Swap

Table of Contents

A swap exchanges two streams of interest payments, its legs, on a notional that the parties never exchange. ORE's Swap trade type covers vanilla fixed-vs-floating, basis, OIS, BMA, and CMS structures. This note records the domain grounding for the whole family, as ORE documents it in its product catalogue.

1. Identifiers

What a trader books it as, and what to grep for. The codes are the trade type catalogue's, which is what the database enforces.

Field Value
Full name Swap
Short name Swap
ORE Studio product code Swap
Asset class rates
Family Swap
ORE trade data node SwapData
ORE documentation swap.tex

2. Summary

An interest rate swap (IRS) is a bilateral contract. It exchanges a stream of interest payments for another stream, both computed on a notional amount in one currency. The notional itself is not exchanged. ORE models the family under the single trade type Swap. The common use is to transform the interest-rate exposure of an asset or a liability. Cash flows are the underlying building block of every leg.

3. Detail

3.1. What it is

ORE defines the core instrument as follows:

An interest rate swap (IRS) is an agreement between two counterparties in which one stream of future interest payments (leg) is exchanged for another based on a specified notional amount.

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

Two properties are common to the whole family. The notional per leg may be fixed, amortising, or accreting. The fixed rate or floating spread may vary over the life of the swap.

3.2. In plain terms

Two parties agree to pay each other interest on the same pile of money for a set period. One pays a rate that is known in advance. The other pays a rate that is reset from the market over time. Only the difference between the two payments changes hands, usually periodically.

3.3. Variants inside the ORE Swap family

  • Vanilla IRS. One fixed leg against one floating leg. The floating leg is benchmarked to an IBOR index of a given tenor.
  • Single-currency basis swap. Two floating legs. They are benchmarked to two different IBOR indices, or to different tenors of one index.
  • OIS. At least one leg is benchmarked to an overnight index rate. That is the rate for overnight unsecured bank lending. The overnight leg compounds on a daily basis.
  • BMA swap. One leg is benchmarked to the US SIFMA municipal swap index.
  • CMS and CMB swaps. One leg is benchmarked to a longer-maturity market rate. CMS uses a swap rate. CMB uses a class of government bond yields. A CMS leg may carry a cap, floor, or collar.

ORE also models related structures as separate products in its catalogue. They are the ZeroCouponSwap, the CrossCurrencySwap, the CallableSwap, the FlexiSwap, the BalanceGuaranteedSwap, and the KnockOutSwap. Each gets its own product note in this set.

3.4. Mathematical notes

The value of a swap is the difference between the present values of its two legs, discounted on the funding curve. A floating leg's expected payments come from the projection curve of its index. These two term structures are distinct. See funding and projection curves. A CMS leg adds convexity, because the index rate and the discount rate are correlated. A cap or floor on the leg prices off the interest-rate volatility surface.

3.5. What moves its value (static sensitivities)

  • The discount curve. One basis point shifts of it give the DV01 of the trade. Every leg is sensitive to it.
  • The projection curve of each floating index. It drives the expected fixings.
  • The paid or received spread on each leg.
  • Index-convention details, such as day count, payment lag, or business calendar.

A vanilla receive-fixed swap gains value when rates fall. A pay-fixed swap gains value when rates rise. The size of the move scales with the notional and the remaining life of the trade.

3.6. How the profile ages (dynamic sensitivities)

The value and risk profile evolve as the trade runs its schedule. Each fixing turns one unknown payment into a known one. The remaining risk migrates along the curve as time passes. An amortising notional shrinks the exposure on schedule. At maturity the swap has no residual market risk, only the last settlement.

3.7. Why a customer would want it

A borrower with floating-rate debt pays fixed to remove rate risk. An investor with fixed coupons pays floating to transform them. Dealers quote swaps to manage their own rate books. OIS swaps are the primary market for funding rates. They are the anchors of discount-curve construction. In ORE Studio a customer books swaps to value them, run sensitivities, and feed XVA on the ORE engine.

3.8. Example

A 20-year EUR fixed-vs-floating swap from the ORE trade corpus that ORE Studio keeps for its round-trip tests. The fixed leg is shown. The floating leg follows in the same file. Source: assets/test_data/golden_dataset/Products/Example_Trades/IR_Swap_Vanilla.xml. 

<Portfolio>
  <Trade id="Swap_20y">
    <TradeType>Swap</TradeType>
    <Envelope>
      <CounterParty>CPTY</CounterParty>
      <NettingSetId>NS</NettingSetId>
    </Envelope>
    <SwapData>
      <LegData>
        <Payer>false</Payer>
        <LegType>Fixed</LegType>
        <Currency>EUR</Currency>
        <PaymentConvention>MF</PaymentConvention>
        <DayCounter>A360</DayCounter>
        <Notionals>
          <Notional>10000000</Notional>
        </Notionals>
        <ScheduleData>
          <Rules>
            <StartDate>2023-02-21</StartDate>
            <EndDate>2043-02-21</EndDate>
            <Tenor>1Y</Tenor>
            <Calendar>TARGET</Calendar>
            <Convention>MF</Convention>
            <Rule>Forward</Rule>
          </Rules>
        </ScheduleData>
      </LegData>

Native ORE example portfolios with swaps sit under external/ore/examples/. The Academy and AmericanMonteCarlo Input/portfolio.xml files both contain swaps.

4. See also

Emacs 29.3 (Org mode 9.6.15)