A YoY-inflation optionlet vol surface, quoted via volatility/totalVariance at (maturity, strike) pairs rather than QuantLib's usual (option date, tenor, strike) grid, since inflation caplets observe a single index fixing rather than a forward rate. A plain VolatilityTermStructure leaf like CapFloorTermVolSurface, constructed and consumed via a Handle (mirroring OptionletVolatilityStructure, since it feeds yoyInflationBlackCapFloorEngine et al. exactly the way OptionletVolatilityStructure feeds blackCapFloorEngineFromVolatilityStructure). See the hierarchy under GenTermStructure.

Prices YoY cap/floors by cap/floor-surface intersection and put/call parity, deriving an ATM YoY swap curve as a side effect -- the market-data input the YoY optionlet stripper (kInterpolatedYoyOptionletVolatilitySurfaceBlack et al.) bootstraps from. A plain TermStructure leaf, constructed and consumed by shared_ptr like CPICapFloorTermPriceSurface, never a Handle. Takes independent Interpolation2D (cap/floor price grid) and Interpolation (per-maturity) choices -- a different template (InterpolatedYoYCapFloorTermPriceSurface) from CPICapFloorTermPriceSurfaces InterpolatedCPICapFloorTermPriceSurface, hence the separate 2-D/1-D pair rather than CPICapFloorTermPriceSurfaces single Interpolation2D. See the hierarchy under GenTermStructure.

Prices CPI cap/floors by interpolation and put/call parity off a market strike/maturity price grid, not by any vol model (see CPICapFloors own comment) -- a plain TermStructure leaf, constructed and consumed by shared_ptr like CommodityCurve, never a Handle (wrapped into one at the point of use, e.g. interpolatingCpiCapFloorEngine). Takes an Interpolation2D choice for the cap/floor price grid -- a different template (InterpolatedCPICapFloorTermPriceSurface) from YoYCapFloorTermPriceSurfaces InterpolatedYoYCapFloorTermPriceSurface, hence its own single 2-D slot rather than YoYCapFloorTermPriceSurfaces separate 2-D/1-D pair. See the hierarchy under GenTermStructure.

A CPI (zero-inflation) volatility surface, quoted via volatility/totalVariance at (maturity, strike) pairs -- same shape as YoYOptionletVolatilitySurface, a plain VolatilityTermStructure leaf constructed and consumed via a Handle. Unlike YoYOptionletVolatilitySurface it feeds no pricing engine in QL 1.43: CPICapFloor prices purely off CPICapFloorTermPriceSurface via interpolatingCpiCapFloorEngine, and CPICouponPricer (the type that would consume this) is itself explicitly unfinished upstream for vol-dependent coupons (no concrete descendant exists to bind, unlike YoYInflationCouponPricers three) -- so this type stands alone as a queryable surface, not (yet) as engine/pricer plumbing. See the hierarchy under GenTermStructure.

Constant YoY-inflation optionlet vol surface, no maturity/strike dependence. Mirrors constantOptionletVolatility, taking a GenQuote rather than a plain Double per the std::variant/overload-collapse rule (the flat case is already reachable via simpleQuote). Not the only concrete leaf of this type any more -- see kInterpolatedYoyOptionletVolatilitySurfaceBlack for the market-quote-bootstrapped alternative.

Strips a YoYOptionletVolatilitySurface from a YoYCapFloorTermPriceSurface by bootstrapping a per-strike vol curve against Black-priced YoY caps/floors (mirrors upstream's own testYoYPriceSurfaceToVol: an InterpolatedYoYOptionletStripper solving each strike's initial vol, then a KInterpolatedYoYOptionletVolatilitySurface interpolating across strikes, both sharing the given Interpolation -- neither is exposed as its own type, since nothing in upstream reaches them from outside this one bootstrap; see this function's C shim for the full pipeline). index/nominalTermStructure price the null-vol engine the stripper solves against; slope is the assumed initial caplet-vol slope for strikes past the edge of good price data (a negative slope for typically low/flat short-dated extreme-strike prices, per upstream's own comment -- too extreme a slope can leave no arbitrage-free solution).

As kInterpolatedYoyOptionletVolatilitySurfaceBlack, but unit-displaced Black.

As kInterpolatedYoyOptionletVolatilitySurfaceBlack, but Bachelier (normal model).

Prices YoY cap/floors by cap/floor-surface intersection and put/call parity, deriving an ATM YoY swap curve as a side effect. Interpolation2D chooses the cap/floor price-grid interpolator, Interpolation the per-maturity one.

Prices CPI cap/floors by interpolation and put/call parity off a market strike/maturity price grid. Interpolation2D chooses the cap/floor price-grid interpolator. cPrice/ fPrice are plain price matrices (rows = strikes, columns = maturities), not quote-linked like capFloorTermVolSurfaces volatility matrix.

Constant CPI (zero-inflation) volatility surface, no maturity/strike dependence -- the only concrete leaf bound here, mirroring constantYoyOptionletVolatility. No engine or coupon pricer consumes this in QL 1.43 (see this type's own haddock in QuantLib.Internal.Type), so it is queryable via cpiVolatility/cpiTotalVariance but not otherwise wired up.

The volatility for a given maturity date and strike, observed with the given observation lag (or the surface's own lag when Nothing).

The total integrated variance for a given exercise date and strike -- useful because it scales out time from the optionlet pricing formulae. As yoyOptionletVolatility, a Nothing observation lag uses the surface's own.

The date the surface's own YoY term structure (and hence any YoYOptionletVolatilitySurface stripped from it) treats as its base -- referenceDate minus the observation lag, rounded to the containing inflation period's start.

The ATM YoY swap curve derived from cap/floor-surface intersection, as (date, rate) pairs.

The same ATM YoY swap curve as yoyCapFloorAtmYoySwapDateRates, but with maturities as year fractions from the surface's reference date rather than dates.

The ATM YoY swap rate at the given maturity date, from put/call parity on the surface's cap/floor price data.

The ATM YoY inflation rate at the given maturity date and observation lag (or the surface's own lag when Nothing), derived from the swap-rate curve above.

The union of cap and floor strikes in the surface's price grid -- the strikes a stripped YoYOptionletVolatilitySurface (via kInterpolatedYoyOptionletVolatilitySurfaceBlack et al.) has a bootstrapped vol curve for.

The volatility for a given maturity date and strike, observed with the given observation lag (or the surface's own lag when Nothing).

The total integrated variance for a given exercise date and strike. As cpiVolatility, a Nothing observation lag uses the surface's own.