ratecurve

R2026b

Create ratecurve object for interest-rate curve from dates and data

Description

Build a ratecurve object using ratecurve.

After creating a ratecurve object, you can use the associated object functions forwardrates, discountfactors, and zerorates.

Note

If you have the interest-rate term structure obtained previously from the intenvset or toRateSpec function for an IRDataCurve or IRFunctionCurve object, refer to Workflow for Creating and Analyzing a ratecurve and parametercurve.

To price a Swap, FixedBond, FloatBond, FRA, or Deposit instrument, you must create a ratecurve object and then create a Discount pricer object.

For more detailed information on this workflow, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

For more information on the available instruments, models, and pricing methods, see Choose Instruments, Models, and Pricers.

Creation

Syntax

ratecurve_obj = ratecurve(Type,Settle,Dates,Rates)

ratecurve_obj = ratecurve(___,Name=Value)

Description

ratecurve_obj = ratecurve(Type,Settle,Dates,Rates) creates a ratecurve object.

ratecurve_obj = ratecurve(___,Name=Value) creates a ratecurve object using name-value pairs and any of the arguments in the previous syntax. For example, myRC = ratecurve("zero",Settle,ZeroDates,ZeroRates,Compounding=2,Basis=5,InterpMethod="pchip",ShortExtrapMethod="linear",LongExtrapMethod="cubic") creates a ratecurve object for a zero curve. You can specify multiple name-value pair arguments.

Input Arguments

Type — Type of interest-rate curve

"zero" | "forward" | "discount"

Type of interest-rate curve, specified as "zero", "forward", or "discount".

Settle — Settlement date

datetime scalar | string scalar

Settlement date, specified as a datetime scalar or string scalar.

To support existing code, ratecurve also accepts serial date numbers as inputs, but they are not recommended.

If you use a date string, the format must be recognizable by the datetime function because the Settle property is stored as a datetime.

Dates — Dates corresponding to rate data

datetime vector | string vector

Dates corresponding to the rate data, specified as a datetime vector or string vector.

To support existing code, ratecurve also accepts serial date numbers as inputs, but they are not recommended.

If you use a date string, the format must be recognizable by the datetime function because the Dates property is stored as a datetime.

Rates — Interest-rate data for curve

numeric vector

Interest-rate data for the curve, specified as a numeric vector.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: myRC = ratecurve("zero",Settle,ZeroDates,ZeroRates,Compounding=2,Basis=5,InterpMethod="pchip",ShortExtrapMethod="linear",LongExtrapMethod="cubic")

Compounding — Compounding frequency

-1 (default) | 0 | 1 | 2 | 3 | 4 | 6 | 12

Compounding frequency, specified as -1, 0, 1, 2, 3, 4, 6, or 12.

Basis — Day count basis

0 (default) | integer from 1 to 13

Day count basis, specified as one of these values:

• 0 — actual/actual

• 1 — 30/360 (SIA)

• 2 — actual/360

• 3 — actual/365

• 4 — 30/360 (PSA)

• 5 — 30/360 (ISDA)

• 6 — 30/360 (European)

• 7 — actual/365 (Japanese)

• 8 — actual/actual (ICMA)

• 9 — actual/360 (ICMA)

• 10 — actual/365 (ICMA)

• 11 — 30/360E (ICMA)

• 12 — actual/365 (ISDA)

• 13 — BUS/252

For more information, see Basis.

InterpMethod — Interpolation method

"linear" (default) | "cubic" | "next" | "previous" | "pchip" | "v5cubic" | "makima" | "spline" | "log-linear" | "log-pchip" | "log-makima" | "log-spline"

Interpolation method, specified as "linear", "cubic", "next", "previous", "pchip", "v5cubic", "makima", "spline", "log-linear", "log-pchip", "log-makima", or "log-spline".

