Target Redemption Forward

ORE introduces the product as follows:

There are two types of knock out

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

A TaRF is a sequence of FX, equity or commodity forward contracts. Strikes and leverage factors apply to ranges of the underlying price. The trade terminates, or knocks out, when its accumulated profit reaches a pre-determined target. ORE distinguishes two knock-out types:

A Continuous TaRF terminates when the profit reaches or exceeds a pre-determined target. A Digital TaRF terminates when the number of fixing days where the buyer makes a profit reaches a pre-determined target.

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

ORE distinguishes three payment types after the knock-out:

exact: the payment is adjusted to match the pre-determined target full: the unadjusted payment is made truncated: no payment is made

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

A target redemption forward is a strip of forwards that stops winning at a target. Each fixing date the buyer settles a forward on the underlying. The fixing is profitable when it sits on the favourable side of the strike. Profits accumulate, and when they reach the target the strip redeems early. The buyer gets the target amount, or the last payment, or nothing, per the payment type. In the digital form the count of profitable days is the target.

The data node FxTaRFData is the trade data container for the FxTaRF trade type. EquityTaRFData and CommodityTaRFData play the same role for the equity and commodity trade types. Currency is the payout currency of the TaRF; the target amount and the payout formula results are expressed in it. FixingAmount is the unlevered amount used at each fixing date. For FX it is in the foreign currency, for equity in shares, for commodity in units. It must be positive for both long and short positions.

ORE describes the target mechanics as follows:

If PayoffType = TargetExact, after a knock-out event the last payout is adjusted so that the cumulated profit since the start of the TaRF matches the target amount.

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

TargetAmount is a currency amount; for FX it is in the domestic currency. TargetPoints expresses the same target as a percentage of the fixing amount. ORE lists the extra features as follows:

European Knock Ins (EKI), where no sells or buys happen if a fixing is between the strike and the EKI level Pivots, where different strikes apply for different ranges of the fixing

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

OptionData holds LongShort and PayoffType. PayoffType takes the values TargetFull, TargetExact or TargetTruncated, matching the three payment types above. ScheduleData holds the fixing dates. SettlementLag, SettlementCalendar and SettlementConvention derive the settlement dates from them.

Strikes can be global or local. The Strike node gives a strike that is constant over time. The Strikes node gives time-varying strikes, either with a startDate attribute from which each strike is valid, or mapped to the fixing dates in order. A global strike is overwritten by a local strike in a range bound, or modified by a range strike adjustment. Without any strike for a range, an error is thrown. RangeBounds defines the ranges with RangeFrom and RangeTo, and each range carries a Leverage and a local Strike or StrikeAdjustment. A range without RangeFrom is unbounded towards minus infinity; a range without RangeTo is unbounded towards plus infinity. When the fixing falls outside every range, no payout occurs. RangeBoundSet is the time-varying form of the same information.

Barriers carries the cap of the trade. CumulatedProfitCap terminates the trade when the profit from the long side's view reaches the cap, quoted in the domestic currency for FX. CumulatedProfitCapPoints measures the same profit as an amount divided by the fixing amount and by the absolute leverage. FixingCap terminates the trade when the number of profitable fixings reaches the cap; it makes the trade digital. CumulatedProfitCapPoints cannot combine with the other barrier types.

ORE also provides a scripted representation with the TaRFData node under the trade type ScriptedTrade:

This representation does not allow for time varying strikes or range bounds and also not for a target amount / cumulated profit cap specification in points.

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

In the scripted node the ranges are given as parallel lists: RangeUpperBounds, RangeLowerBounds, RangeLeverages and RangeStrikes. A range without an upper bound takes the sentinel value 100000; a range without a lower bound takes 0. A positive leverage makes a bullish TaRF, a negative leverage a bearish one. KnockOutProfitAmount caps the accumulated profit, KnockOutProfitEvents caps the profitable fixing days, and TargetType selects the payment type: minus 1 for truncated, 0 for exact, 1 for full. A digital knock-out requires the full type.

ORE states the payout formula for each fixing date of a TaRF, for a long position, as the range-bound leverage times the fixing amount times the fixing minus the global or local strike. The fixing only pays when it falls inside a defined range. Profits accumulate from zero: each positive payout adds to the accumulated profit and to the count of profitable days. The cap conditions fire when the accumulated profit reaches the cap amount, or the count reaches the cap number. Under the exact payment type the last payout is adjusted so the accumulated profit matches the target. The current notional of the scripted trade is the fixing amount times the first range strike.

• The underlying price. Each fixing decides the payout size and whether the fixing is profitable.
• The volatility of the underlying. It drives how fast the profit accumulates toward the cap.
• The strikes, the range boundaries and the range leverages.
• The cap level and the target amount.
• The interest rates that discount the payments.

The per-fixing payout is linear in the fixing. The cap adds a binary termination: the trade value concentrates on the path that reaches the target.

Each fixing date settles its forward while the trade is alive. Profitable fixings accumulate toward the cap. In the continuous form the trade terminates on the fixing that first takes the accumulated profit to the cap; the exact payment type tops the last payout up to the target. In the digital form the count of profitable days decides the termination. Without a cap event the strip runs to its last fixing date and then settles.

A target redemption forward sells a strip of forwards at an attractive rate in exchange for capping the upside. Corporate treasuries use it to hedge or convert currency at better-than-market levels; the cap is the price of the improvement. In ORE Studio a customer books target redemption forwards to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long FX TaRF on EUR-USD with exact payment. It buys one million euros at 1.1 per fixing, with double leverage below 1.05, and a cumulated profit cap of 100000:

<Trade id="FX_TARF">
  <TradeType>FxTaRF</TradeType>
  <Envelope/>
  <FxTaRFData>
    <Currency>USD</Currency>
    <FixingAmount>1000000</FixingAmount>
    <TargetAmount>100000</TargetAmount>
    <Strike>1.1</Strike>
    <Underlying>
      <Type>FX</Type>
      <Name>ECB-EUR-USD</Name>
    </Underlying>
    <ScheduleData>
      <Dates>
        <Dates>
          <Date>2017-03-01</Date>
          <Date>2020-03-01</Date>
          <Date>2025-03-01</Date>
          <Date>2029-03-01</Date>
        </Dates>
      </Dates>
    </ScheduleData>
    <OptionData>
      <LongShort>Long</LongShort>
      <PayoffType>TargetExact</PayoffType>
    </OptionData>
    <RangeBounds>
      <RangeBound>
        <RangeTo>1.05</RangeTo>
        <Leverage>2</Leverage>
      </RangeBound>
      <RangeBound>
        <RangeFrom>1.1</RangeFrom>
        <Leverage>1</Leverage>
      </RangeBound>
    </RangeBounds>
    <Barriers>
      <BarrierData>
        <Type>CumulatedProfitCap</Type>
        <Levels>
          <Level>100000</Level>
        </Levels>
      </BarrierData>
    </Barriers>
  </FxTaRFData>
</Trade>

Source: ORE User Guide, Products catalogue, tarf.tex, listing FxTaRF data. The catalogue also shows an equity TaRF with a FixingCap of three profitable fixings, a two-times leverage above 3300 and a strike adjustment of 100.