irbootstrap

Bootstrap interest-rate curve from market data

Syntax

outCurve = irbootstrap(BootInstruments,Settle)

outCurve = irbootstrap(___,Name,Value)

Description

outCurve = irbootstrap(BootInstruments,Settle) creates a data structure for storing interest-rate term structure data. The outCurve output is a ratecurve object.

outCurve = irbootstrap(___,Name,Value) specifies options using one or more name-value pair arguments in addition to any of the input argument combinations in the previous syntax. For example, OutCurve = irbootstrap(Settle,BootInstruments,'Type',"zero",'Compounding',2,'Basis',5,'InterpMethod',"cubic") bootstraps a zero curve from BootInstruments.

Examples

Bootstrap ratecurve Object from Market Data

Define Deposit and Swap Parameters

Settle = datetime(2018,3,21);
DepRates = [.0050769 .0054934 .0061432 .0072388 .0093263]';
DepTimes = [1 2 3 6 12]';
DepDates = datemnth(Settle,DepTimes);
nDeposits = length(DepTimes);
 
SwapRates = [.0112597 0;.0128489 0;.0138917 0;.0146135 0;.0151175 0;...
      .0155184 0;.0158536 0;.0161435 0];
SwapTimes = (2:9)';
SwapDates = datemnth(Settle,12*SwapTimes);
nSwaps = length(SwapTimes);
 
nInst = nDeposits + nSwaps;

Create a Vector of Market Swap Instruments

Use fininstrument to create a vector of market Deposit and Swap instrument objects.

 BootInstruments(nInst,1) = fininstrument.FinInstrument;
 for ii=1:length(DepDates)
      BootInstruments(ii) = fininstrument("deposit",'Maturity',DepDates(ii),'Rate',DepRates(ii));
 end
 
 for ii=1:length(SwapDates)
      BootInstruments(ii+nDeposits) = fininstrument("swap",'Maturity',SwapDates(ii),'LegRate',[SwapRates(ii) 0]);
 end

Create ratecurve Object for Zero-Rate Curve

Use irbootstrap to create a ratecurve object for the zero-rate curve.

ZeroCurve = irbootstrap(BootInstruments,Settle)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [13×1 datetime]
                Rates: [13×1 double]
               Settle: 21-Mar-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create Zero Curve Using DiscountCurve Input

This example shows how to create a ratecurve object using irbootstrap with Deposit and Swap instruments and a DiscountCurve for discounting cash flows.

Settle = datetime(2021,4,15); 
crvDates = Settle + [calmonths([1 2 3 6]) calyears([1 2 3 5 7 10 20 30])]';
crvRates = [0.0004 0.0004 0.0005 0.0006 0.0008 0.0018 0.0037 0.0088 0.013 0.0165 0.022 0.0233]';
DiscountCurve = ratecurve("zero",Settle,crvDates,crvRates);

DepRates = [0.002 0.0021 0.0023 0.0024 .0028]';
DepDates = Settle + calmonths([1 2 3 6 12]');

SwapRates = [0.0041 0;0.0057 0;0.017 0;0.0193 0;0.024 0;0.027 0];
SwapTimes = [2 3 5 10 20 30]';
SwapDates = datemnth(Settle,12*SwapTimes);

BootInstruments = [fininstrument("deposit","Maturity",DepDates,"Rate",DepRates); ...
    fininstrument("swap","Maturity",SwapDates,"LegRate",SwapRates)];

ZeroCurve = irbootstrap(BootInstruments,Settle,'DiscountCurve',DiscountCurve)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [11×1 datetime]
                Rates: [11×1 double]
               Settle: 15-Apr-2021
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Bootstrap ratecurve Object from BootInstruments for OIS Futures and Overnight Indexed Swaps

Create a BootInstruments variable as an input argument to irbootstrap to create a ratecurve object. The BootInstruments variable has OISFuture instrument objects for one-month SOFR Futures and three-month SOFR Futures, and an OvernightIndexedSwap instrument object.

Create Instruments

Use fininstrument to create an OISFuture instrument object for one-month SOFR Futures.

Settle = datetime(2021,3,4);
HFDates = datetime(2021,3,1) + caldays(0:3)';
HistFixing = timetable(HFDates,[0.02;0.04;0.04;0.02]);

% Data from the following: https://www.cmegroup.com/trading/interest-rates/stir/one-month-sofr_quotes_globex.html
Prices_1M = [99.97 99.96 99.95]';
Maturity_1M = lbusdate(2021,[3 4 5]',[],[],'datetime');
StartDate_1M = fbusdate(2021,[3 4 5]',[],[],'datetime');
FutInstruments_1M = fininstrument("OISFuture","Maturity",Maturity_1M ,"QuotedPrice",Prices_1M,"StartDate",StartDate_1M,"Method","Average",...
    'HistoricalFixing',HistFixing,'Name',"1MonthSOFRFuture")

FutInstruments_1M=3×1 OISFuture array with properties:
    QuotedPrice
    Method
    Basis
    StartDate
    Maturity
    Notional
    BusinessDayConvention
    Holidays
    ProjectionCurve
    HistoricalFixing
    Name

Use fininstrument to create an OISFuture instrument object for three-month SOFR Futures.

