How does a range accrual swap work and why use one?

Question

AcadiFi · Accepted Answer

In a range accrual swap, the coupon on one leg accrues only on days when a reference index stays inside a pre-defined range. Days outside the range contribute zero.

Typical structure: Coupon = Max_Rate × (N_in / N_total), where N_in is the count of days the reference fixing is inside [Lower, Upper] and N_total is total days in the period.

Example: 1Y range accrual swap on SOFR, range 3.00% to 4.50%, max coupon 7%. Period has 252 business days.

- SOFR was inside [3%, 4.5%] on 180 days.
- Coupon = 7% × (180/252) = 5.00%.

Economic motivation: the receiver of the range accrual earns an above-market coupon in exchange for bearing the risk that the index drifts outside the band. Structurally equivalent to selling a strip of digital options: one long-digital-at-Lower minus one short-digital-at-Upper for each business day.

Payer's perspective: pays enhanced coupon, receives embedded digital option value as hedge against rate spikes or collapses.

Risks for the receiver:

1. Path dependence: only days inside the range count, so vol and mean reversion drive value.
2. Hedging complexity: digital options have discontinuous deltas at the strike — dealers hedge with vertical spreads, accepting gap risk.
3. Liquidity: bespoke structures have wide bid-ask at unwind.

Avoid marketing range accruals to unsophisticated investors — SEC has flagged misselling cases when coupon formulas weren't adequately explained.

How does a range accrual swap work and why use one?

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