Time Structures and Tenors

A business day is any day that is not a weekend and is not a holiday for any of a specified set of currencies. USD is a special case: USD holidays are conventionally treated as valid business days and are excluded from business day calculations.

A settlement day is any day that is both a valid business day for the relevant currencies and is not a USD holiday. Settlement day conventions govern when cash actually moves.

The spot days (also called settlement days) for a single currency is the number of business days required for delivery of cash. For a currency pair the spot days are the maximum of the two individual currencies' spot days. Most major pairs (e.g. EUR/USD) settle T+2, giving a spot date of today + 2 business days.

The spot date is the settlement date for an FX trade entered today. It is today plus the spot days of the currency pair, adjusted for holidays in both currencies and in the settlement currency (typically USD).

The horizon date is the reference date from which tenored dates are computed. All tenor calculations start here. It is sometimes called the reval date when used in a valuation context.

• Reval Date: The date at which valuation is performed. Not necessarily today.
• Spot Date: The settlement date derived from the reval date and spot days.
• Valuation Spot Date: A normalised spot date used to ensure consistent treatment across currencies when valuing settled cash, also called the adjusted or normalised spot date.

A critical cross-asset convention: for rate curves, tenors beyond S/N are measured from spot. For volatility surfaces, tenors are measured from today. This distinction means that 1W on a rate curve and 1W on a vol surface refer to different calendar dates. Failure to align these conventions leads to significant pricing errors.

To avoid ambiguity at the short end, the following canonical names are useful:

The standard convention used by most FX and interest rate curves:

• O/N: horizon date to next business day (tomorrow)
• T/N: next business day to spot
• Spot: horizon date + spot days
• S/N: spot to spot + 1 business day
• All subsequent tenors (1W, 1M, 1Y, …): measured from spot

Used for short-dated FX swap quotation. Tenors are quoted in terms of the near leg:

• O/N: today (not tomorrow)
• T/N: tomorrow

This convention differs from the forward curve convention and models the near leg of a one-day FX swap. The tenor set typically runs up to S/N.

CDS instruments use a restricted tenor set tied to the four CDS roll dates per year: 20 March, 20 June, 20 September, 20 December. Tenors resolve to the first business day following the appropriate roll date, which can make nominal tenors such as 1Y resolve to materially different dates than on a rates curve. A common disambiguation convention appends the roll quarter: e.g. 1Y 1RQ (one year, one roll quarter).

Single-valued inputs with no tenor dimension. These may be global or report-specific:

• Global scalars: bid/offer strike shift, Hull-White mean reversion (mid), number of replication dates. These are unlikely to vary report-by-report but can evolve over time.
• Report-specific scalars: number of Monte Carlo simulations, number of spatial/time steps, use of Sobol sequences. These are set per analytics run.

Model parameters that carry a value at each tenor, structurally identical to a market data curve but used as model inputs rather than market observables. Examples from SABR: correlation sensitivity (up/down), vol adjustments, risk reversal infinite flag, vol swap adjustments, standard deviation weighting. Like global scalars, these do not typically require per-report overrides.

For currencies with a T+2 spot lag, there is a two-day region before spot: today → tomorrow (O/N) and tomorrow → spot (T/N). For currencies with a T+1 spot lag (e.g. USD/CAD, USD/TRY) this region collapses to a single day.

To value an FX position as of today rather than spot, the spot rate must be adjusted by the short-end rates:

• T+1 spot currencies:
  • Outright today = Spot rate − O/N points × scaling factor
  • Outright tomorrow = Spot rate
• T+2 spot currencies:
  • Outright today = Spot rate − T/N points × scaling factor − O/N points × scaling factor
  • Outright tomorrow = Spot rate − T/N points × scaling factor

A forward rate ladder can be expressed starting from different reference points:

• Out of Spot (standard): rates beyond S/N are computed off spot.
• Out of Tomorrow: rates beyond T/N are computed off tomorrow.
• Out of Today: all rates are computed off today. Tenors in this mode are non-standard and should be visually distinguished to alert users.

Tom/Next serves a dual role:

1. A time reference: the standard settlement convention for rolling an open spot position to the next business day.
2. A funding mechanism: interest accrues on accumulated cash up to the Tom/Next date.

A broken date (also called an odd date) is a maturity that does not correspond to a standard tenor label — for example, a 47-day or 63-day forward. Broken dates arise in bespoke trade structures and require interpolation between the surrounding standard tenor points.

Turn points mark discontinuities in the short-end rate curve caused by calendar effects — most commonly year-end, where funding costs spike. They appear in pairs:

• Turn Start: the date the turn effect begins (e.g. 31 Dec)
• Turn End: the date it ends (e.g. 2 Jan)

Unlike standard tenors, turn points are fixed in calendar time; they do not roll forward as the horizon date advances. They require special handling in interpolation so that the spike does not bleed into adjacent tenors.