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bondbyhjm

价格bond from Heath-Jarrow-Morton interest-rate tree

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Syntax

[Price,PriceTree] = bondbyhjm(HJMTree,CouponRate,Settle,Maturity)
[Price,PriceTree] = bondbyhjm(___,Name,Value)

Description

example

[价格,价格Tree) = bondbyhjm (HJMTree,CouponRate,Settle,Maturity)prices bond from a Heath-Jarrow-Morton interest-rate tree.bondbyhjmcomputes prices of vanilla bonds, stepped coupon bonds and amortizing bonds.

example

[价格,价格Tree) = bondbyhjm (___,Name,Value)adds additional name-value pair arguments.

Examples

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打开生活的脚本

价格4%bond using an HJM interest-rate tree.

Loadderiv.mat, which providesHJMTree. TheHJMTreestructure contains the time and interest-rate information needed to price the bond.

loadderiv.mat;

Define the bond using the required arguments. Other arguments use defaults.

CouponRate = 0.04; Settle ='01-Jan-2000'; Maturity ='01-Jan-2004';

Usebondbyhjmto compute the price of the bond.

Period = 1; Price = bondbyhjm(HJMTree, CouponRate, Settle, Maturity, Period)
价格= 97.3600
打开生活的脚本

价格single stepped coupon bonds using market data.

Define the interest-rate term structure.

Rates = [0.035; 0.042147; 0.047345; 0.052707]; ValuationDate ='Jan-1-2010'; StartDates = ValuationDate; EndDates = {'Jan-1-2011';'Jan-1-2012';'Jan-1-2013';'Jan-1-2014'}; Compounding = 1;

Create theRateSpec.

RS = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,...'EndDates', EndDates,'Rates', Rates,'Compounding', Compounding);

Create the stepped bond instrument.

Settle ='01-Jan-2010'; Maturity = {'01-Jan-2011';'01-Jan-2012';'01-Jan-2013';'01-Jan-2014'}; CouponRate = {{'01-Jan-2012'.0425;'01-Jan-2014'.0750}}; Period = 1;

Build the HJM tree using the following market data:

Volatility = [.2; .19; .18; .17]; CurveTerm = [ 1; 2; 3; 4]; HJMTimeSpec = hjmtimespec(ValuationDate, EndDates); HJMVolSpec = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6); HJMT = hjmtree(HJMVolSpec,RS,HJMTimeSpec);

Compute the price of the stepped coupon bonds.

PHJM= bondbyhjm(HJMT, CouponRate, Settle,Maturity , Period)
PHJM =4×1100.7246 100.0945 101.5900 102.0820
打开生活的脚本

价格a bond with an amortization schedule using theFaceinput argument to define the schedule.

Define the interest-rate term structure.

Rates = 0.065; ValuationDate ='1-Jan-2011'; StartDates = ValuationDate; EndDates='1-Jan-2017'; Compounding = 1;

Create theRateSpec.

RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,...'EndDates', EndDates,'Rates', Rates,'Compounding', Compounding)
RateSpec =struct with fields:FinObj: 'RateSpec' Compounding: 1 Disc: 0.6853 Rates: 0.0650 EndTimes: 6 StartTimes: 0 EndDates: 736696 StartDates: 734504 ValuationDate: 734504 Basis: 0 EndMonthRule: 1

Create the bond instrument. The bond has a coupon rate of 7%, a period of one year, and matures on 1-Jan-2017.

CouponRate = 0.07; Settle ='1-Jan-2011'; Maturity ='1-Jan-2017'; Period = 1; Face = {{'1-Jan-2015'100;'1-Jan-2016'90;'1-Jan-2017'80}};

Build the HJM tree using the following market data:

Volatility = [.2; .19; .18; .17]; CurveTerm = [ 1; 2; 3; 4]; MaTree = {'Jan-1-2012';'Jan-1-2013';'Jan-1-2014';'Jan-1-2015';...'Jan-1-2016';'Jan-1-2017'}; HJMTimeSpec = hjmtimespec(ValuationDate, MaTree); HJMVolSpec = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6); HJMT = hjmtree(HJMVolSpec,RateSpec,HJMTimeSpec);

Compute the price of the amortizing bond.

价格= bondbyhjm(HJMT, CouponRate, Settle, Maturity,'Period',...Period,'Face', Face)
价格= 102.3155

Compare the results with price of a vanilla bond.

价格Vanilla = bondbyhjm(HJMT, CouponRate, Settle, Maturity, Period)
价格Vanilla = 102.4205

Input Arguments

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Interest-rate tree structure, created byhjmtree

Data Types:struct

Bond coupon rate, specified as anNINST-by-1decimal annual rate orNINST-by-1cell array, where each element is aNumDates-by-2cell array. The first column of theNumDates-by-2cell array is dates and the second column is associated rates. The date indicates the last day that the coupon rate is valid.

Data Types:double|cell

Settlement date, specified either as a scalar orNINST-by-1vector of serial date numbers or date character vectors.

TheSettledate for every bond is set to theValuationDateof the HJM tree. The bond argumentSettleis ignored.

Data Types:char|double

Maturity date, specified as aNINST-by-1vector of serial date numbers or date character vectors representing the maturity date for each bond.

