InflationBond

InflationBond instrument object

Since R2021a

Description

Create and price an InflationBond instrument object for one or more Inflation Bond instruments using this workflow:

Use fininstrument to create an InflationBond instrument object for one or more Inflation Bond instruments.
Use ratecurve to specify an interest-rate model for the InflationBond instrument object.
Use inflationcurve to specify an inflation curve model for the InflationBond instrument object.
Use finpricer to specify an Inflation pricing method for one or more InflationBond instruments.
Use inflationCashflows to compute cash flows for each one of the InflationBond instruments.

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 models and pricing methods for an InflationBond instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

InflationBond = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date)

InflationBond = fininstrument(___,Name,Value)

Description

InflationBond = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date) creates an InflationBond object for one or more Inflation Bond instruments by specifying InstrumentType and sets the properties for the required name-value pair arguments CouponRate and Maturity.

example

InflationBond = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, InflationBond = fininstrument("InflationBond",'Maturity',Maturity,'CouponRate',CouponRate,'IssueDate',IssueDate) creates a InflationBond option.

example

Input Arguments

expand all

`InstrumentType` — Instrument type
string with value `"InflationBond"` | string array with values of `"InflationBond"` | character vector with value `'InflationBond'` | cell array of character vectors with values of `'InflationBond'`

Instrument type, specified as a string with the value of "InflationBond", a character vector with the value of 'InflationBond', an NINST-by-1 string array with values of "InflationBond", or an NINST-by-1 cell array of character vectors with values of 'InflationBond'.

Data Types: char | cell | string

Name-Value Arguments

Specify required and 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: InflationBond = fininstrument("InflationBond",'Maturity',Maturity,'CouponRate',CouponRate,'IssueDate',IssueDate)

Required InflationBond Name-Value Pair Arguments

expand all

`CouponRate` — `InflationBond` coupon rate
scalar decimal | vector of decimals

InflationBond coupon rate, specified as the comma-separated pair consisting of 'CouponRate' and a scalar decimal or an NINST-by-1 vector of decimals for an annual rate.

Data Types: double

`Maturity` — `InflationBond` maturity date
datetime array | string array | date character vector

InflationBond maturity date, specified as the comma-separated pair consisting of 'Maturity' and a scalar or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

If you use date character vectors or strings, the format must be recognizable by datetime because the Maturity property is stored as a datetime.

Optional InflationBond Name-Value Pair Arguments

expand all

`Period` — Frequency of payments per year
`2` (default) | scalar numeric with value of `0`, `1`, `2`, `3`, `4`, `6`, or `12` | numeric vector with values of `0`, `1`, `2`, `3`, `4`, `6`, or `12`

Frequency of payments, specified as the comma-separated pair consisting of 'Period' and a scalar integer or an NINST-by-1 vector of integers. Values for Period are 1, 2, 3, 4, 6, or 12.

Data Types: double

`Basis` — Day count basis
`0` (actual/actual) (default) | scalar integer from `0` to `13` | vector of integers from `0` to `13`

Day count basis, specified as the comma-separated pair consisting of 'Basis' and scalar integer or an NINST-by-1 vector of integers using the following 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

`Principal` — Initial principal amount
`100` (default) | scalar numeric | numeric vector

Initial principal amount, specified as the comma-separated pair consisting of 'Principal' and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

`DaycountAdjustedCashFlow` — Flag indicating whether cash flow adjusts for day count convention
`false` (default) | scalar logical value of `true` or `false` | vector of logical values of `true` or `false`

Flag indicating whether cash flow is adjusted by day count convention, specified as the comma-separated pair consisting of 'DaycountAdjustedCashFlow' and a scalar logical or an NINST-by-1 vector of logicals with values of true or false.

Data Types: logical

`IssueDate` — Bond issue date
`NaT` (default) | datetime array | string array | date character vector

Bond issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

If you use date character vectors or strings, the format must be recognizable by datetime because the IssueDate property is stored as a datetime.

