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floatbyhjm

Price floating-rate note from Heath-Jarrow-Morton interest-rate tree

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Syntax

[Price,PriceTree] = floatbyhjm(HJMTree,Spread,Settle,Maturity)
[Price,PriceTree] = floatbyhjm(___,Name,Value)

Description

example

[Price,PriceTree] = floatbyhjm(HJMTree,Spread,Settle,Maturity)prices a floating-rate note from a Heath-Jarrow-Morton interest-rate tree.

floatbyhjmcomputes prices of vanilla floating-rate notes, amortizing floating-rate notes, capped floating-rate notes, floored floating-rate notes and collared floating-rate notes.

example

[Price,PriceTree] = floatbyhjm(___,Name,Value)adds additional name-value pair arguments.

Examples

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Open Live Script

Price a 20-basis point floating-rate note using an HJM forward-rate tree.

Load the filederiv.mat, which providesHJMTree. TheHJMTreestructure contains the time and interest-rate information needed to price the note.

loadderiv.mat;

Define the floating-rate note using the required arguments. Other arguments use defaults.

Spread = 20; Settle ='01-Jan-2000'; Maturity ='01-Jan-2003';

Usefloatbyhjmto compute the price of the note.

Price = floatbyhjm(HJMTree, Spread, Settle, Maturity)
Price = 100.5529
Open Live Script

Price an amortizing floating-rate note using thePrincipalinput argument to define the amortization schedule.

创建RateSpec.

Rates = [0.03583; 0.042147; 0.047345; 0.052707; 0.054302]; ValuationDate ='15-Nov-2011'; StartDates = ValuationDate; EndDates = {'15-Nov-2012';'15-Nov-2013';'15-Nov-2014';'15-Nov-2015';'15-Nov-2016'}; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,...'EndDates', EndDates,'Rates', Rates,'Compounding', Compounding)
RateSpec =struct with fields:FinObj: 'RateSpec' Compounding: 1 Disc: [5x1 double] Rates: [5x1 double] EndTimes: [5x1 double] StartTimes: [5x1 double] EndDates: [5x1 double] StartDates: 734822 ValuationDate: 734822 Basis: 0 EndMonthRule: 1

创建floating-rate instrument using the following data:

Settle ='15-Nov-2011'; Maturity ='15-Nov-2015'; Spread = 15;

Define the floating-rate note amortizing schedule.

Principal ={{'15-Nov-2012'100;'15-Nov-2013'70;'15-Nov-2014'40;'15-Nov-2015'10}};

Build the HJM tree using the following data:

MatDates = {'15-Nov-2012';'15-Nov-2013';'15-Nov-2014';'15-Nov-2015';'15-Nov-2016';'15-Nov-2017'}; HJMTimeSpec = hjmtimespec(RateSpec.ValuationDate, MatDates); Volatility = [.10; .08; .06; .04]; CurveTerm = [ 1; 2; 3; 4]; HJMVolSpec = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6); HJMT = hjmtree(HJMVolSpec,RateSpec,HJMTimeSpec);

Compute the price of the amortizing floating-rate note.

Price = floatbyhjm(HJMT, Spread, Settle, Maturity,'Principal', Principal)
Price = 100.3059
Open Live Script

Price a collar with a floating-rate note using theCapRateandFloorRateinput argument to define the collar pricing.

Price a portfolio of collared floating-rate notes using the following data:

Rates = [0.0287; 0.03024; 0.03345; 0.03861; 0.04033]; ValuationDate ='1-April-2012'; StartDates = ValuationDate; EndDates = {'1-April-2013';'1-April-2014';'1-April-2015';...'1-April-2016';'1-April-2017'}; Compounding = 1;

创建RateSpec.

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

Build the HJM tree with the following data:

MatDates = {'1-April-2013';'1-April-2014';'1-April-2015';...'1-April-2016';'1-April-2017';'1-April-2018'}; HJMTimeSpec = hjmtimespec(RateSpec.ValuationDate, MatDates); Volatility = [.10; .08; .06; .04]; CurveTerm = [ 1; 2; 3; 4]; HJMVolSpec = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6); HJMT = hjmtree(HJMVolSpec,RateSpec,HJMTimeSpec);

创建floating-rate note instrument.

