Curve Conventions and Day-Count
Day-count, compounding, and calendars connect abstract rates to real cash-flow accruals.
Day-count conventions (e.g., ACT/360, ACT/365, 30/360) define how time fractions are computed between dates.
Compounding conventions (simple, annual, continuous) determine how quoted rates translate into discount factors.
Calendars and business-day rules affect accrual periods, fixing dates, and payment dates in interest-rate products.
A robust pricing library centralises these conventions so all products and curves use consistent time calculations.
This graph compares year fractions for ACT/365, ACT/360 and 30/360 for the same number of calendar days, and shows the resulting discount factors under different compounding styles. Use the sliders to change tenor and rate and see how small convention choices move accrual and PV.
Day-count is a mapping from date pairs to year fractions. Compounding is a mapping from (rate, τ) to discount factor. Both are conventions, not laws of nature, but once fixed they must be applied consistently across products and curves.
For short tenors the numerical differences look small, but on large books they add up to material P&L and reconciliation noise. The practitioner’s rule: centralise convention logic in one place, never re-implement it per product, and always log the day-count and compounding assumptions used for a given curve or price.