`Lag` — Indexation lag in months
`3` (default) | scalar numeric | numeric vector

Indexation lag in months, specified as the comma-separated pair consisting of 'Lag' and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

`BusinessDayConvention` — Business day conventions for cash flow dates
`"actual"` (default) | string | string array | character vector | cell array of character vectors

Business day conventions for cash flow dates, specified as the comma-separated pair consisting of 'BusinessDayConvention' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array. The selection for business day convention determines how nonbusiness days are treated. Nonbusiness days are defined as weekends plus any other date that businesses are not open (for example, statutory holidays). Values are:

"actual" — Nonbusiness days are effectively ignored. Cash flows that fall on nonbusiness days are assumed to be distributed on the actual date.
"follow" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day.
"modifiedfollow" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day. However, if the following business day is in a different month, the previous business day is adopted instead.
"previous" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day.
"modifiedprevious" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day. However, if the previous business day is in a different month, the following business day is adopted instead.

Data Types: char | cell | string

`Holidays` — Holidays used in computing business days
`NaT` (default) | datetime array | string array | date character vector

Holidays used in computing business days, specified as the comma-separated pair consisting of 'Holidays' and dates using an NINST-by-1 vector of a datetime array, string array, or date character vectors. For example:

H = holidays(datetime('today'),datetime(2025,12,15));
InflationBondObj = fininstrument("InflationBond",'CouponRate',0.34,'Maturity',datetime(2025,12,15),'Holidays',H)

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

`EndMonthRule` — End-of-month rule flag for generating dates when `Maturity` is end-of-month date for month with 30 or fewer days
`true` (in effect) (default) | scalar logical values of `true` or `false` | vector of logical values with `true` or `false`

End-of-month rule flag for generating dates when Maturity is an end-of-month date for a month with 30 or fewer days, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar logical value or an NINST-by-1 vector of logical values of true or false.

If you set EndMonthRule to false, the software ignores the rule, meaning that a payment date is always the same numerical day of the month.
If you set EndMonthRule to true, the software sets the rule on, meaning that a payment date is always the last actual day of the month.

Data Types: logical

`FirstCouponDate` — Irregular first coupon date
`NaT` (default) | datetime array | string array | date character vector

Irregular first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a scalar or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure. If you do not specify FirstCouponDate, the cash flow payment dates are determined from other inputs.

If you use date character vectors or strings, the format must be recognizable by datetime because the FirstCouponDate property is stored as a datetime.

`LastCouponDate` — Irregular last coupon date
`NaT` (default) | datetime array | string array | date character vector

Irregular last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a scalar or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

If you specify LastCouponDate but not FirstCouponDate, LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at LastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date. If you do not specify LastCouponDate, the cash flow payment dates are determined from other inputs.

If you use date character vectors or strings, the format must be recognizable by datetime because the LastCouponDate property is stored as a datetime.

`IssueIndex` — Inflation index at issue date
`InflationIndexValues` for issue date in `inflationcurve` model object (default) | numeric

Inflation index at issue date, specified as the comma-separated pair consisting of 'IssueIndex' and a scalar numeric or an NINST-by-1 vector of numeric values. For example, the IssueIndex for the inflation index depends on the country and can be from any of the following:

US — CPI (US Consumer Price Index Urban Consumers (CPI-U))
UK — RPI (UK Retail Price Index (RPI)
Canada — CPI (Canada All-Items Consumer Price Index)
European Union (EU) — HICP-ex Tobacco (EU Harmonized Indices of Consumer Prices (HICP) ex Tobacco)
Japan — CPI (Japan Consumer Price Index)
China — CPI (China Consumer Price Index)

Note

If you specify an IssueIndex, the Inflation pricing method overrides the index value (InflationIndexValues) for the issue date (Dates) in the inflationcurve model object.

Data Types: double

`Name` — User-defined name for instrument
`" "` (default) | string | string array | character vector | cell array of character vectors

User-defined name for one of more instruments, specified as the comma-separated pair consisting of 'Name' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Data Types: char | cell | string

Properties

expand all

`CouponRate` — `InflationBond` coupon annual rate
scalar decimal | vector of decimals

InflationBond coupon annual rate, returned as a scalar decimal or an NINST-by-1 vector of decimals.

Data Types: double

`Maturity` — `InflationBond` maturity date
datetime | vector of datetimes

InflationBond maturity date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

`Period` — Frequency of payments per year
`2` (default) | scalar integer | vector of integers

Frequency of payments per year, returned as a scalar integer or an NINST-by-1 vector of integers.

