How does a range accrual note pay coupon based on an index staying within a range?

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AcadiFi · Accepted Answer

A range accrual pays a coupon that accrues only on days when a reference rate or index closes within a predefined range. Consider Falconbridge Investment Bank's 3-year note paying 7% annually, accruing only on days when 3-month SOFR is between 2.50% and 4.25%. Daily accrual formula: coupon × (N_in / N_total), where N_in is days inside the range. If SOFR stays inside 220 of 365 days, the annual coupon is 7% × (220/365) = 4.22%. The note is structurally a strip of digital options — each observation day is a binary bet on SOFR remaining in range.

Pricing requires modeling correlation between observation days and volatility of the reference rate, typically done via a Hull-White or LMM interest rate model. Investors win when rates are stable; they lose if rates break out of the range early in the period. Issuers often set the range wide enough to look attractive but narrow enough that their expected accrual is around 60-70% of days, creating a profit margin. Risks include: rate regime shifts (e.g., Fed cutting below 2.50%), mis-forecasting volatility, and illiquid secondary markets. Range accruals can also be structured on FX or equity indices.

How does a range accrual note pay coupon based on an index staying within a range?

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