fixed-income.wiki

A machine-readable reference for fixed income mechanics: every common day-count convention with its exact algorithm and worked accrual, price and yield arithmetic from a cash-flow schedule, duration and convexity checked against exact repricing, curve bootstrapping and the four spread measures, settlement and quotation conventions by market, and the reset mechanics of floating-rate and inflation-linked instruments.

Fixed income has the highest ratio of formula to opinion of anything in finance, and it is still got wrong constantly, because the conventions that feed the formulas are numerous, market-specific, and almost never written down in one place. This reference states the conventions and the arithmetic. Every entry that changes a settlement amount, a yield, or a risk number carries an explicit formula and a worked example whose figures compute. It is not a glossary: definitions of bond terminology are free everywhere and worth nothing, while the day-count algorithm that decides whether an accrual is 180 or 182 days is not. One instrument runs through every section so the numbers tie together. The reference bond is a 4.500 percent semiannual bond with coupon dates of 15 May and 15 November, maturing 2034-11-15, settling 2026-08-27 at a quoted price of 98.750 per 100 of par, which is 98-24 in thirty-seconds. Its current accrual period runs 2026-05-15 to 2026-11-15, so A = 104 accrued days out of E = 184 in the period, with 80 days remaining to the next coupon. On ACT/ACT (ICMA) the accrued interest is 1.271739, the full price 100.021739, the street-convention yield 4.684070 percent nominal semiannual, the modified duration 6.706168, the DV01 0.067076 per 100 of par and the convexity 53.827761. Those figures reappear throughout. Where a section needs a second instrument, an illustrative curve, a repo rate or a call schedule, it says so explicitly at the point of use. Notation is uniform. P is the quoted or clean price per 100 of par and P_full = P + AI the full or dirty price, where AI is accrued interest per 100 of par. C is the annual coupon rate in percent of par, f the number of coupon periods per year and c = C/f the periodic coupon. y is an annual yield quoted nominal and compounded f times a year, so a discount factor over n periods is (1 + y/f) raised to the power -n. n_k counts coupon periods, possibly fractional, from settlement to cash flow k, and w = n_1 is the fraction of the current period still to run, equal to the days from settlement to the next coupon divided by E. A is accrued days and E days in the coupon period, in the ICMA sense, so A + (E - A) = E and w + A/E = 1. A day-count fraction is written D/B, where D is a convention's numerator in days and B its denominator. z(t) is a zero or spot rate at time t on a stated compounding basis and DF(t) the matching discount factor. s is a spread expressed as a decimal, and one basis point is 0.0001. D_mac, D_mod and Cx are Macaulay duration, modified duration and convexity, and DV01, also written PVBP, is the price change per 100 of par for a one-basis-point move. In money-market arithmetic d is a discount rate and t a day count. In compounded-in-arrears arithmetic r_i is an overnight fixing, n_i the calendar days it applies for, d_b the business days in the period and d_c its calendar days. QM is a quoted margin and DM a discount margin. IR is an inflation index ratio. Notional amounts in worked examples are 10,000,000 of par unless stated otherwise. Prices, coupons, curve levels, repo rates, discount rates, overnight fixings, index values, call schedules and option-model outputs used in worked examples are chosen to make the arithmetic legible. None of them is a market observation, a typical level, or a benchmark, and none should be read as one. Where a convention is fixed by a published rule the rule is named in the entry's source field; where a convention varies by market the entry says which market it describes.

Sections

• Day count and accrual The conventions that decide how many days a period contains, and the accrued interest that follows from them. - 13 entries, 5 tables
• Price and yield Discounting a cash-flow schedule, the yield measures that invert it, and the money-market conventions that do not compound at all. - 13 entries, 6 tables
• Risk measures Duration, convexity, DV01 and the hedge ratios built from them, worked against an exact reprice. - 13 entries, 5 tables
• Curves and spreads Zero, par and forward curves, the bootstrap that connects them, and the four spread measures against them. - 12 entries, 5 tables
• Settlement and market conventions When a trade settles, how a date is adjusted, how a price is quoted, and what actually moves. - 12 entries, 6 tables
• Floaters, index-linked and structures Coupon reset mechanics, SOFR compounding conventions, the statutory LIBOR spread adjustments, and inflation index ratios. - 11 entries, 4 tables

For machine readers

Every section has a parallel JSON endpoint at /{section}.json containing the same facts without markup. A manifest of the full corpus is at /llms.txt. Structured data is emitted as schema.org DefinedTermSet on every page.

Related references

This site is one of 9 topical references built from the same open generator, indexed at wallstreet.wiki. Each one owns a single subject. Where two subjects touch, the arithmetic lives on one site and the other links to it rather than restating it. The whole network is machine-readable at /network.json.