Data Types: double

`Basis` — Day count basis
`0` (actual/actual) (default) | scalar integer from `0` to `13` | vector of integers from `0` to `13`

Day count basis, returned as a scalar integer or an NINST-by-1 vector of integers.

Data Types: double

`Principal` — Initial principal amount
`100` (default) | scalar numeric | numeric vector

Initial principal amount, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

`DaycountAdjustedCashFlow` — Flag indicating whether cash flow adjusts for day count convention
`false` (default) | scalar logical value of `true` or `false` | vector of logical values with `true` or `false`

Flag indicating whether cash flow adjusts for day count convention, returned as scalar logical or an NINST-by-1 vector of logicals with values of true or false.

Data Types: logical

`IssueDate` — Bond issue date
`NaT` (default) | datetime | vector of datetimes

Bond issue date, returned as a datetime or an NINST-by-1 datetime vector.

Data Types: datetime

`Lag` — Indexation lag in months
`3` (default) | scalar numeric | numeric vector

Indexation lag in months, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

`BusinessDayConvention` — Business day conventions
`"actual"` (default) | string | string array

Business day conventions, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

`Holidays` — Holidays used in computing business days
`NaT` (default) | datetimes

Holidays used in computing business days, returned as an NINST-by-1 vector of datetimes.

Data Types: datetime

`EndMonthRule` — End-of-month rule flag for generating dates when `Maturity` is end-of-month date for month with 30 or fewer days
`true` (in effect) (default) | scalar logical value of `true` or `false` | vector of logicals with value of `true` or `false`

End-of-month rule flag for generating dates when Maturity is an end-of-month date for a month having 30 or fewer days, returned as a scalar logical or an NINST-by-1 vector of logicals.

Data Types: logical

`FirstCouponDate` — Irregular first coupon date
`NaT` (default) | datetime | vector of datetimes

Irregular first coupon date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

`LastCouponDate` — Irregular last coupon date
`NaT` (default) | datetime | vector of datetimes

Irregular last coupon date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

`IssueIndex` — Inflation index at issue date
`InflationIndexValues` for issue date in `inflationcurve` model object (default) | numeric

Inflation index at issue date, returned as a scalar numeric or an NINST-by-1 vector of numeric values.

Data Types: double

`Name` — User-defined name for instrument
`" "` (default) | string | string array

User-defined name for the instrument, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Object Functions

inflationCashflows Compute cash flows for InflationBond instrument

Examples

collapse all

Price `InflationBond` Instrument Using `inflationcurve` and `Inflation` Pricer

Open Live Script

This example shows the workflow to price an InflationBond instrument when you use an inflationcurve and an Inflation pricing method.

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2021,1,15);
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;
ZeroCurve = ratecurve('zero',Settle,ZeroDates,ZeroRates)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Jan-2021
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create inflationcurve Object

Create an inflationcurve object using inflationcurve.

BaseDate = datetime(2020,10,1);
InflationTimes = [0 calyears([1 2 3 4 5 7 10 20 30])]';
InflationIndexValues = [100 102 103.5 105 106.8 108.2 111.3 120.1 130.4 150.2]';
InflationDates = BaseDate + InflationTimes;
myInflationCurve = inflationcurve(InflationDates,InflationIndexValues)

myInflationCurve = 
  inflationcurve with properties:

                    Basis: 0
                    Dates: [10x1 datetime]
     InflationIndexValues: [10x1 double]
    ForwardInflationRates: [9x1 double]
              Seasonality: [12x1 double]

Create InflationBond Instrument Object

Use fininstrument to create an InflationBond instrument object.

IssueDate = datetime(2021,1,1);
Maturity = datetime(2026,1,1);
CouponRate = 0.02;

InflationBond = fininstrument("InflationBond", 'IssueDate', IssueDate, 'Maturity', Maturity, 'CouponRate', CouponRate,'Name',"inflation_bond_instrument")

InflationBond = 
  InflationBond with properties:

                  CouponRate: 0.0200
                      Period: 2
                       Basis: 0
                   Principal: 100
    DaycountAdjustedCashFlow: 0
                         Lag: 3
                  IssueIndex: NaN
       BusinessDayConvention: "actual"
                    Holidays: NaT
                EndMonthRule: 1
                   IssueDate: 01-Jan-2021
             FirstCouponDate: NaT
              LastCouponDate: NaT
                    Maturity: 01-Jan-2026
                        Name: "inflation_bond_instrument"

