Worst Of Basket Swap

ORE defines the product as follows:

The buyer receives an initial fixed amount from the seller and then pays a floating rate over the life of the contract and in turn receives coupons based on an equity notional amount, subject to a coupon trigger event.

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

ORE describes the life of the contract as follows:

If a knock-out event occurs for any given determination date, then the contract is deemed to have terminated at the corresponding settlement date, and all payments will cease thereafter, and no final equity amount will be paid out (or shares delivered). If no knock-out events are triggered, and a knock-in event occurs at the final determination date, then a final equity amount will be delivered to the buyer.

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

A worst of basket swap is a structured coupon product on a basket of assets. The buyer gets an upfront payment, pays a floating rate, and collects a high fixed coupon on each date when every asset in the basket is above its trigger level. If all assets rise above their knock-out levels, the product dies and the payments stop. At the end the buyer receives an amount based on the worst performing asset, unless that asset fell so far that a knock-in condition fires. The worst asset drives the final payout.

The trade types FxWorstOfBasketSwap, EquityWorstOfBasketSwap and CommodityWorstOfBasketSwap have the data containers FxWorstOfBasketSwapData, EquityWorstOfBasketSwapData and CommodityWorstOfBasketSwapData. A scripted representation with the WorstOfBasketSwapData node is also available. LongShort is the own party position. Quantity is the equity notional amount, or the quantity multiplier. Currency is the payout currency for all cashflows; for FX it is the domestic CCY2 currency.

The product pays three kinds of flows. The first is the initial fixed amount: InitialFixedRate times the quantity, paid on InitialFixedPayDate, which defaults to the first floating pay date.

At each determination date the floating leg pays the quantity times the floating rate times the accrual fraction, as long as no knock-out occurred before. FloatingPeriodSchedule gives the period dates and FloatingPayDates the payment dates. The floating rate fixes on FloatingFixingSchedule against FloatingIndex, plus the Floatingspread, and accrues with FloatingDayCountFraction. For overnight index legs, FloatingLookback, FloatingRateCutoff, IsAveraged and IncludeSpread tune the fixing mechanics.

The coupon leg pays when a coupon trigger event fires. The trigger is checked on each determination date: when every underlying in the basket is at or above its FixedTriggerLevel, the buyer receives FixedRate times the quantity. ORE describes the level nodes as follows:

For each fixed trigger determination date, the barrier level used to determine whether a coupon trigger event has occurred, upon which a fixed coupon is paid out at the corresponding payment date.

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

Coupons can accumulate. In the traditional data, a coupon not paid because its trigger did not fire is paid together with the next coupon whose trigger fires, unless AccumulatingFixedCoupons is false. In the scripted data the node is AccumulatingCoupons. Alternatively AccruingFixedCoupons scales the coupon by the fraction of days in the period on which the trigger held, using FixedAccrualSchedule.

The knock-out is checked on KnockOutDeterminationSchedule with the KnockOutLevels barrier nodes. Each KnockOutLevel applies to its own determination date, except the first date of the schedule. When every asset is at or above its level, a knock-out trigger event occurs and the contract terminates at the corresponding settlement date.

The final equity amount is decided on the last determination date. BermudanKnockIn selects whether the knock-in is observed on a regular basis on KnockInDeterminationSchedule, or only on the final date. KnockInLevel is the barrier, expressed as a percentage of the initial prices. The equity amount is paid on KnockInPayDate, which defaults to the last floating pay date.

ORE states the cashflow amounts, at every settlement date from the second on, in terms of the equity notional Q. The floating amount is Q times phi times the accrual fraction times the floating rate fixing for the previous period. Phi is plus 1 for a long and minus 1 for a short position. The coupon amount is Q times delta times the fixed coupon rate times N. Delta is 1 when a coupon trigger event occurs on the determination date, and zero otherwise. N is the number of periods until the next coupon trigger event, for accumulating coupons; without accumulation N is 1 for the life of the contract.

