Equity European Barrier Option

ORE defines the product as follows:

An Equity European Barrier option gives the buyer the right, but not the obligation, to buy a set number of shares of a single name equity or an equity index, at a predetermined strike price, at one predetermined time in the future. This right may be withdrawn depending upon an Equity spot price or index reaching a predetermined barrier level at the predetermined time, the underlying is monitored only at expiry with a single barrier.

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

ORE adds the settlement terms as follows:

For this right the buyer pays a premium to the seller. Settlement can be either cash or physical delivery.

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

A European barrier option is the once-checked relative of the barrier family. The barrier does not watch the price through the life of the option. It is checked at expiry only. If the price sits on the wrong side of the barrier at that moment, the option dies. Otherwise it settles like a vanilla option.

The EquityEuropeanBarrierOptionData node is the trade data container for the EquityEuropeanBarrierOption trade type. It has one OptionData sub-node and one BarrierData sub-node. Only the European option style is allowed. The barrier level in BarrierData is quoted in the same currency as the underlying equity spot. Changing the option from call to put does not require switching the barrier level. The underlying comes from Name or an Underlying node. StrikeData holds the strike and supports StrikePrice only. Quantity is the number of units of the underlying covered by the transaction.

The four main types are up-and-out, down-and-out, up-and-in and down-and-in. An up option starts below the barrier. A down option starts above it. The barrier is compared with the spot at expiry, not through the life of the option. A knock-out option that expires on the wrong side of the barrier pays zero, or a cash rebate paid as a fraction of the original premium. A knock-in option becomes active only if the spot is on the right side at expiry. The value of the product is the vanilla value adjusted for the probability of the spot finishing on the wrong side of the barrier.

• The spot price of the underlying equity and its distance to the barrier.
• The implied volatility of the underlying. It drives the chance of the expiry check failing.
• The strike and the barrier level.
• The interest rates and dividends of the underlying.

Only the terminal spot matters for the barrier, so the product behaves like a vanilla option until near expiry.

The barrier event is decided at expiry, so no breach can end the option early. The product ages like a European option for its whole life. At expiry the spot is checked against the barrier. A knock-out option on the wrong side pays zero or the rebate. A knock-in option on the right side pays its vanilla payoff.

The European barrier is cheaper than a vanilla option and less path-dependent than a continuously monitored barrier. It suits a customer who accepts a barrier check at the settlement moment only. In ORE Studio a customer books equity European barrier options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows an option on the S&P 500 index with a strike of 3200 and a quantity of 1000:

<EquityEuropeanBarrierOptionData>
    <OptionData>
        ...
    </OptionData>
    <BarrierData>
        ...
    </BarrierData>
    <Name>RIC:.SPX</Name>
    <StrikeData>
      <StrikePrice>
        <Value>3200.00</Value>
        <Currency>USD</Currency>
      </StrikePrice>
    </StrikeData>
    <Quantity>1000</Quantity>
</EquityEuropeanBarrierOptionData>

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