Create Inflation Pricer Object

Use finpricer to create an Inflation pricer object and use the ratecurve object with the 'DiscountCurve' name-value pair argument and the inflationcurve object with the 'InflationCurve' name-value pair argument.

outPricer = finpricer("Inflation",'DiscountCurve',ZeroCurve,'InflationCurve',myInflationCurve)

outPricer = 
  Inflation with properties:

     DiscountCurve: [1x1 ratecurve]
    InflationCurve: [1x1 inflationcurve]

Price InflationBond Instrument

Use price to compute the price and sensitivities for the InflationBond instrument.

[Price, outPR] = price(outPricer, InflationBond)

Price = 
112.1856

outPR = 
  priceresult with properties:

       Results: [1x1 table]
    PricerData: []

outPR.Results

ans=table
    Price 
    ______

    112.19

Price Multiple `InflationBond` Instruments Using `inflationcurve` and `Inflation` Pricer

Open Live Script

This example shows the workflow to price multiple InflationBond instruments when you use an inflationcurve and an Inflation pricing method.

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2020,1,15);
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;
ZeroCurve = ratecurve('zero',Settle,ZeroDates,ZeroRates)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Jan-2020
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create inflationcurve Object

Create an inflationcurve object using inflationcurve.

BaseDate = datetime(2019,8,1);
InflationTimes = [0 calyears([1 2 3 4 5 7 10 20 30])]';
InflationIndexValues = [100 102 103.5 105 106.8 108.2 111.3 120.1 130.4 150.2]';
InflationDates = BaseDate + InflationTimes;
myInflationCurve = inflationcurve(InflationDates,InflationIndexValues)

myInflationCurve = 
  inflationcurve with properties:

                    Basis: 0
                    Dates: [10x1 datetime]
     InflationIndexValues: [10x1 double]
    ForwardInflationRates: [9x1 double]
              Seasonality: [12x1 double]

Create InflationBond Instrument Object

Use fininstrument to create an InflationBond instrument object for three Inflation Bond instruments.

IssueDate = datetime([2020,1,1 ; 2019,12,1 ; 2019,11,1]);
Maturity = datetime([2026,1,1 ; 2026,2,1 ; 2026,3,1]);
CouponRate = 0.02;

InflationBond = fininstrument("InflationBond",'IssueDate',IssueDate,'Maturity',Maturity,'CouponRate',CouponRate,'Name',"inflation_bond_instrument")

InflationBond=3×1 InflationBond array with properties:
    CouponRate
    Period
    Basis
    Principal
    DaycountAdjustedCashFlow
    Lag
    IssueIndex
    BusinessDayConvention
    Holidays
    EndMonthRule
    IssueDate
    FirstCouponDate
    LastCouponDate
    Maturity
    Name

Create Inflation Pricer Object

outPricer = finpricer("Inflation",'DiscountCurve',ZeroCurve,'InflationCurve',myInflationCurve)

outPricer = 
  Inflation with properties:

     DiscountCurve: [1x1 ratecurve]
    InflationCurve: [1x1 inflationcurve]

Price InflationBond Instruments

Use price to compute the prices and sensitivities for the InflationBond instruments.

[Price, outPR] = price(outPricer, InflationBond)

Price = 3×1

  112.8769
  113.1022
  113.3434

outPR=1×3 priceresult array with properties:
    Results
    PricerData

outPR.Results

ans=table
    Price 
    ______

    112.88

ans=table
    Price
    _____

    113.1

ans=table
    Price 
    ______

    113.34

Price `InflationBond` Instrument With Specified `IssueIndex` Using `inflationcurve` and `Inflation` Pricer

Open Live Script

This example shows the workflow to price an InflationBond instrument with a specified IssueIndex when you use an inflationcurve and an Inflation pricing method.

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2021,1,15);
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;
ZeroCurve = ratecurve('zero',Settle,ZeroDates,ZeroRates)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Jan-2021
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create inflationcurve Object

Create an inflationcurve object using inflationcurve.

