Accumulator

ORE defines the accumulator behaviour as follows:

The product settles periodically (e.g. monthly) and allows the investor to accumulate a holding in the underlying security over the term of the contract. A potential feature of an accumulator is a knock-out, i.e. the contract terminates early if the underlying price exceeds some threshold above strike.

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

ORE defines the decumulator as follows:

A decumulator is the reverse of an accumulator – in this case, the investor is required to sell shares periodically at a pre-determined fixed price. A potential knock-out is set below the strike price (and below the spot price at inception).

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

The accumulator investor speculates that the security stays between the strike and the knock-out level for the life of the contract.

An accumulator is a series of forwards on one asset. Each fixing date the investor buys the asset at a price fixed when the trade starts. If the market runs away to the knock-out level, the program ends early. In the leveraged form the investor buys more on the days the asset trades at or above the strike. A decumulator is the same program in reverse: the investor sells on each fixing date.

The data node FxAccumulatorData is the trade data container for the FxAccumulator trade type. EquityAccumulatorData and CommodityAccumulatorData play the same role for the equity and commodity trade types. ORE distinguishes two product types by the settlement pattern:

Here the FX accumulator is of "type 01" meaning that a settlement takes place on each observation date while the equity accumulator is of "type 02" meaning that a settlement takes place on specific period end dates for all observation dates in that period.

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

ObservationDates are the dates on which the underlying is fixed. PricingDates are optional and define the period end dates. When they are present the product is of type 02, and one settlement per period replaces one settlement per observation date. SettlementDates can be given as an explicit list. For type 01 the number of settlement dates equals the number of observation dates. For type 02 it equals the number of pricing dates. Alternatively SettlementLag, SettlementCalendar and SettlementConvention derive the settlement dates from the observation dates. DailyFixingAmount applies to type 01 only. When true, the fixing amount for a period is the given amount times the number of calendar days in the period. StartDate starts the first period and is mandatory in this case.

Strike is the global strike. FX strikes are domestic currency (CCY2) per unit of foreign currency (CCY1). Equity and commodity strikes are per share or per unit, in the currency of the underlying. Local strikes can be defined per range inside RangeBounds, or a range strike adjustment can modify the global strike. The logic is as follows: a local strike for an interval wins over the global strike; otherwise a global strike plus a local adjustment is used; otherwise the global strike stands; without either strike an error is thrown. For equity accumulators the StrikeData node carries the global strike and its currency. FixingAmount is the unleveraged notional accumulated at each fixing date. For FX it is in the foreign currency, for equity in shares, for commodity in units. A negative amount turns an accumulator into a decumulator and vice versa. Currency is the payout currency. OptionData holds LongShort and PayoffType, which takes the values Accumulator and Decumulator. A long accumulator is equivalent to a short decumulator, except when a FixingFloor barrier is present.

RangeBounds contains one RangeBound node per price range, with RangeFrom, RangeTo and Leverage. A leverage of 1 applies by default to a range without one. All leverage values in one instrument must have the same sign. Type 01 accumulators may give a range its own strike.

Barriers contains BarrierData nodes. Type can be UpAndOut, DownAndOut or FixingFloor. Style can be European, monitored on the observation dates, or American, monitored continuously from the start date to the first observation date and between observation dates. ORE describes the guaranteed fixings as follows:

For type 01 accumulators (no pricing dates are given), the FixingFloor guarantees a specific number of fixings to be settled even in case of a knock out. On a guaranteed fixing date, Only positive payouts (from the buyer/long perspective) are realised.

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

For type 02 accumulators the FixingFloor guarantees a number of periods instead of observation dates. When a knock-out happens inside a guaranteed period, the remaining fixings of that period settle on the knock-out day plus the settlement delay. StrictComparison chooses the barrier comparison: 0 uses less-or-equal and greater-or-equal, 1 uses strict comparisons. For equity accumulators each barrier level carries its own Value and Currency in a LevelData node. KnockOutSettlementAtPeriodEnd and KnockOutFixingAtKOSettlement tune the knock-out settlement of type 02 products. FxIndex defines the FX conversion for composite accumulators, where the strike, barrier and pay currency differ from the quote currency of the underlying.

ORE also describes the naked option variant as follows:

If true, the payoff represents that of an option, and only positive values are accumulated in the instrument. The option type (Call or Put) is inferred from the sign of the Leverage values in RangeBound, which are all required to be the same.

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

ORE states the payout formula from the perspective of the long party, for each observation date of an accumulator, as:

Payout = RangeBound(Leverage) x FixingAmount x (fix - Strike).

The holder pays the strike times the fixing amount times the leverage and receives, or buys, the same number of units of the underlying at the fixing. For a decumulator the formula is:

Payout = RangeBound(Leverage) x FixingAmount x (Strike - fix).

The holder pays the fixing value and receives the strike. In the naked option form the payout is the absolute leverage times the fixing amount times the positive part of the option payoff. The sign of the leverage values fixes the option type: a positive leverage with a positive part on rising fixings behaves as a call, a negative leverage as a put.

ORE also provides a scripted representation of both product types, with the trade types ScriptedTrade and the nodes Accumulator01Data and Accumulator02Data. In the scripted form the ranges are given as parallel lists: RangeUpperBounds, RangeLowerBounds and RangeLeverages. A range without an upper bound takes the sentinel value 100000; a range without a lower bound takes 0. KnockOutType takes the values UpOut and DownOut. AmericanKO selects continuous barrier monitoring; otherwise the barrier is monitored on the fixing dates only. GuaranteedFixings is the number of first fixings that settle even after a knock-out. The current notional of the trade is the fixing amount times the strike.

