Rate Digital Option

ORE defines the product as follows:

A Rate Digital Option is a European cash-or-nothing option on an interest rate fixing. It pays a fixed cash amount if the underlying rate index fixing on the fixing date is above the strike (Call) or below the strike (Put). This trade type is useful for hedging or replicating Range Accrual coupons, where each daily observation can be decomposed into a digital option on the rate.

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

The payout direction follows the option type. A call pays when the rate fixing is above the strike. A put pays when the rate fixing is below the strike.

A rate digital is a binary bet on a rate. The rate either beats the level or it does not. The payout is fixed in advance. There is no graduated payoff.

The RateDigitalOptionData node is the trade data container for the RateDigitalOption trade type. It includes one OptionData sub-node plus elements specific to the product. LongShort sets the direction. OptionType names the condition, call or put. ExerciseDates holds the single European exercise date. Index names the underlying rate, for example EUR-EURIBOR-6M. Strike sets the level in decimal form. PayoffAmount and PayoffCurrency set the fixed payout. FixingDate is when the index fixes. PaymentDate is when the payout settles.

The payout is a fixed cash amount conditional on one event. A call pays if the fixing is above the strike. A put pays if the fixing is below the strike. The value is the payout times the discounted probability of the event under the pricing measure. A digital behaves like the limit of a tight call or put spread. Near the strike its sensitivity to the rate and to volatility is at its peak.

• The forward level of the reference rate against the strike.
• The volatility of the reference index.
• The discount rate to the payment date.
• The gap between the fixing date and the payment date.
• The payout amount and its currency.

Far from the strike the value saturates. Deep in the money the payout is near certain. Deep out of the money it is near zero.

Until the fixing, the trade prices the probability of the payout. The fixing date decides the outcome. After the fixing the payoff is known. Only the discount to the payment date remains. At the payment date the cash settles and the trade stops.

A customer uses the product to hedge Range Accrual coupons. Each daily observation of such a coupon is a digital on the rate. A trader expresses a cheap binary view on a rate level. In ORE Studio a customer books rate digital options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long call digital on euro six-month Euribor. It pays 10000 euros if the fixing is above 2 percent:

<RateDigitalOptionData>
      <OptionData>
        <LongShort>Long</LongShort>
        <OptionType>Call</OptionType>
        <ExerciseDates>
          <ExerciseDate>2027-06-20</ExerciseDate>
        </ExerciseDates>
      </OptionData>
      <Index>EUR-EURIBOR-6M</Index>
      <Strike>0.02</Strike>
      <PayoffAmount>10000.0</PayoffAmount>
      <PayoffCurrency>EUR</PayoffCurrency>
      <FixingDate>2027-06-18</FixingDate>
      <PaymentDate>2027-06-20</PaymentDate>
</RateDigitalOptionData>

Source: ORE User Guide, Products catalogue, ratedigitaloption.tex, listing Rate Digital Option data.