BaseDate = datetime(2020,10,1);
InflationTimes = [0 calyears([1 2 3 4 5 7 10 20 30])]';
InflationIndexValues = [100 102 103.5 105 106.8 108.2 111.3 120.1 130.4 150.2]';
InflationDates = BaseDate + InflationTimes;
myInflationCurve = inflationcurve(InflationDates,InflationIndexValues)

myInflationCurve = 
  inflationcurve with properties:

                    Basis: 0
                    Dates: [10x1 datetime]
     InflationIndexValues: [10x1 double]
    ForwardInflationRates: [9x1 double]
              Seasonality: [12x1 double]

Create InflationBond Instrument Object With Specified IssueIndex

Use fininstrument to create an InflationBond instrument object with a specified issue index by using the IssueIndex name-value argument. Specifying the IssueIndex in the InflationBond instrument overrides the issue index implied by the inflationcurve object.

IssueDate = datetime(2021, 1, 1);
Maturity = datetime(2026, 1, 1);
CouponRate = 0.02;
Period = 1;
IssueIndex = 100.15;

InflationBond = fininstrument("InflationBond", ...
    IssueDate=IssueDate, Maturity=Maturity, IssueIndex=IssueIndex, ...
    CouponRate=CouponRate, Period=Period)

InflationBond = 
  InflationBond with properties:

                  CouponRate: 0.0200
                      Period: 1
                       Basis: 0
                   Principal: 100
    DaycountAdjustedCashFlow: 0
                         Lag: 3
                  IssueIndex: 100.1500
       BusinessDayConvention: "actual"
                    Holidays: NaT
                EndMonthRule: 1
                   IssueDate: 01-Jan-2021
             FirstCouponDate: NaT
              LastCouponDate: NaT
                    Maturity: 01-Jan-2026
                        Name: ""

Create Inflation Pricer Object

Use finpricer to create an Inflation pricer object and use the ratecurve object with the DiscountCurve name-value argument and the inflationcurve object with the InflationCurve name-value argument.

outPricer = finpricer("Inflation",DiscountCurve=ZeroCurve,...
    InflationCurve=myInflationCurve)

outPricer = 
  Inflation with properties:

     DiscountCurve: [1x1 ratecurve]
    InflationCurve: [1x1 inflationcurve]

Price InflationBond Instrument

Use price to compute the price for the InflationBond instrument.

Price = price(outPricer,InflationBond)

Price = 
112.0263

More About

expand all

Inflation-Indexed Bond

An inflation-indexed bond is a security ensuring a return above inflation if held to maturity. Inflation-indexed securities link their capital appreciation, or coupon payments, to inflation rates.

The Inflation-indexed bond principal value and interest payments are linked to an inflation index like the Consumer Price Index (CPI), that adjusts with inflation. This adjustment ensures the bondholder's investment and interest income maintain their purchasing power, providing a return that keeps pace with inflation.

Algorithms

To price an inflation-indexed bond, use an inflation curve and a nominal discount curve (model-free approach), where the cash flows are discounted using the nominal discount curve.

$\begin{array}{l} I (0, T) P_{n} (0, T) = I (0) P_{r} (0, T) \\ B_{T I P S} (0, T_{M}) = \frac{1}{I (T_{0})} \sum_{i = 1}^{M} c I (0) P_{r} (0, T_{i}) + F I (0) P_{r} (0, T_{M}) \\ = \frac{1}{I (T_{0})} \sum_{i = 1}^{M} c I (0, T_{i}) P_{n} (0, T_{i}) + F I (0, T_{M}) P_{n} (0, T_{M}) \end{array}$

where

P_n is the nominal zero-coupon bond price.
P_r is the real zero-coupon bond price.
k is the fixed inflation rate.
I(0,T) is the breakeven inflation index for period (0,T).
I(0) is the inflation index at (t = 0).
I(T₀) is the base inflation index at the issue date (t = T₀).
B_TIPS(0,T_M) is the inflation-indexed bond price.
I(T_i-1) is the inflation index at the start date with some lag (for example, three months).
C is the coupon.
F is the face value.

References

[1] Brody, D. C., Crosby, J., and Li, H. "Convexity Adjustments in Inflation-Linked Derivatives." Risk Magazine. November 2008, pp. 124–129.

[2] Kerkhof, J. "Inflation Derivatives Explained: Markets, Products, and Pricing." Fixed Income Quantitative Research, Lehman Brothers, July 2005.