• The underlying price. It decides which range the fixing falls into, whether the barrier is hit, and the size of each installment.
• The volatility of the underlying. It drives the probability of a knock-out and of range crossings.
• The strike, the range boundaries and the knock-out level.
• The leverage values, which scale the exposure within each range.
• The interest rates that discount the installment payments.

The payoffs are linear in each fixing. The barrier and the range structure add path dependence.

The fixings settle on their own dates. For type 01 each observation date settles alone. For type 02 each observation period settles on its period end date. The barrier is observed on the observation dates in the European style, and continuously from the start date in the American style. A knock-out ends the accumulation, except for the guaranteed fixings. The current notional grows with each installment until the trade runs off or knocks out.

An accumulator lets a customer build a position in an asset over time, at a price fixed today. The decumulator lets a customer sell a position over time in the same way. Banks distribute these products to investors who want to accumulate or run down holdings without trading each day. In ORE Studio a customer books accumulators and decumulators to value them and run sensitivities on the ORE engine.

ORE's catalogue shows an FX accumulator of type 01, with one settlement per observation date. The barrier structure adds an American up-and-out at 1.5 and a fixing floor of two guaranteed fixings:

<Trade id="FX_ACCUMULATOR">
  <TradeType>FxAccumulator</TradeType>
  <Envelope>
    ...
  </Envelope>
  <FxAccumulatorData>
    <Currency>USD</Currency>
    <FixingAmount>1000000</FixingAmount>
    <Strike>1.1</Strike>
    <Underlying>
      <Type>FX</Type>
      <Name>ECB-EUR-USD</Name>
    </Underlying>
    <OptionData>
      <LongShort>Long</LongShort>
      <PayoffType>Accumulator</PayoffType>
    </OptionData>
    <StartDate>2016-03-01</StartDate>
    <ObservationDates>
      <Dates>
        <Dates>
          <Date>2017-03-01</Date>
          <Date>2020-03-01</Date>
          <Date>2025-03-01</Date>
          <Date>2029-03-01</Date>
        </Dates>
      </Dates>
    </ObservationDates>
    <SettlementDates>
      <Dates>
        <Dates>
          <Date>2017-03-03</Date>
          <Date>2020-03-03</Date>
          <Date>2025-03-03</Date>
          <Date>2029-03-03</Date>
        </Dates>
      </Dates>
    </SettlementDates>
    <RangeBounds>
      <RangeBound>
        <RangeTo>1.14</RangeTo>
        <Leverage>1</Leverage>
      </RangeBound>
      <RangeBound>
        <RangeFrom>1.14</RangeFrom>
        <Leverage>1</Leverage>
      </RangeBound>
    </RangeBounds>
    <Barriers>
      <BarrierData>
        <Type>UpAndOut</Type>
        <Style>American</Style>
        <Levels>
          <Level>1.5</Level>
        </Levels>
      </BarrierData>
      <BarrierData>
        <Type>FixingFloor</Type>
        <Levels>
          <Level>2</Level>
        </Levels>
      </BarrierData>
    </Barriers>
  </FxAccumulatorData>
</Trade>

The catalogue then shows an equity decumulator of type 02. Its observation dates run daily over one year, its settlements take place on the pricing dates, and its down-and-out barrier sits at 3500 with a fixing floor of one guaranteed period:

<Trade id="Equity_Decumulator">
  <TradeType>EquityAccumulator</TradeType>
  <Envelope>
    ...
  </Envelope>
  <EquityAccumulatorData>
    <FixingAmount>30</FixingAmount>
    <StrikeData>
      <Value>4000</Value>
      <Currency>EUR</Currency>
    </StrikeData>
    <Underlying>
      <Type>Equity</Type>
      <Name>.STOXX50</Name>
      <IdentifierType>RIC</IdentifierType>
    </Underlying>
    <OptionData>
      <LongShort>Long</LongShort>
      <PayoffType>Decumulator</PayoffType>
    </OptionData>
    <StartDate>20190925</StartDate>
    <ObservationDates>
      <Rules>
        <StartDate>20190925</StartDate>
        <EndDate>20200925</EndDate>
        <Tenor>1D</Tenor>
        <Calendar>TARGET</Calendar>
        <Convention>F</Convention>
        <TermConvention>F</TermConvention>
        <Rule>Forward</Rule>
      </Rules>
    </ObservationDates>
    <PricingDates>
      <Dates>
        <Dates>
          <Date>20211025</Date>
          <Date>20211125</Date>
          ...
        </Dates>
      </Dates>
    </PricingDates>
    <SettlementLag>2D</SettlementLag>
    <SettlementCalendar>TARGET</SettlementCalendar>
    <SettlementConvention>F</SettlementConvention>
    <RangeBounds>
      <RangeBound>
        <RangeTo>4000</RangeTo>
        <Leverage>1</Leverage>
      </RangeBound>
      <RangeBound>
        <RangeFrom>4000</RangeFrom>
        <Leverage>2</Leverage>
      </RangeBound>
    </RangeBounds>
    <Barriers>
      <BarrierData>
        <Type>DownAndOut</Type>
        <LevelData>
          <Level>
            <Value>3500</Value>
            <Currency>EUR</Currency>
          </Level>
        </LevelData>
      </BarrierData>
      <BarrierData>
        <Type>FixingFloor</Type>
        <Levels>
          <Level>1</Level>
        </Levels>
      </BarrierData>
    </Barriers>
    <KnockOutSettlementAtPeriodEnd>false<KnockOutSettlementAtPeriodEnd>
  </EquityAccumulatorData>
</Trade>

Source: ORE User Guide, Products catalogue, accumulator.tex, the example FX accumulator and equity decumulator trades.