Equity Digital Option

ORE defines the product as follows:

An Equity Digital Option is an option whose payout is either zero or a fixed predetermined amount (Cash-or-Nothing). Payout depends on whether the underlying Equity spot rate expires in-the-money at the expiration date.

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

ORE adds the exercise terms as follows:

Equity Digital Options have European exercise with payout at expiry. The buyer of a Equity Digital Option pays a premium to the seller.

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

A digital option is a binary bet on a share price. If the price ends on the right side of the strike, the buyer receives the fixed payoff amount. If not, the buyer receives nothing. There is no middle ground. The option is a pure view on the direction.

The EquityDigitalOptionData node is the trade data container for the EquityDigitalOption trade type. It has one OptionData sub-node plus elements specific to the equity digital option. LongShort names the side. OptionType takes Call or Put. A call is in the money when the underlying equity price is above the strike. A put is in the money when it is below. The Style is European only. Exactly one ExerciseDate must be given. Premiums is optional and holds the premium amounts paid by the buyer. Strike is the option strike per unit of the underlying, expressed in the currency of the underlying equity. PayoffCurrency is the currency of the payoff amount and must be consistent with the currency of the underlying equity spot. PayoffAmount is the fixed payoff amount per unit of underlying, expressed in the payoff currency. The underlying comes from Name or an Underlying node. Quantity is the number of units of the underlying covered by the transaction.

The payoff per unit is the fixed PayoffAmount when the option is in the money at expiry, and zero otherwise. For a call the condition is the spot above the strike at expiry. For a put it is the spot below the strike. The total payout scales with the quantity. The value is the discounted probability of finishing in the money times the payoff amount.

• The spot price of the underlying equity and its distance to the strike.
• The implied volatility of the underlying.
• The strike and the expiry.
• The interest rates and dividends of the underlying.

Near the strike the digital is most sensitive to the spot and to volatility. The payout does not grow with the depth of the finish in the money.

The digital decays toward its settlement as expiry approaches. Its value is the discounted probability of the payoff event. With the spot far from the strike, the payout becomes almost certain or almost worthless. At expiry the spot decides the payoff and the option settles.

A customer with a fixed view on a share price can take a binary payout. The digital pays a known amount for a known premium. It also builds spreads and structured payouts where a fixed cash amount is needed. In ORE Studio a customer books equity digital options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long call digital on the S&P 500 index that pays 1000 per unit above strike 3300:

<EquityDigitalOptionData>
    <OptionData>
        <LongShort>Long</LongShort>
        <OptionType>Call</OptionType>
        <Style>European</Style>
        <ExerciseDates>
            <ExerciseDate>2027-02-26</ExerciseDate>
        </ExerciseDates>
        ...
    </OptionData>
    <Strike>3300</Strike>
    <PayoffCurrency>USD</PayoffCurrency>
    <PayoffAmount>1000</PayoffAmount>
    <Name>RIC:.SPX</Name>
    <Quantity>1000</Quantity>
</EquityDigitalOptionData>

Source: ORE User Guide, Products catalogue, eq_digitaloption.tex, listing Equity Digital Option data.