[3] Treasury Inflation-Protected Securities (TIPS) at: https://www.treasurydirect.gov/.

[4] Zhang, J. X. "Limited Price Indexation (LPI) Swap Valuation Ideas." Wilmott Magazine. no. 57, January 2012, pp. 58–69.

Version History

Introduced in R2021a

expand all

R2023b: Support for `IssueIndex` Property

You can use the name-value argument IssueIndex to specify the Consumer Price Index (CPI) at the instrument issue date.

R2022b: Serial date numbers not recommended

Although InflationBond 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.

InflationBond

Description

Creation

Syntax

Description

Input Arguments

InstrumentType — Instrument type string with value "InflationBond" | string array with values of "InflationBond" | character vector with value 'InflationBond' | cell array of character vectors with values of 'InflationBond'

CouponRate — InflationBond coupon rate scalar decimal | vector of decimals

Maturity — InflationBond maturity date datetime array | string array | date character vector

Period — Frequency of payments per year 2 (default) | scalar numeric with value of 0, 1, 2, 3, 4, 6, or 12 | numeric vector with values of 0, 1, 2, 3, 4, 6, or 12

Basis — Day count basis 0 (actual/actual) (default) | scalar integer from 0 to 13 | vector of integers from 0 to 13

Principal — Initial principal amount 100 (default) | scalar numeric | numeric vector

DaycountAdjustedCashFlow — Flag indicating whether cash flow adjusts for day count convention false (default) | scalar logical value of true or false | vector of logical values of true or false

IssueDate — Bond issue date NaT (default) | datetime array | string array | date character vector

Lag — Indexation lag in months 3 (default) | scalar numeric | numeric vector

BusinessDayConvention — Business day conventions for cash flow dates "actual" (default) | string | string array | character vector | cell array of character vectors

Holidays — Holidays used in computing business days NaT (default) | datetime array | string array | date character vector

EndMonthRule — End-of-month rule flag for generating dates when Maturity is end-of-month date for month with 30 or fewer days true (in effect) (default) | scalar logical values of true or false | vector of logical values with true or false

FirstCouponDate — Irregular first coupon date NaT (default) | datetime array | string array | date character vector

LastCouponDate — Irregular last coupon date NaT (default) | datetime array | string array | date character vector

IssueIndex — Inflation index at issue date InflationIndexValues for issue date in inflationcurve model object (default) | numeric

Name — User-defined name for instrument " " (default) | string | string array | character vector | cell array of character vectors

Properties

CouponRate — InflationBond coupon annual rate scalar decimal | vector of decimals

Maturity — InflationBond maturity date datetime | vector of datetimes

Period — Frequency of payments per year 2 (default) | scalar integer | vector of integers

Basis — Day count basis 0 (actual/actual) (default) | scalar integer from 0 to 13 | vector of integers from 0 to 13

Principal — Initial principal amount 100 (default) | scalar numeric | numeric vector

DaycountAdjustedCashFlow — Flag indicating whether cash flow adjusts for day count convention false (default) | scalar logical value of true or false | vector of logical values with true or false

IssueDate — Bond issue date NaT (default) | datetime | vector of datetimes

Lag — Indexation lag in months 3 (default) | scalar numeric | numeric vector

BusinessDayConvention — Business day conventions "actual" (default) | string | string array

Holidays — Holidays used in computing business days NaT (default) | datetimes

EndMonthRule — End-of-month rule flag for generating dates when Maturity is end-of-month date for month with 30 or fewer days true (in effect) (default) | scalar logical value of true or false | vector of logicals with value of true or false

FirstCouponDate — Irregular first coupon date NaT (default) | datetime | vector of datetimes

LastCouponDate — Irregular last coupon date NaT (default) | datetime | vector of datetimes

IssueIndex — Inflation index at issue date InflationIndexValues for issue date in inflationcurve model object (default) | numeric

Name — User-defined name for instrument " " (default) | string | string array

Object Functions

Examples

Price InflationBond Instrument Using inflationcurve and Inflation Pricer

Price Multiple InflationBond Instruments Using inflationcurve and Inflation Pricer

Price InflationBond Instrument With Specified IssueIndex Using inflationcurve and Inflation Pricer