The "log-linear", "log-pchip", "log-makima", and "log-spline" methods perform interpolation in the logarithmic domain. The function applies the corresponding base interpolation method ("linear", "pchip", "makima", or "spline") to the natural logarithm of the rate data and then exponentiates the result. These methods are commonly used in fixed-income applications where interpolation on discount factors or rates benefits from log-space smoothness.

For more information on interpolation methods, see interp1.

ShortExtrapMethod — Extrapolation method for data before first data

"linear" (default) | "cubic" | "next" | "previous" | "pchip" | "v5cubic" | "makima" | "spline" | "log-linear" | "log-pchip" | "log-makima" | "log-spline"

Extrapolation method for data before first data, specified as "linear", "cubic", "next", "previous", "pchip", "v5cubic", "makima", "spline", "log-linear", "log-pchip", "log-makima", or "log-spline".

The "log-linear", "log-pchip", "log-makima", and "log-spline" methods perform interpolation in the logarithmic domain. The function applies the corresponding base interpolation method ("linear", "pchip", "makima", or "spline") to the natural logarithm of the rate data and then exponentiates the result. These methods are commonly used in fixed-income applications where interpolation on discount factors or rates benefits from log-space smoothness.

For more information on interpolation methods, see interp1.

LongExtrapMethod — Extrapolation method for data after last data

"linear" (default) | "cubic" | "next" | "previous" | "pchip" | "v5cubic" | "makima" | "spline" | "log-linear" | "log-pchip" | "log-makima" | "log-spline"

Extrapolation method for data after last data, specified as "linear", "cubic", "next", "previous", "pchip", "v5cubic", "makima", "spline", "log-linear", "log-pchip", "log-makima", or "log-spline".

The "log-linear", "log-pchip", "log-makima", and "log-spline" methods perform interpolation in the logarithmic domain. The function applies the corresponding base interpolation method ("linear", "pchip", "makima", or "spline") to the natural logarithm of the rate data and then exponentiates the result. These methods are commonly used in fixed-income applications where interpolation on discount factors or rates benefits from log-space smoothness.

For more information on interpolation methods, see interp1.

Output Arguments

ratecurve_obj — Rate curve

ratecurve object

Rate curve, returned as a ratecurve object.

Properties

Type — Type of interest-rate curve

"zero" | "forward" | "discount"

Type of interest-rate curve, returned as "zero", "forward", or "discount".

Data Types: string

Compounding — Compounding frequency

-1 | 0 | 1 | 2 | 3 | 4 | 6 | 12

Compounding frequency, returned as -1, 0, 1, 2, 3, 4, 6, or 12.

Data Types: double

Basis — Day count basis

integer from 0 to 13

Day count basis, returned as one of these values:

• 0 — actual/actual

• 1 — 30/360 (SIA)

• 2 — actual/360

• 3 — actual/365

• 4 — 30/360 (PSA)

• 5 — 30/360 (ISDA)

• 6 — 30/360 (European)

• 7 — actual/365 (Japanese)

• 8 — actual/actual (ICMA)

• 9 — actual/360 (ICMA)

• 10 — actual/365 (ICMA)

• 11 — 30/360E (ICMA)

• 12 — actual/365 (ISDA)

• 13 — BUS/252

For more information, see Basis.

Data Types: double

Dates — Dates corresponding to rate data

datetime vector

Dates corresponding to the rate data, returned as a datetime vector.

Data Types: datetime

Rates — Interest-rate data for curve

numeric vector

Interest-rate data for the curve, returned as a numeric vector.

Data Types: double

Settle — Settlement date

datetime scalar

Settlement date, returned as a datetime scalar.

Data Types: datetime

InterpMethod — Interpolation method

"linear" | "cubic" | "next" | "previous" | "pchip" | "v5cubic" | "makima" | "spline" | "log-linear" | "log-pchip" | "log-makima" | "log-spline"

Interpolation method, returned as "linear", "cubic", "next", "previous", "pchip", "v5cubic", "makima", "spline", "log-linear", "log-pchip", "log-makima", or "log-spline".