After a knock-out, all floating and coupon amounts are zero. At the final determination date the performance of each asset is its final price over its initial price. The worst performance is the minimum of these. When the worst performance is below the smaller of the strike and the knock-in level, the equity amount pays the quantity times the difference between the strike and the worst performance.

ORE notes the settlement mechanics as follows:

In the case of a physical settlement, the seller will deliver a number of shares of one of the underlying assets to the buyer at the final settlement date for the cost of an agreed strike price. For a cash settlement, the net difference between the strike price and the price at the determination date is paid, although the settlement type does not affect pricing.

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

• The prices of the basket assets. The worst performer drives the final equity amount.
• The correlation between the assets. The coupon and knock-out triggers fire only when every asset is above its level, so lower correlation makes both events less likely.
• The volatility of each asset.
• The trigger, knock-out and knock-in levels.
• The floating rate of the floating leg and its spread.
• The interest rates that discount the flows.

The initial fixed amount settles at the start. On each determination date the floating leg pays while the contract is alive, and the coupon trigger is checked across all assets. Unpaid coupons accumulate until a trigger fires, or scale by the accrual fraction in the accruing variant. A knock-out on any determination date terminates the contract at the corresponding settlement date. On the final date the worst performing asset is measured against the knock-in level to settle the equity amount.

A worst of basket swap pays an enhanced coupon while the basket stays within its trigger structure. The product suits investors who expect the assets to hold their levels. The seller keeps the equity risk of the worst performer, which is the natural hedge for owning a diversified basket. In ORE Studio a customer books worst of basket swaps to value them and run sensitivities on the ORE engine.

ORE's catalogue shows an equity worst of basket swap on the Euro Stoxx 50 and the S&P 500. The trade receives 4% coupons while the basket stays inside the trigger structure, and its knock-in level stands at 75% of the initial prices:

<Trade id="EQ_WorstOfBasketSwap">
  <TradeType>EquityWorstOfBasketSwap</TradeType>
  <Envelope>
    ......
  </Envelope>
  <EquityWorstOfBasketSwapData>
    <LongShort>Long</LongShort>
    <Currency>EUR</Currency>
    <Quantity>1955000</Quantity>
    <Underlyings>
      <Underlying>
        .......
      </Underlying>
    </Underlyings>
    <InitialPrices>
      <InitialPrice>...</InitialPrice>
    </InitialPrices>
    <FloatingPeriodSchedule>
      <Dates>
        ...
      </Dates>
    </FloatingPeriodSchedule>
    <FixedDeterminationSchedule>
            ............
    </FixedDeterminationSchedule>
    <KnockOutDeterminationSchedule>
             .............
    </KnockOutDeterminationSchedule>
    <FloatingPayDates>
      <Dates>
        ....
      </Dates>
    </FloatingPayDates>
    <KnockInDeterminationSchedule>
            ............
    </KnockInDeterminationSchedule>
    <FixedPayDates>
      ............
    </FixedPayDates>
    <KnockOutLevels>
      <KnockOutLevel>...</KnockOutLevel>
    </KnockOutLevels>
    <FixedTriggerLevels>
      <FixedTriggerLevel>...</FixedTriggerLevel>
    </FixedTriggerLevels>
    <KnockInLevel>0.75</KnockInLevel>
    <FixedRate>0.04</FixedRate>
    <FixedAccrualSchedule>
      <Rules>
        ...
      </Rules>
    </FixedAccrualSchedule>
    <FloatingIndex>EUR-EURIBOR-3M</FloatingIndex>
    <FloatingDayCountFraction>Actual/360</FloatingDayCountFraction>
    <FloatingFixingSchedule>
          ............
    </FloatingFixingSchedule>
  </EquityWorstOfBasketSwapData>
</Trade>

Source: ORE User Guide, Products catalogue, worstofbasketswap.tex, listing EquityWorstOfBasketSwap data. The catalogue also shows the scripted representation, in which the basket names the two assets explicitly: EQ-RIC:.STOXX50E and EQ-RIC:.SPX with initial prices 3481.44 and 3714.24.