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InflationBond

InflationBond instrument object

Description

Create and price an InflationBond instrument object using this workflow:

  1. Use fininstrument to create an InflationBond instrument object.

  2. Use ratecurve to specify an interest-rate model for the InflationBond instrument.

  3. Use inflationcurve to specify an inflation curve model.

  4. Use finpricer to specify an Inflation pricing method for the InflationBond instrument.

  5. Use inflationCashflows to compute cash flows for the InflationBond instrument.

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

Description

example

InflationBond = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date) creates an InflationBond object 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.

Input Arguments

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Instrument type, specified as a string with the value of "InflationBond" or a character vector with a value of 'InflationBond'.

Data Types: char | string

InflationBond Name-Value Pair Arguments

Specify required and optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: InflationBond = fininstrument("InflationBond",'Maturity',Maturity,'CouponRate',CouponRate,'IssueDate',IssueDate)
Required InflationBond Name-Value Pair Arguments

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InflationBond coupon rate, specified as the comma-separated pair consisting of 'CouponRate' and a scalar decimal for an annual rate.

Data Types: double

InflationBond maturity date, specified as the comma-separated pair consisting of 'Maturity' and a scalar datetime, serial date number, date character vector, or date string.

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

Data Types: char | double | string | datetime

Optional InflationBond Name-Value Pair Arguments

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

Data Types: double

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

Initial principal amount, specified as the comma-separated pair consisting of 'Principal' and a scalar numeric.

Data Types: double

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

Data Types: logical

Bond issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar datetime, serial date number, date character vector, or date string.

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

Data Types: double | char | string | datetime

Indexation lag in months, specified as the comma-separated pair consisting of 'Lag' and a scalar numeric value.

Data Types: double

Business day conventions for cash flow dates, specified as the comma-separated pair consisting of 'BusinessDayConvention' and a scalar string or character vector. 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 | string

Holidays used in computing business days, specified as the comma-separated pair consisting of 'Holidays' and dates using datetimes, serial date numbers, cell array of date character vectors, or date string array. For example:

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

Data Types: double | cell | datetime | string

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 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

Irregular first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a scalar datetime, serial date number, date character vector, or date string.

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 a date character vector or date string, the format must be recognizable by datetime because the FirstCouponDate property is stored as a datetime.

Data Types: double | char | string | datetime

Irregular last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a scalar datetime, serial date number, date character vector, or date string.

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 a date character vector or date string, the format must be recognizable by datetime because the LastCouponDate property is stored as a datetime.

Data Types: double | char | string | datetime

User-defined name for the instrument, specified as the comma-separated pair consisting of 'Name' and a scalar string or character vector.

Data Types: char | string

Properties

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InflationBond coupon annual rate, returned as a scalar decimal.

Data Types: double

InflationBond maturity date, returned as a datetime.

Data Types: datetime

Frequency of payments per year, returned as a scalar integer.

Data Types: double

Day count basis, returned as a scalar integer.

Data Types: double

Initial principal amount, returned as a scalar numeric.

Data Types: double

Flag indicating whether cash flow adjusts for day count convention, returned as scalar logical with a value of true or false.

Data Types: logical

Bond issue date, returned as a datetime.

Data Types: datetime

Indexation lag in months, returned as a scalar numeric.

Data Types: double

Business day conventions, returned as a string.

Data Types: string

Holidays used in computing business days, returned as datetimes.

Data Types: datetime

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.

Data Types: logical

Irregular first coupon date, returned as a datetime.

Data Types: datetime

Irregular last coupon date, returned as a datetime.

Data Types: datetime

User-defined name for the instrument, returned as a string.

Data Types: string

Object Functions

inflationCashflowsCompute cash flows for InflationBond instrument

Examples

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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
       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

More About

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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.

I(0,T)Pn(0,T)=I(0)Pr(0,T)BTIPS(0,TM)=1I(T0)i=1McI(0)Pr(0,Ti)+FI(0)Pr(0,TM)                  =1I(T0)i=1McI(0,Ti)Pn(0,Ti)+FI(0,TM)Pn(0,TM)

where

  • Pn is the nominal zero-coupon bond price.

  • Pr 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).

  • BTIPS(0,TM) is the inflation-indexed bond price.

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

Introduced in R2021a