAmount>
    <Name>RIC:.SPX</Name>
    <StartDate>2021-03-01</StartDate>
    <Calendar>USD</Calendar>
    <EQIndex>EQ-RIC:.SPX</EQIndex>
</EquityDoubleTouchOptionData>

Source: ORE User Guide, Products catalogue, eq_doubletouchoption.tex, listing Equity Double Touch Option data.