Term Structure
Table of Contents
Summary
A term structure (also curve) is an ordered series of tenor points representing the time profile of a quantity — a rate, a price, a volatility — across a series of future dates, together with the metadata needed to interpret those points (holiday calendars, non-deliverable currency flags, interpolation method). It is the structural concept a curve family's individual curves each instantiate. A term structure is defined in explicit contrast to a scalar — a market value with no tenor dimension at all — and this document covers both, since scalar is understood almost entirely in relation to term structure rather than as an independent concept.
Detail
Definition
A term structure orders a set of tenor points, each anchored to a common horizon date, and carries metadata beyond the raw (tenor, value) pairs:
- A holiday calendar (or calendars) governing which dates are valid business days for the instrument the term structure represents.
- Non-deliverable-currency flags, where relevant (see Deliverability and non-deliverable instruments).
- An interpolation method, used to derive values at dates falling between the term structure's own tenor points (see Interpolation for why this is needed and the concrete local/non-local method families).
One bootstrapped interest rate curve is one term structure; a curve family is several term structures related by a discounting dependency, not a single, larger term structure — curve identity within a family is a discrete label, not a tenor-like continuous axis, so a family does not itself satisfy this document's definition of a term structure.
Contrast: scalar parameters
A scalar is a single, dimensionless market data value that carries no tenor dimension — it may still evolve over time, but at any given horizon date it has exactly one value, not a series of values indexed by tenor. Examples include spot FX rates, scalar model parameters (e.g. Hull-White mean reversion, bid/offer strike shift), or general valuation settings (e.g. number of Monte Carlo simulations).
Scalars separate further into:
- Global scalars: bid/offer strike shift, Hull-White mean reversion (mid), number of replication dates. 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. Set per analytics run.
Term structure parameters
Model parameters that carry a value at each tenor are structurally identical to a market data curve, but used as model inputs rather than market observables — a term structure parameter. 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; the distinction from a scalar parameter is purely whether the quantity carries one value or a tenor-indexed series of values.
See also
- Term Structures and Tenors — the hub.
- Tenor — the individual points a term structure orders.
- Horizon Date — the anchor every term structure's tenor points are relative to.
- Interest Rate Curves — the concrete bootstrapping mechanics for one interest rate term structure.
- Interpolation — the concrete methods this document's interpolation-method metadata refers to.
- Extrapolation — the policy for values outside the term structure's own range entirely.
- Term Structure Extent — how far a term structure's own range extends, by curve type.
- Funding and Projection Curves — several term structures related by a discounting dependency, not one larger term structure.