Zero Coupon Swap

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Zero-Coupon Swap

A zero-coupon swap is an interest-rate derivative in which one counterparty pays a fixed amount as a single lump-sum at swap maturity, while the other pays floating-rate interest periodically (as in a plain-vanilla interest-rate swap). The defining feature is that the fixed leg is tied to a zero-coupon structure: a single payment at maturity rather than periodic fixed coupons.

How it works

  • Parties: one party is the fixed-rate payer (makes one payment at maturity), the other is the floating-rate payer (makes regular payments tied to a benchmark such as LIBOR or EURIBOR).
  • Payment timing: fixed leg — single lump-sum at maturity; floating leg — periodic payments over the life of the swap. Variations can structure the floating leg as a lump sum or provide the fixed side up-front.
  • Economic effect: cash flows are exchanged net of each leg’s value on payment dates, so only the net amount is actually transferred.

Valuation

Valuing a zero-coupon swap requires discounting each leg to present value using appropriate zero-coupon (spot) rates:

  • Fixed (zero-coupon) leg: value equals the lump-sum fixed payment discounted by the spot rate for the maturity:
    PV_fixed = LumpSum / (1 + z_T)^T
    where z_T is the T-period zero-coupon rate.
  • Floating leg: value is derived from implied forward rates and the current yield/spot curve. Practically, the floating leg’s present value can be obtained by bootstrapping spot rates from market instruments and constructing the schedule of discounted expected floating payments.
  • Net value: swap value = PV_floating − PV_fixed (sign depends on which side you stand).

Key techniques used:
– Spot (zero-coupon) curve construction through bootstrapping.
– Deriving forward rates from spot rates when projecting floating payments.

Variations

  • Reverse zero-coupon swap: fixed payment is made at initiation (up-front), reducing credit exposure for the fixed receiver.
  • Exchangeable zero-coupon swap: embeds an option that allows converting the lump-sum fixed payment into a series of fixed periodic payments (or vice versa). This can shift payment timing or create flexibility if interest-rate volatility or preferences change.
  • Both legs lumped: swaps can be structured so either or both legs are paid as lump sums at maturity, depending on counterparty needs.

Uses

  • Hedging: manage exposure to future interest-rate movements where a single maturity cash flow better matches liabilities or assets.
  • Funding and cash-flow timing: firms or investors who prefer or require a single future payment (or who want to delay receiving fixed cash flows) can use zero-coupon swaps to match timing.
  • Speculation: traders can express views on the shape of the zero-coupon curve or on credit/exposure differences caused by payment timing.

Risks

  • Credit/Counterparty risk: the party receiving the fixed lump sum is exposed to greater credit risk because they do not receive interim cash flows; if the counterparty defaults before maturity, the fixed receiver may lose expected payment.
  • Liquidity risk: nonstandard payment timing can make market exit more difficult compared with plain-vanilla swaps.
  • Valuation risk: relies on accurate spot-curve construction and forward-rate estimation; model or curve errors affect pricing.
  • Market risk: changes in interest rates alter the present values of both legs and the swap’s mark-to-market.

Example (illustrative)

If a swap’s fixed leg promises a single payment of 100 at maturity 5 years from now and the 5-year zero-coupon rate is 3% (annual compounding), the present value of the fixed leg is:
PV_fixed = 100 / (1.03)^5 ≈ 86.26.
The floating leg’s present value would be calculated from the spot/forward curve and then compared to this PV to determine the swap’s net value at inception or later.

Key takeaways

  • A zero-coupon swap replaces periodic fixed payments with a single fixed payment at maturity, while the floating side typically pays periodically.
  • Valuation depends on zero-coupon (spot) rates and forward-rate construction (bootstrapping).
  • Payment timing creates additional credit and liquidity considerations compared with plain-vanilla swaps.
  • Variants exist to shift upfront payment, convert lump sums to series, or make the floating side a lump sum as well.