European Option Contingent on a Barrier

ORE defines the product as follows:

This product is a plain vanilla European option on a single underlying (FX, Equity, Commodity or InterestRate) with a knock-in/knock-out feature on another underlying asset. The barrier can be continuously monitored (American) or only at the option expiry date (European).

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

ORE describes the knock-in and knock-out logic:

For a knock-in (knock-out) barrier, the option is valid when the price of the underlying barrier moves inside (outside) the barrier, otherwise the payoff is zero.

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

ORE scopes the supported asset classes:

For a European-style barrier, we support FX, Equity, Commodity and InterestRate underlyings. We do not support InterestRate for American-style barriers.

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

This trade is an option on one market, gated by another market. The option part is a normal European call or put on the option underlying. The gate is a barrier on a second underlying. With a down-and-in barrier, the option only lives when the second market has touched the level from above. With an up-and-out barrier, a touch from below kills the option. The gate can watch the second market all the time, or only on the expiry date.

The trade container for this product is the EuropeanOptionBarrierData node, and the trade type is EuropeanOptionBarrier. Quantity is the number of option contracts, PutCall the option type and LongShort the own party position. Strike is the option strike price. The premium terms are PremiumAmount, PremiumCurrency and PremiumDate. OptionExpiry is the option expiry date. OptionUnderlying names the asset the option is written on; its supported types are equity, FX, commodity and interest rate. PayCcy is the settlement currency, and SettlementDate the settlement date of the exercise payoff, on or after the option expiry date.

BarrierUnderlying is the underlying monitored against the barrier level. Its supported types follow the barrier style. ORE describes the European-style input as follows:

For a European-style barrier, the BarrierType must be set to European and the BarrierSchedule can be omitted.

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

BarrierLevel is the knock-in or knock-out level. BarrierType takes DownIn, UpIn, DownOut or UpOut. BarrierStyle takes American or European. BarrierSchedule is optional and lists the trading days over which a continuous barrier is monitored. It is required only for the American style.

ORE illustrates the barrier mechanics with two examples:

For example, for a European option with a continuous down-in barrier, the option payoff will only apply if the barrier underlying price was less than or equal to the agreed barrier level at any point over the life of the trade.

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

The companion example describes an up-out barrier: the option is knocked out when the barrier underlying price reaches or exceeds the agreed level at any point over the life of the trade, and the final payoff is then zero.

The payoff is the payoff of a vanilla European option on the option underlying, scaled by a barrier indicator on the barrier underlying. The barrier indicator is one when the barrier condition holds, and zero otherwise. For a knock-in the option is valid only when the indicator is one. For a knock-out the option is valid only when the indicator is zero. Under American monitoring the condition checks the barrier underlying at every point of the barrier schedule. Under European monitoring it checks the barrier underlying once, at the option expiry date.

• The level of the option underlying at expiry. It drives the vanilla payoff.
• The volatility of the option underlying.
• The path of the barrier underlying. It decides whether the barrier condition fires.
• The volatility of the barrier underlying, and its correlation with the option underlying. Both shape the probability that the barrier is touched.
• The barrier level, the barrier type and the barrier style.
• The strike, and the interest rates that discount the payoff.

Until expiry the option is a vanilla European option whose life depends on the barrier. Under the American style the barrier underlying is watched on each day of the barrier schedule; a touch knocks the option in or out there and then. Under the European style the barrier is decided once at expiry, together with the option payoff. The payoff settles on the settlement date when the option survives.

A barrier on a second asset prices in a view on two markets with one payoff. The knock-in form is cheaper than the plain option because it demands a condition on another market. The structure suits investors who want equity exposure, say, whose payoff depends on an FX level or an interest rate. In ORE Studio a customer books European options contingent on barriers to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a short call on the Euro Stoxx 50 with a continuous down-and-in FX barrier on EUR-USD. The trade is continuously monitored from 2019-12-11 to the expiry date:

<Trade id="Equity_EuropeanOptionWithAmericanFxBarrier">
  <TradeType>EuropeanOptionBarrier</TradeType>
  <Envelope>
    .....
  </Envelope>
  <EuropeanOptionBarrierData>
    <Quantity>8523</Quantity>
    <PutCall>Call</PutCall>
    <LongShort>Short</LongShort>
    <Strike>3520</Strike>
    <PremiumAmount>114.40</PremiumAmount>
    <PremiumCurrency>EUR</PremiumCurrency>
    <PremiumDate>2019-12-13</PremiumDate>
    <OptionExpiry>2020-06-19</OptionExpiry>
    <OptionUnderlying>
      <Type>Equity</Type>
      <Name>RIC:.STOXX50E</Name>
    </OptionUnderlying>
    <BarrierUnderlying>
      <Type>FX</Type>
      <Name>ECB-EUR-USD</Name>
    </BarrierUnderlying>
    <BarrierLevel>1.09335</BarrierLevel>
    <BarrierType>DownAndIn</BarrierType>
    <BarrierStyle>American</BarrierStyle>
    <BarrierSchedule>
      <Rules>
        <StartDate>2019-12-11</StartDate>
        <EndDate>2020-06-19</EndDate>
        <Tenor>1D</Tenor>
        <Calendar>USA</Calendar>
        <Convention>Following</Convention>
        <TermConvention>Following</TermConvention>
        <Rule>Forward</Rule>
      </Rules>
    </BarrierSchedule>
    <SettlementDate>2020-06-24</SettlementDate>
    <PayCcy>USD</PayCcy>
  </EuropeanOptionBarrierData>
</Trade>

Source: ORE User Guide, Products catalogue, europeanoptioncontingentonabarrier.tex, listing European Option Barrier data (continuous barrier). The call pays a premium of 114.40 EUR per contract on 2019-12-13.