QUANT.KEYRATE OpenBI

Where a bond's rate risk sits on the curve: its value change when each instrument's rate rises by a basis point.

Group: Quantitative finance. OpenBI’s own: DAX has no function of this name.

Syntax

QUANT.KEYRATE ( <table>, <kind>, <tenor>, <rate>, <asOf>, <maturity>, <coupon> [, <frequency>] [, <notional>] [, <calendar>] [, <settlementDays>] )

Returns

Table. Tenor, Kind, Rate, Years, DV01 and Share: a row for each instrument, its DV01 the change in the bond's value when that instrument alone is a basis point higher, and Share that change's part of all of them.

Remarks

• The bond's coupons fall a period apart counting back from its maturity; each one after the curve's date, and the notional at maturity, is discounted on the curve. Then, one instrument at a time, its rate is raised by 0.0001 and the bond is valued on a curve built anew with that one change.
• The DV01s are negative for a bond: a higher rate lowers its value. Their sum is close to the value change for every rate a basis point higher at once (the third example).
• The ladder shows which maturities to hedge: a bond to April 2034 sits mostly on the 7-year and 10-year swaps around it. The shortest deposit moves it a little even though it ends before the first coupon: every other instrument starts two business days after the curve's date, and that deposit sets the curve there.
• A maturity after the curve's last instrument is an error: the curve would have to be extended.
• A deposit is a simple rate on the Actual/360 count. A swap pays a fixed rate once a year on 30/360 against a six-month floating rate. A zero rate is continuous on Actual/365; when every row is "zero", the rates are the curve as they are and nothing is bootstrapped.
• Deposits and swaps can be mixed; zero rates cannot be mixed with them.
• Between the instruments the discount factors are interpolated log-linearly, so the forward rate is flat from one instrument's maturity to the next.

Compared with DAX

An OpenBI function: DAX has none like it, so a measure or query that uses it works in OpenBI only, not in Power BI or Analysis Services.

Examples

NOK 100 million of a 5 % bond to April 2034

Paid twice a year, valued on the NOK curve as the Brewery's planning page does.

EVALUATE
SELECTCOLUMNS (
    QUANT.KEYRATE (
        Rates, Rates[Kind], Rates[Tenor], Rates[Rate],
        DATE ( 2026, 10, 13 ), DATE ( 2034, 4, 13 ), 0.05, 2, 100000000, "Norway"
    ),
    "Tenor", [Tenor],
    "DV01", ROUND ( [DV01], 0 ),
    "Share", ROUND ( [Share], 4 )
)

A five-year bond on the same curve

A bond with annual coupons to October 2031: almost all of its risk is on the 5-year swap, whose dates its coupons share.

EVALUATE
SELECTCOLUMNS (
    QUANT.KEYRATE (
        Rates, Rates[Kind], Rates[Tenor], Rates[Rate],
        DATE ( 2026, 10, 13 ), DATE ( 2031, 10, 13 ), 0.04
    ),
    "Tenor", [Tenor],
    "Share", ROUND ( [Share], 4 )
)

The ladder adds up

The 2034 bond valued from the curve's monthly discount factors (its coupons fall on the 13th), with every rate a basis point higher, against the sum of its ladder.

EVALUATE
VAR AsOf = DATE ( 2026, 10, 13 )
VAR Maturity = DATE ( 2034, 4, 13 )
VAR Ladder =
    QUANT.KEYRATE ( Rates, Rates[Kind], Rates[Tenor], Rates[Rate], AsOf, Maturity, 0.05, 2, 100000000, "Norway" )
VAR Base = QUANT.CURVE ( Rates, Rates[Kind], Rates[Tenor], Rates[Rate], AsOf, "curve", "Norway" )
VAR Up = QUANT.CURVE ( Rates, Rates[Kind], Rates[Tenor], Rates[Rate] + 0.0001, AsOf, "curve", "Norway" )
VAR Value0 =
    SUMX (
        FILTER ( Base, [Date] > AsOf && [Date] <= Maturity && ( MONTH ( [Date] ) = 4 || MONTH ( [Date] ) = 10 ) ),
        ( 2500000 + IF ( [Date] = Maturity, 100000000 ) ) * [Discount]
    )
VAR Value1 =
    SUMX (
        FILTER ( Up, [Date] > AsOf && [Date] <= Maturity && ( MONTH ( [Date] ) = 4 || MONTH ( [Date] ) = 10 ) ),
        ( 2500000 + IF ( [Date] = Maturity, 100000000 ) ) * [Discount]
    )
RETURN
    ROW (
        "Value", ROUND ( Value0, 0 ),
        "All rates up 1 bp", ROUND ( Value1 - Value0, 0 ),
        "Sum of the ladder", ROUND ( SUMX ( Ladder, [DV01] ), 0 )
    )

Related functions

QUANT.CURVE, QUANT.BOND.DV01, QUANT.BOND.DURATION, VALUATION.

Last updated 3 November 2026 · OpenBI Studio 0.3.74