Settle ='1-April-2012'; Maturity ='1-April-2016'; Spread = 10; Principal = 100;

Compute the price of two capped collared floating-rate notes.

CapStrike = [0.04;0.055]; PriceCapped = floatbyhjm(HJMT, Spread, Settle, Maturity,...'CapRate', CapStrike)
PriceCapped =2×198.9986 100.2051

Compute the price of two collared floating-rate notes.

FloorStrike = [0.035;0.040]; PriceCollared = floatbyhjm(HJMT, Spread, Settle, Maturity,...'CapRate', CapStrike,'FloorRate', FloorStrike)
PriceCollared =2×199.9246 102.2321

Input Arguments

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Interest-rate tree structure, created byhjmtree

Data Types:struct

Number of basis points over the reference rate, specified as aNINST-by-1vector.

Data Types:double

Settlement date, specified either as a scalar orNINST-by-1矢量c串行数字或日期haracter vectors.

TheSettledate for every floating-rate note is set to theValuationDateof the HJM tree. The floating-rate note argumentSettleis ignored.

Data Types:char|double

Maturity date, specified as aNINST-by-1矢量c串行数字或日期haracter vectors representing the maturity date for each floating-rate note.

Data Types:char|double

Name-Value Arguments

Specify optional pairs of arguments asName1=Value1,...,NameN=ValueN, whereNameis the argument name andValueis 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 encloseNamein quotes.

Example:[Price,PriceTree] = floatbyhjm(HJMTree,Spread,Settle,Maturity,'Basis',3)

Frequency of payments per year, specified as the comma-separated pair consisting of'FloatReset'and aNINST-by-1vector.

Note

Payments on floating-rate notes (FRNs) are determined by the effective interest-rate between reset dates. If the reset period for an FRN spans more than one tree level, calculating the payment becomes impossible due to the recombining nature of the tree. That is, the tree path connecting the two consecutive reset dates cannot be uniquely determined because there is more than one possible path for connecting the two payment dates.

Data Types:double

Day count basis representing the basis used when annualizing the input forward rate tree, 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

Notional principal amounts, specified as the comma-separated pair consisting of'Principal'and a vector or cell array.

Principalaccepts aNINST-by-1vector orNINST-by-1cell array, where each element of the cell array is aNumDates-by-2cell array and the first column is dates and the second column is its associated notional principal value. The date indicates the last day that the principal value is valid.

Data Types:cell|double

Derivatives pricing options structure, specified as the comma-separated pair consisting of'Options'and a structure usingderivset.

Data Types:struct

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

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

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

Business day conventions, specified as the comma-separated pair consisting of'BusinessDayConvention'and a character vector or aN-by-1cell 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— Cash flows that fall on a non-business day are assumed to be distributed on the following business day.

  • modifiedfollow— Cash flows that fall on a non-business 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 non-business day are assumed to be distributed on the previous business day.

  • modifiedprevious— Cash flows that fall on a non-business 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

Annual cap rate, specified as the comma-separated pair consisting of'CapRate'and aNINST-by-1decimal annual rate orNINST-by-1cell array, where each element is aNumDates-by-2cell array, and the cell array first column is dates, and the second column is associated cap rates. The date indicates the last day that the cap rate is valid.

Data Types:double|cell

Annual floor rate, specified as the comma-separated pair consisting of'FloorRate'and aNINST-by-1decimal annual rate orNINST-by-1cell array, where each element is aNumDates-by-2cell array, and the cell array first column is dates, and the second column is associated floor rates. The date indicates the last day that the floor rate is valid.

Data Types:double|cell

Output Arguments

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浮动汇率注意价格预期时间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. WithinPriceTree:

  • PriceTree.PBushcontains the clean prices.

  • PriceTree.AIBushcontains the accrued interest.

  • PriceTree.tObscontains the observation times.

More About

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Floating-Rate Note

Afloating-rate noteis a security like a bond, but the interest rate of the note is reset periodically, relative to a reference index rate, to reflect fluctuations in market interest rates.

Version History

Introduced before R2006a

See Also

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