% Data from the following: https://www.cmegroup.com/trading/interest-rates/stir/three-month-sofr_quotes_globex.html
Prices_3M = [99.92 99.895 99.84 99.74]';
Dates_3M_Maturity = thirdwednesday([6 9 12 3]',[2021 2021 2021 2022]','datetime');
Dates_3M_Start = thirdwednesday([3 6 9 12]',2021,'datetime');
FutInstruments_3M = fininstrument("OISFuture","Maturity",Dates_3M_Maturity,...
    "QuotedPrice",Prices_3M,"StartDate",Dates_3M_Start,'HistoricalFixing',HistFixing,'Name',"3MonthSOFRFuture");

Use fininstrument to create an OvernightIndexedSwap instrument object.

SOFRSwapRates = [.0023 0;.0064 0;.013 0;.017 0;.0175 0];
SOFRSwapTimes = [3 5 10 20 30];
SOFRSwapDates = datemnth(Settle,12*SOFRSwapTimes)';
SOFRSwapInstruments = fininstrument("OvernightIndexedSwap","Maturity",SOFRSwapDates,"LegRate",SOFRSwapRates,'Name',"overnight_swap_instrument")

SOFRSwapInstruments=5×1 OvernightIndexedSwap array with properties:
    LegRate
    LegType
    Reset
    Basis
    Notional
    HistoricalFixing
    ResetOffset
    PaymentDelay
    ProjectionCurve
    BusinessDayConvention
    Holidays
    EndMonthRule
    DaycountAdjustedCashFlow
    StartDate
    Maturity
    Name

Define BootInstruments for the three types of instruments.

BootInstruments = [FutInstruments_1M;FutInstruments_3M;SOFRSwapInstruments]

BootInstruments=12×1 heterogeneous FinInstrument (OISFuture, OvernightIndexedSwap) array with properties:
    Name

Create ratecurve Object

Use irbootstrap to create a ratecurve object.

SOFRCurve = irbootstrap(BootInstruments,Settle)

SOFRCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [12×1 datetime]
                Rates: [12×1 double]
               Settle: 04-Mar-2021
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Bootstrap ratecurve Object from STIRFuture, Deposit, and Swap BootInstruments

Create BootInstruments for multiple Deposit, STIRFuture, and Swap instruments and then use irbootstrap to create and display a ratecurve object.

Create Instruments

Use fininstrument to create a Deposit instrument object.

Settle = datetime(2021,6,15); 
DepRates = [0.0016 0.0017 .00175]';
DepDates = Settle + calmonths([1 2 3]');

Deposits = fininstrument("Deposit","Maturity",DepDates,"Rate",DepRates,'Name',"deposit_instrument")

Deposits=3×1 Deposit array with properties:
    Rate
    Period
    Basis
    Maturity
    Principal
    BusinessDayConvention
    Holidays
    Name

Use fininstrument to create a STIRFuture instrument object.

FutureRates = [0.002 0.0025 0.0035]';
FutMat = [datetime(2021,9,15) datetime(2021,12,15) datetime(2022,3,16)]';
FutEndDates = [datetime(2021,12,15) datetime(2022,3,15) datetime(2022,6,15)]';

Futures = fininstrument("STIRFuture","Maturity",FutMat,"RateEndDate",FutEndDates,"QuotedPrice",100 - 100*FutureRates,'Name',"stir_future_instrument")

Futures=3×1 STIRFuture array with properties:
    QuotedPrice
    Basis
    RateEndDate
    Maturity
    Notional
    BusinessDayConvention
    Holidays
    ProjectionCurve
    Name

Use fininstrument to create a Swap instrument object.

SwapRates = [.0063 0;.0108 0;.013 0;.015 0;0.017 0;.018 0;0.019 0];
SwapTimes = [2 5 7 10 15 20 30]';
SwapDates = datemnth(Settle,12*SwapTimes);

Swaps = fininstrument("Swap","Maturity",SwapDates,"LegRate",SwapRates,'Name',"swap_instrument")

Swaps=7×1 Swap array with properties:
    LegRate
    LegType
    Reset
    Basis
    Notional
    LatestFloatingRate
    ResetOffset
    DaycountAdjustedCashFlow
    ProjectionCurve
    BusinessDayConvention
    Holidays
    EndMonthRule
    StartDate
    Maturity
    Name

Define BootInstruments for the three instruments.