More About

Inflation-Indexed Bond

Algorithms

References

Version History

R2023b: Support for IssueIndex Property

R2022b: Serial date numbers not recommended

See Also

Functions

Topics

`InstrumentType` — Instrument type
string with value `"InflationBond"` | string array with values of `"InflationBond"` | character vector with value `'InflationBond'` | cell array of character vectors with values of `'InflationBond'`

`CouponRate` — `InflationBond` coupon rate
scalar decimal | vector of decimals

`Maturity` — `InflationBond` maturity date
datetime array | string array | date character vector

`Period` — Frequency of payments per year
`2` (default) | scalar numeric with value of `0`, `1`, `2`, `3`, `4`, `6`, or `12` | numeric vector with values of `0`, `1`, `2`, `3`, `4`, `6`, or `12`

`Basis` — Day count basis
`0` (actual/actual) (default) | scalar integer from `0` to `13` | vector of integers from `0` to `13`

`Principal` — Initial principal amount
`100` (default) | scalar numeric | numeric vector

`DaycountAdjustedCashFlow` — Flag indicating whether cash flow adjusts for day count convention
`false` (default) | scalar logical value of `true` or `false` | vector of logical values of `true` or `false`

`IssueDate` — Bond issue date
`NaT` (default) | datetime array | string array | date character vector

`Lag` — Indexation lag in months
`3` (default) | scalar numeric | numeric vector

`BusinessDayConvention` — Business day conventions for cash flow dates
`"actual"` (default) | string | string array | character vector | cell array of character vectors

`Holidays` — Holidays used in computing business days
`NaT` (default) | datetime array | string array | date character vector

`EndMonthRule` — End-of-month rule flag for generating dates when `Maturity` is end-of-month date for month with 30 or fewer days
`true` (in effect) (default) | scalar logical values of `true` or `false` | vector of logical values with `true` or `false`

`FirstCouponDate` — Irregular first coupon date
`NaT` (default) | datetime array | string array | date character vector

`LastCouponDate` — Irregular last coupon date
`NaT` (default) | datetime array | string array | date character vector

`IssueIndex` — Inflation index at issue date
`InflationIndexValues` for issue date in `inflationcurve` model object (default) | numeric

`Name` — User-defined name for instrument
`" "` (default) | string | string array | character vector | cell array of character vectors

`CouponRate` — `InflationBond` coupon annual rate
scalar decimal | vector of decimals

`Maturity` — `InflationBond` maturity date
datetime | vector of datetimes

`Period` — Frequency of payments per year
`2` (default) | scalar integer | vector of integers

`Basis` — Day count basis
`0` (actual/actual) (default) | scalar integer from `0` to `13` | vector of integers from `0` to `13`

`Principal` — Initial principal amount
`100` (default) | scalar numeric | numeric vector

`DaycountAdjustedCashFlow` — Flag indicating whether cash flow adjusts for day count convention
`false` (default) | scalar logical value of `true` or `false` | vector of logical values with `true` or `false`

`IssueDate` — Bond issue date
`NaT` (default) | datetime | vector of datetimes

`Lag` — Indexation lag in months
`3` (default) | scalar numeric | numeric vector

`BusinessDayConvention` — Business day conventions
`"actual"` (default) | string | string array

`Holidays` — Holidays used in computing business days
`NaT` (default) | datetimes

`EndMonthRule` — End-of-month rule flag for generating dates when `Maturity` is end-of-month date for month with 30 or fewer days
`true` (in effect) (default) | scalar logical value of `true` or `false` | vector of logicals with value of `true` or `false`

`FirstCouponDate` — Irregular first coupon date
`NaT` (default) | datetime | vector of datetimes

`LastCouponDate` — Irregular last coupon date
`NaT` (default) | datetime | vector of datetimes

`IssueIndex` — Inflation index at issue date
`InflationIndexValues` for issue date in `inflationcurve` model object (default) | numeric

`Name` — User-defined name for instrument
`" "` (default) | string | string array

Price `InflationBond` Instrument Using `inflationcurve` and `Inflation` Pricer

Price Multiple `InflationBond` Instruments Using `inflationcurve` and `Inflation` Pricer

Price `InflationBond` Instrument With Specified `IssueIndex` Using `inflationcurve` and `Inflation` Pricer

R2023b: Support for `IssueIndex` Property