Curve Building Script

Built-In Functions

asMonths

A curve function that breaks a single contract into a list of monthly contracts, e.g. a quarter into 3 months

Syntax

Contracts = asMonths(Contract)

Result

A Contracts object

Example

c = Contract(ondate, "2021Q01", 26.85)
contracts = asMonths(c)
for tenor in contracts
    print tenor.absolute + " : " + tenor.value
next

2021M01 : 26.85
2021M02 : 26.85
2021M03 : 26.85

bootstrapCurve

Creates an arbitrage free monthly curve from an input curve

Description

The bootstrap function converts quarters, seasons and years into months and performs an arbitrage-free calculation on any overlapping periods.

Syntax

bootstrapped = bootstrapCurve(Curve)

Result

A curve with monthly tenors

Example

ondate = CurveDate(Date("2020-12-14"), "REOMHENG")

curve = Curve(ondate)
curve.add(Contract(ondate, "2021M01", 26.87))
curve.add(Contract(ondate, "2021Q01", 26.85))
curve.add(Contract(ondate, "2021Q02", 26.75))

bootstrapped = bootstrapCurve(curve)
for tenor in bootstrapped.contracts
    print tenor.absolute + " : " + tenor.value
next

2021M01 : 26.87
2021M02 : 26.84
2021M03 : 26.84
2021M04 : 26.75
2021M05 : 26.75
2021M06 : 26.75

You can see in the example that 2021M02 and 2021M03 are calculated using the formula:

((2021Q01 * 3) - 2021M01) / 2

extendCurve

Extends a curve by a required number of years by using the value of the last maturity

Syntax

extended = extendCurve(curve, years)

The years parameter represents the number of years to extend the curve by. For example, if a curve ends in May 2022 and you specify 2 for years, the curve will be extends to December 2024.

Example

function agricultural(input)
    // Agricultural curve forward filled and extended to end of 3 years
    filled = forwardFillCurve(input)
    extended = extendCurve(filled, 3)
    agricultural = shape(extended)
end

forwardFillCurve

Fills any gaps in a curve by using the value from a previous maturity

Syntax

filled = forwardFillCurve(curve)

Result

The function checks for any gaps in the maturities of a curve and forward fills using the value of the maturity immediately before it.

Example

ondate = CurveDate(Date("2020-10-30"), "REOMHENG")

curve = Curve(ondate)
curve.add(Contract(ondate, "2020M11", 26.87))
curve.add(Contract(ondate, "2020M12", 26.85))
curve.add(Contract(ondate, "2021M01", 26.75))
curve.add(Contract(ondate, "2021M03", 26.62))
curve.add(Contract(ondate, "2021M04", 26.55))

filled = forwardFillCurve(curve)

for tenor in filled.contracts
    other = curve\[tenor.tenor\]
    if other
        print tenor.tenor + " = " + tenor.value + " was " + other.value
    else
        print tenor.tenor + " = " + tenor.value
    end
next

This produces the following output:

M00 = 26.870000 was 26.870000
M01 = 26.870000 was 26.850000
M02 = 26.750000 was 26.750000
M03 = 26.750000
M04 = 26.620000 was 26.620000
M05 = 26.550000 was 26.550000

shape

A curve function that shapes a monthly curve

Syntax

Curve = shape(Curve)

Result

A curve that is shaped using the a normalised shape based on the first 12 months of the input curve. It then shapes the rest of the curve in blocks of 12 months retaining the correct average values.

Example

ondate = CurveDate(Date("2020-10-30"), "REOMHENG")

curve = Curve(ondate)
curve.currency = "EUR"
curve.units = "MWH"
curve.add(Contract(ondate, "2020M11", 26.87))
curve.add(Contract(ondate, "2020M12", 26.85))
curve.add(Contract(ondate, "2021M01", 26.75))
curve.add(Contract(ondate, "2021M02", 26.65))
curve.add(Contract(ondate, "2021M03", 26.62))
curve.add(Contract(ondate, "2021M04", 26.55))
curve.add(Contract(ondate, "2021M05", 26.68))
curve.add(Contract(ondate, "2021M06", 26.89))
curve.add(Contract(ondate, "2021M07", 27.05))
curve.add(Contract(ondate, "2021M08", 27.15))
curve.add(Contract(ondate, "2021M09", 27.02))
curve.add(Contract(ondate, "2021M10", 26.85))
curve.add(Contract(ondate, "2021Q04", 26.92))
curve.add(Contract(ondate, "2022Y", 27.12))
curve.add(Contract(ondate, "2023Y", 27.20))

bootstrapped = bootstrapCurve(curve)
shaped = shape(bootstrapped)

for tenor in shaped.contracts
    print tenor.absolute + " : " + tenor.value
next

2020M11 : 26.870000
2020M12 : 26.850000
2021M01 : 26.750000
2021M02 : 26.650000
2021M03 : 26.620000
2021M04 : 26.550000
2021M05 : 26.680000
2021M06 : 26.890000
2021M07 : 27.050000
2021M08 : 27.150000
2021M09 : 27.020000
2021M10 : 26.850000
2021M11 : 26.955000
2021M12 : 26.955000
2022M01 : 27.025839
2022M02 : 26.924628
2022M03 : 26.894362
2022M04 : 26.823741
2022M05 : 26.954893
2022M06 : 27.167080
2022M07 : 27.328824
2022M08 : 27.429710
2022M09 : 27.298558
2022M10 : 27.126726
2022M11 : 27.232819
2022M12 : 27.232819
2023M01 : 27.105562
2023M02 : 27.004051
2023M03 : 26.973696
2023M04 : 26.902867
2023M05 : 27.034406
2023M06 : 27.247219
2023M07 : 27.409440
2023M08 : 27.510624
2023M09 : 27.379085
2023M10 : 27.206746
2023M11 : 27.313152
2023M12 : 27.313152

This is the bootstrapped curve:

And here is the shaped curve:

SmartCurve Functions

#CurveScript is the default script used for expressions in Smart Curves.

bootstrap

bootstrap is a shortcut version of bootstrapCurve which creates an arbitrage-free monthly curve from an input curve containing any number of:

• Months
• Quarters
• Seasons
• Years

Syntax

bootstrap(BASE)

bootstrapAndShape

This function first bootstraps an input curve and then shapes it using the default shaping algorithm.

Syntax

bootstrapAndShape(BASE)

multiplyByFactor

This function multiplies an input curve by a fixed factor

Syntax

multiplyByFactor(BASE, factor)

divideByFactor

This function divides an input curve by a fixed factor

Syntax

divideByFactor(BASE, factor)

addPremium

This function adds a fixed premium to an input curve

Syntax

addPremium(BASE, premium)

discount

This function subtracts a fixed discount from an input curve

Syntax

discount(BASE, discount)

flatCurve

This function creates a monthly curve with the same value for every tenor. It takes 2 parameters:

• Months - the number of months you want the curve to be
• Value - the value you want to assign every tenor

Syntax

flatCurve(12, 25.2)

interpolate

The function fills in any missing tenors in the input curve using the specified method, which can be one of:

• FORWARD
• BACKWARD
• LINEAR
• CUBIC

Syntax

interpolate(BASE, 'LINEAR')