BootInstruments = [Deposits;Futures;Swaps];

Create ratecurve Object Using irbootstrap

Use irbootstrap to create a ratecurve object.

ConvexityAdj = (1:3)'/10000;
ZeroCurve = irbootstrap(BootInstruments,Settle,'ConvexityAdjustment',ConvexityAdj,'InterpMethod','pchip')

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [13×1 datetime]
                Rates: [13×1 double]
               Settle: 15-Jun-2021
         InterpMethod: "pchip"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Plot Bootstrapped Curve

PlottingDates = Settle + calmonths(1:360);
plot(PlottingDates,zerorates(ZeroCurve,PlottingDates))
xlabel('Maturity (Years)') 
ylabel('Zero Rate')
title('Bootstrapped Curve')

Input Arguments

BootInstruments — Collection of instruments

array of instrument objects

Collection of instruments, specified as an array of instrument objects. The collection of instruments can include Deposit, Swap, FRA, STIRFuture, OISFuture, and OvernightIndexedSwap instruments.

Data Types: object

Settle — Settlement date

datetime scalar | string scalar | date character vector

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

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

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: OutCurve = irbootstrap(Settle,BootInstruments,'Type',"zero",'Compounding',2,'Basis',5,'InterpMethod',"cubic")

Type — Type of interest-rate curve

"zero" (default) | string with value "discount", "forward", or "zero" | character vector with value 'discount', 'forward', or 'zero'

Type of interest-rate curve, specified as the comma-separated pair consisting of 'Type' and a scalar string or character vector.

Note

When you use irbootstrap, the value you specify for Type can impact the curve construction because it affects the type of data that is interpolated on (that is, forward rates, zero rates, or discount factors) during the bootstrapping process.

Data Types: char | string

Compounding — Compounding frequency

Compounding for the ratecurve object (default) | possible values include: –1, 0, 1, 2, 3, 4, 6, 12.

Compounding frequency, specified as the comma-separated pair consisting of 'Compounding' and a scalar numeric using the supported values: –1, 0, 1, 2, 3, 4, 6, or 12.

Data Types: double

Basis — Day-count basis

0 (actual/actual) (default) | integer from 0 to 13

Day-count basis, specified as the comma-separated pair consisting of 'Basis' and a scalar integer.

• 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

InterpMethod — Interpolation method

"linear" (default) | string with value "linear", "cubic", "next", "previous", "pchip", "v5cubic", "makima", or "spline" | character vector with value 'linear', 'cubic', 'next', 'previous', 'pchip', 'v5cubic', 'makima', or 'spline'

Interpolation method, specified as the comma-separated pair consisting of 'InterpMethod' and a scalar string or character vector using a supported value. For more information on interpolation methods, see interp1.

Data Types: char | string

ShortExtrapMethod — Extrapolation method for data before first data

"next" (default) | string with value "linear", "next", "previous", "pchip", "cubic","v5cubic", "makima", or "spline" | character vector with value 'linear', 'next', 'previous', 'pchip', 'cubic','v5cubic', 'makima', or 'spline'

Extrapolation method for data before first data, specified as the comma-separated pair consisting of 'ShortExtrapMethod' and a scalar string or character vector using a supported value. For more information on interpolation methods, see interp1.

Data Types: char | string

LongExtrapMethod — Extrapolation method for data after last data

"previous" (default) | string with value "linear", "next", "previous", "pchip", "cubic","v5cubic", "makima", or "spline" | character vector with value 'linear', 'next', 'previous', 'pchip', 'cubic','v5cubic', 'makima', or 'spline'

Extrapolation method for data after last data, specified as the comma-separated pair consisting of 'LongExtrapMethod' and a scalar string or character vector using a supported value. For more information on interpolation methods, see interp1.

Data Types: char | string

DiscountCurve — ratecurve object for discounting cash flows

ratecurve.empty (default) | scalar ratecurve object

ratecurve object for discounting cash flows, specified as the comma-separated pair consisting of 'DiscountCurve' and the name of a previously created ratecurve object.

Data Types: object

ConvexityAdjustment — Convexity adjustment for STIRFuture instrument

0 (default) | numeric vector

Convexity adjustment for one or more STIRFuture instruments, specified as the comma-separated pair consisting of 'ConvexityAdjustment' and an NFutures-by-1 vector of numeric values.

Note

You can only use ConvexityAdjustment when using irbootstrap with a STIRFuture instrument. Also, the length of the ConvexityAdjustment vector must match the number of STIRFuture instruments.

Data Types: double

Output Arguments

outCurve — Rate curve

ratecurve object

Rate curve, returned as a ratecurve object. The object has the following properties:

• Type

• Settle

• Compounding

• Basis

• Dates

• Rates

• InterpMethod

• ShortExtrapMethod

• LongExtrapMethod

Version History

Introduced in R2020a

R2022b: Serial date numbers not recommended

Although irbootstrap 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.