Data Types: string

ShortExtrapMethod — Extrapolation method for data before first data

"linear" | "cubic" | "next" | "previous" | "pchip" | "v5cubic" | "makima" | "spline" | "log-linear" | "log-pchip" | "log-makima" | "log-spline"

Extrapolation method for data before first data, returned as "linear", "cubic", "next", "previous", "pchip", "v5cubic", "makima", "spline", "log-linear", "log-pchip", "log-makima", or "log-spline".

Data Types: string

LongExtrapMethod — Extrapolation method for data after last data

"linear" | "cubic" | "next" | "previous" | "pchip" | "v5cubic" | "makima" | "spline" | "log-linear" | "log-pchip" | "log-makima" | "log-spline"

Extrapolation method for data after last data, specified as "linear", "cubic", "next", "previous", "pchip", "v5cubic", "makima", "spline", "log-linear", "log-pchip", "log-makima", or "log-spline".

Data Types: string

Object Functions

forwardrates	Calculate forward rates for ratecurve object
discountfactors	Calculate discount factors for a ratecurve object
zerorates	Calculate zero rates for ratecurve object
irbootstrap	Bootstrap interest-rate curve from market data

Examples

Create ratecurve Object

Create a ratecurve object using the ratecurve function.

Settle = datetime(2018,9,15);
Type = "zero";
ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
 
myRC = ratecurve("zero",Settle,ZeroDates,ZeroRates,Compounding=2,Basis=5,InterpMethod="pchip",ShortExtrapMethod="linear",LongExtrapMethod="pchip")

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: 2
                Basis: 5
                Dates: [10×1 datetime]
                Rates: [10×1 double]
               Settle: 15-Sep-2018
         InterpMethod: "pchip"
    ShortExtrapMethod: "linear"
     LongExtrapMethod: "pchip"

Use Log-Linear Interpolation

Create a ratecurve object using log-linear interpolation and compare discount factors with a standard linear interpolation curve.

Define the settlement date, zero rate data, and corresponding dates. Then create a ratecurve object using standard linear interpolation.

Type = "zero";
Settle = datetime(2026,2,11);
Dates = Settle + [calmonths([1 2 3 6]) calyears([1 2 3 5 7 10 20 30])]';
Rates = [3.71 3.73 3.70 3.60 3.47 3.52 3.55 3.75 3.96 4.18 4.76 4.82]'/100;
Compounding = -1;
Basis = 3;

RC_linear = ratecurve(Type,Settle,Dates,Rates,Compounding=Compounding,Basis=Basis,InterpMethod="linear");

Compute the discount factors from the linear curve.

DF = discountfactors(RC_linear,Dates);

Create a second ratecurve object using the discount factors as inputs and specify log-linear interpolation. Log-linear interpolation operates in the logarithmic domain, which helps preserve positivity of implied forward rates.

RC_loglinear = ratecurve("discount",Settle,Dates,DF,InterpMethod="log-linear",Compounding=Compounding,Basis=Basis);

Define a finer set of query dates for comparison.

QueryDates = Settle + calmonths(1:360)';

Compute discount factors from both curves at the query dates.

DF_linear = discountfactors(RC_linear,QueryDates);
DF_loglinear = discountfactors(RC_loglinear,QueryDates);

Plot the discount factors to compare the two interpolation methods.

figure
plot(QueryDates,DF_linear,QueryDates,DF_loglinear)
legend("Linear","Log-Linear")
xlabel("Date")
ylabel("Discount Factor")
title("Discount Factor Comparison: Linear vs. Log-Linear Interpolation")

Version History

Introduced in R2020a

R2026b: Interpolate and extrapolate rate curves using log methods

The object now supports logarithmic interpolation and extrapolation methods. You can specify these new values for the InterpMethod, ShortExtrapMethod, and LongExtrapMethod name-value arguments:

• "log-linear"

• "log-pchip"

• "log-makima"

• "log-spline"

R2022b: Serial date numbers not recommended

Although ratecurve supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.