Zero Coupon Swap

ORE defines the product as follows:

A Zero-Coupon Swap has at least one zero-coupon leg. This leg has no interest rate coupon payments during the life of the swap, just one final interest payment at maturity, akin to a zero-coupon bond. The zero-coupon leg compounds at the tenor of the swap.

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

ORE sets the product up as a swap, trade type Swap, with one leg of type ZeroCouponFixed. The ZeroCouponFixed leg carries an additional ZeroCouponFixedLegData block. The block holds the rates and the compounding convention of the leg.

Swap legs usually exchange coupon streams at regular dates. A zero-coupon leg changes that rhythm. It pays nothing during its life. One final payment then settles the interest that has accrued. The leg suits a party that wants a single bullet payment at a known date.

The product data uses the SwapData container of the Swap trade type. One LegData node describes the floating leg. The other LegData node sets LegType to ZeroCouponFixed and embeds a ZeroCouponFixedLegData block. The block lists the Rates and the Compounding convention. ORE's example below pays floating and receives zero-coupon fixed at 2 percent with simple compounding.

The zero-coupon leg compounds at the tenor of the swap. It behaves like a zero-coupon bond written on the leg notional. The final payment depends on the fixed rate, the notional, the tenor, and the compounding convention. Simple compounding accrues one payment over the full life of the leg. The floating leg accrues and pays coupons in the usual way.

• The discount curve and the swap rates across maturities.
• The fixed rate and the compounding convention of the zero-coupon leg.
• The floating index fixings on the other leg.
• The notional and the day-count convention.
• The distance to the single payment date.

The trade concentrates most interest-rate risk in the one final payment. Its value therefore loads on the discount factor to that maturity.

The zero-coupon leg accrues steadily toward its final payment. The present value of that payment grows as maturity approaches. The discount sensitivity of the payment shrinks as the payment date gets nearer. The floating leg keeps resetting with the market until maturity. At maturity the final payment settles and the trade stops.

A customer with a bullet liability can match it with a zero-coupon leg. A zero-coupon bond issuer can hedge the redemption payment. The structure removes the reinvestment decisions that coupon streams bring. In ORE Studio a customer books zero coupon swaps to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a swap with a floating leg and a zero-coupon fixed leg:

<SwapData>
  <LegData>
    <LegType>Floating</LegType>
    <Payer>true</Payer>
    ...
  </LegData>
  <LegData>
    <LegType>ZeroCouponFixed</LegType>
    <Payer>false</Payer>
    ...
    <ZeroCouponFixedLegData>
        <Rates>
            <Rate>0.02</Rate>
        </Rates>
        <Compounding>Simple</Compounding>
    </ZeroCouponFixedLegData>
  </LegData>
</SwapData>

Source: ORE User Guide, Products catalogue, zerocouponswap.tex, listing Zero Coupon Swap Data.

The plain vanilla swap family sits in the Swap note. The zero coupon swap is that product with a deferred payment leg.