Equity Touch Option

Table of Contents

An equity touch option pays a fixed amount or nothing, decided by a single barrier on the equity spot. The barrier is monitored continuously. ORE models it with the trade type EquityTouchOption. This note records the domain grounding, as ORE documents it in its product catalogue.

1. Identifiers

What a trader books it as, and what to grep for. The codes are the trade type catalogue's, which is what the database enforces.

Field Value
Full name Equity Touch Option
Short name Equity Touch Option
ORE Studio product code EquityTouchOption
Asset class equity
Family Option
ORE trade data node EquityTouchOptionData
ORE documentation eq_touchoption.tex

2. Summary

An equity touch option has a continuously monitored single barrier with a cash-or-nothing digital underlying. At expiry it pays either a fixed predetermined payoff amount or zero, depending on whether the equity spot reached the barrier. The four main types are up-and-out, down-and-out, up-and-in and down-and-in. A knock-in, or one-touch, pays when the barrier is breached. A knock-out, or no-touch, pays when it is not. The container node is EquityTouchOptionData.

3. Detail

3.1. What it is

ORE defines the product as follows:

This product has a continuously monitored single barrier with a Cash-or-Nothing digital underlying.

At expiry an Equity Touch Option pays either a fixed predetermined payoff amount or zero (Cash-or-Nothing) depending upon an Equity spot rate reaching a pre-set barrier level.

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

ORE describes the four forms as follows:

A Knock-In or One-Touch option has a fixed payout if the barrier is breached, and no payout otherwise. The payout can be at expiry or at hit.

A Knock-Out or No-Touch option has no payout if the barrier is breached, and fixed payout at expiry otherwise.

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

3.2. In plain terms

A touch option is a binary bet on a level. One level sits above or below the current price. The one-touch form pays when the price hits the level at any time. The no-touch form pays when the price never hits it. The payout is a fixed cash amount or nothing.

3.3. How it works in ORE

The EquityTouchOptionData node is the trade data container for the EquityTouchOption trade type. It has one OptionData sub-node and one BarrierData sub-node. The OptionType is not required. It is inferred from the barrier type: Call for an up barrier and Put for a down barrier. LongShort names the side. PayOffAtExpiry is optional: true for payoff at expiry and false for payoff at hit. For up-and-out and down-and-out barriers only payoff at expiry is supported. It defaults to true. Settlement takes Cash or Physical. Exactly one ExerciseDate must be given. Premiums is optional. BarrierData holds the level in Levels. The level is quoted in the same currency as the underlying equity spot. StrictComparison is optional and selects the strict or non-strict barrier check. PayoffCurrency must be consistent with the currency of the underlying equity spot. 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.

3.4. Mathematical notes

The product is a digital claim on a barrier event. The one-touch form pays the payoff amount if the spot touches the barrier at any time during the life. The payout can be at the moment of the hit or at expiry. The no-touch form pays at expiry if the spot never touched the barrier. No rebates are supported. The value is the discounted probability of the event times the payoff amount.

3.5. What moves its value (static sensitivities)

  • The spot price of the underlying equity and its distance to the barrier.
  • The implied volatility of the underlying. It drives the chance of a touch.
  • The barrier level and the time to expiry.
  • The payoff amount and the timing of the payout.

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

3.6. How the profile ages (dynamic sensitivities)

The barrier is monitored continuously from the start date. A one-touch option that touches the barrier has its event decided. The payout arrives at the hit or at expiry as the trade specifies. A no-touch option that touches the barrier is dead from that moment. A no-touch option that survives ages toward a more certain payout, while its survival probability falls as time passes without a touch.

3.7. Why a customer would want it

A one-touch pays when a level breaks, which suits a customer who expects a large move. A no-touch pays when the price stays on one side of the level. The fixed payout and known premium make the trade easy to size. In ORE Studio a customer books equity touch options to value them and run sensitivities on the ORE engine.

3.8. Example

ORE's catalogue shows an up-and-in touch on the S&P 500 index that pays one million when the spot reaches 3300: 

<EquityTouchOptionData>
    <OptionData>
        <LongShort>Long</LongShort>
        <PayOffAtExpiry>true</PayOffAtExpiry>
        <Settlement>Cash</Settlement>
        <ExerciseDates>
          <ExerciseDate>2022-03-01</ExerciseDate>
        </ExerciseDates>
        ...
    </OptionData>
    <BarrierData>
      <Type>UpAndIn</Type>
      <Levels>
        <Level>3300</Level>
      </Levels>
    </BarrierData>
    <PayoffCurrency>USD</PayoffCurrency>
    <PayoffAmount>1000000</PayoffAmount>
    <Name>RIC:.SPX</Name>
    <StartDate>2019-12-27</StartDate>
    <Calendar>US-NYSE</Calendar>
    <EQIndex>EQ-RIC:.SPX</EQIndex>
</EquityTouchOptionData>

Source: ORE User Guide, Products catalogue, eq_touchoption.tex, listing Equity Touch Option data. The source ends the EQIndex line with a stray > character; it is normalised here.

4. See also

Emacs 29.3 (Org mode 9.6.15)