Data Types:char|double

Name-Value Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name and价值is the corresponding value.Namemust appear inside quotes. You can specify several name and value pair arguments in any order asName1,Value1,...,NameN,ValueN.

Example:[Price,PriceTree] = bondbyhjm(HJMTree,CouponRate,Settle,Maturity,'Period',4,'Face',10000)

Coupons per year, specified as the comma-separated pair consisting of'Period'and aNINST-by-1vector. Values forPeriodare1,2,3,4,6, and12.

Data Types:double

Day-count basis of the instrument, specified as the comma-separated pair consisting of'Basis'and aNINST-by-1vector.

  • 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, seeBasis.

Data Types:double

End-of-month rule flag for generating dates whenMaturityis an end-of-month date for a month having 30 or fewer days, specified as the comma-separated pair consisting of'EndMonthRule'and a nonnegative integer [0,1] using aNINST-by-1vector.

  • 0= Ignore rule, meaning that a payment date is always the same numerical day of the month.

  • 1= Set rule on, meaning that a payment date is always the last actual day of the month.

Data Types:logical

Bond issue date, specified as the comma-separated pair consisting of'IssueDate'and aNINST-by-1vector using a serial nonnegative date number or date character vector.

Data Types:double|char

Irregular first coupon date, specified as the comma-separated pair consisting of'FirstCouponDate'and aNINST-by-1vector using a serial nonnegative date number or date character vector.

WhenFirstCouponDateandLastCouponDateare both specified,FirstCouponDatetakes precedence in determining the coupon payment structure. If you do not specify aFirstCouponDate, the cash flow payment dates are determined from other inputs.

Data Types:double|char

Irregular last coupon date, specified as the comma-separated pair consisting of'LastCouponDate'and aNINST-by-1vector using a serial nonnegative date number or date character vector.

In the absence of a specifiedFirstCouponDate, a specifiedLastCouponDatedetermines the coupon structure of the bond. The coupon structure of a bond is truncated at theLastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date. If you do not specify aLastCouponDate, the cash flow payment dates are determined from other inputs.

Data Types:double|char

Forward starting date of payments (the date from which a bond cash flow is considered), specified as the comma-separated pair consisting of'StartDate'and aNINST-by-1vector using serial date numbers or date character vectors.

If you do not specifyStartDate, the effective start date is theSettledate.

Data Types:char|double

Face or par value, specified as the comma-separated pair consisting of'Face'and aNINST-by-1vector of nonnegative face values or anNINST-by-1cell array of face values or face value schedules. For the latter case, each element of the cell array is aNumDates-by-2cell array, where the first column is dates and the second column is its associated face value. The date indicates the last day that the face value is valid.

Data Types:cell|double

Derivatives pricing options, specified as the comma-separated pair consisting of'Options'and a structure that is created withderivset.

Data Types:struct

Flag to adjust cash flows based on actual period day count, specified as the comma-separated pair consisting of'AdjustCashFlowsBasis'and aNINST-by-1vector of logicals with values of0(false) or1(true).

Data Types:logical

Business day conventions, specified as the comma-separated pair consisting of'BusinessDayConvention'and a character vector or aN-by-1(或NINST-by-2ifBusinessDayConventionis different for each leg) cell array of character vectors of business day conventions. The selection for business day convention determines how non-business days are treated. Non-business days are defined as weekends plus any other date that businesses are not open (e.g. statutory holidays). Values are:

  • actual— Non-business days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.

  • follow——现金流,落在非业务的一天ssumed to be distributed on the following business day.

  • modifiedfollow——现金流,落在非业务的一天ssumed 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——现金流,落在非业务的一天ssumed to be distributed on the previous business day.

  • modifiedprevious——现金流,落在非业务的一天ssumed 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

Holidays used in computing business days, specified as the comma-separated pair consisting of'Holidays'and MATLAB date numbers using aNHolidays-by-1vector.

Data Types:double

Output Arguments

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Expected bond prices at time 0, returned as aNINST-by-1vector.

Tree structure of instrument prices, returned as a MATLAB structure of trees containing vectors of instrument prices and accrued interest, and a vector of observation times for each node. Within价格Tree:

  • 价格Tree.PBushcontains the clean prices.

  • 价格Tree.AIBushcontains the accrued interest.

  • 价格Tree.tObscontains the observation times.

More About

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Vanilla Bond

A vanilla coupon bond is a security representing an obligation to repay a borrowed amount at a designated time and to make periodic interest payments until that time.

The issuer of a bond makes the periodic interest payments until the bond matures. At maturity, the issuer pays to the holder of the bond the principal amount owed (face value) and the last interest payment.

Stepped Coupon Bond

A step-up and step-down bond is a debt security with a predetermined coupon structure over time.

With these instruments, coupons increase (step up) or decrease (step down) at specific times during the life of the bond.

Bond with an Amortization Schedule

An amortized bond is treated as an asset, with the discount amount being amortized to interest expense over the life of the bond.

See Also

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Topics

Introduced before R2006a

Financial Instruments Toolbox Documentation

金宝app

A Practical Guide to Modeling Financial Risk with MATLAB

A Practical Guide to Modeling Financial Risk with MATLAB

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