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pyld2zero

Zero curve given par yield curve

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In R2017b, the specification of optional input arguments has changed. While the previous ordered inputs syntax is still supported, it may no longer be supported in a future release. Use the new optional name-value pair inputs:InputCompounding,InputBasis,OutputCompounding, andOutputBasis.

Syntax

[ZeroRates,CurveDates] = pyld2zero(ParRates,CurveDates,Settle)
[ZeroRates,CurveDates] = pyld2zero(___,Name,Value)

Description

example

[ZeroRates,CurveDates] = pyld2zero(ParRates,CurveDates,Settle)返回一个零线投入en a par yield curve and its maturity dates. If either input forCurveDatesorSettleis a datetime array,CurveDatesis returned as a datetime array. Otherwise,CurveDatesis returned as a serial date number.

[ZeroRates,CurveDates] = pyld2zero(___,Name,Value)adds optional name-value pair arguments

Examples

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Open Live Script

Define the settlement date, maturity, and zero rates.

Settle = datenum('01-Feb-2013'); CurveDates = datemnth(Settle,12*[1 2 3 5 7 10 20 30]'); ZeroRates = [.11 0.30 0.64 1.44 2.07 2.61 3.29 3.55]'/100; InputCompounding = 2; InputBasis = 1; OutputCompounding = 2; OutputBasis = 1;

Compute par yield curve from zero rates.

ParRates = zero2pyld(ZeroRates, CurveDates, Settle,“InputCompounding”,2,...'InputBasis',1,'OutputCompounding',2,'OutputBasis',1)
ParRates =8×10.0011 0.0030 0.0064 0.0142 0.0201 0.0251 0.0309 0.0330

Compute zero curve from the par yield curve.

ZeroRates = pyld2zero(ParRates, CurveDates, Settle,“InputCompounding”,2,...'InputBasis',1,'OutputCompounding',2,'OutputBasis',1)
ZeroRates =8×10.0011 0.0030 0.0064 0.0144 0.0207 0.0261 0.0329 0.0355
Open Live Script

Usedatetimeinputs to compute the zero curve given the par yield curve.

Settle = datenum('01-Feb-2013'); CurveDates = [datenum('01-Feb-2014') datenum('01-Feb-2015') datenum('01-Feb-2016') datenum('01-Feb-2018') datenum('01-Feb-2020') datenum('01-Feb-2023') datenum('01-Feb-2033') datenum('01-Feb-2043')]; OriginalParRates = [0.11 0.30 0.64 1.42 2.02 2.51 3.10 3.31]'/100; InputCompounding = 1; InputBasis = 0; OutputCompounding = 1; OutputBasis = 0; Settle = datetime(Settle,'ConvertFrom','datenum','Locale','en_US'); CurveDates = datetime(CurveDates,'ConvertFrom','datenum','Locale','en_US'); [ZeroRates Dates] = pyld2zero(OriginalParRates, CurveDates, Settle,...'OutputCompounding', OutputCompounding,'OutputBasis', OutputBasis,...“InputCompounding”, InputCompounding,'InputBasis', InputBasis)
ZeroRates =8×10.0011 0.0030 0.0064 0.0144 0.0207 0.0261 0.0329 0.0356
日期=8x1 datetime01-Feb-2014 01-Feb-2015 01-Feb-2016 01-Feb-2018 01-Feb-2020 01-Feb-2023 01-Feb-2033 01-Feb-2043
Open Live Script

Given the following a par yield curve and its maturity dates, return theZeroRates.

Settle = datenum('01-Feb-2013'); CurveDates = [datenum('01-Feb-2014') datenum('01-Feb-2015') datenum('01-Feb-2016') datenum('01-Feb-2018') datenum('01-Feb-2020') datenum('01-Feb-2023') datenum('01-Feb-2033') datenum('01-Feb-2043')]; OriginalParRates = [0.11 0.30 0.64 1.42 2.02 2.51 3.10 3.31]'/100; InputCompounding = 1; InputBasis = 0; OutputCompounding = 1; OutputBasis = 0; ZeroRates = pyld2zero(OriginalParRates, CurveDates, Settle,...'OutputCompounding', OutputCompounding,'OutputBasis', OutputBasis,...“InputCompounding”, InputCompounding,'InputBasis', InputBasis)
ZeroRates =8×10.0011 0.0030 0.0064 0.0144 0.0207 0.0261 0.0329 0.0356

With theZeroRates, use thezero2pyldfunction to return theParRatesOutand determine the roundtrip error.

ParRatesOut = zero2pyld(ZeroRates, CurveDates, Settle,...'OutputCompounding', OutputCompounding,'OutputBasis', OutputBasis,...“InputCompounding”, InputCompounding,'InputBasis', InputBasis)
ParRatesOut =8×10.0011 0.0030 0.0064 0.0142 0.0202 0.0251 0.0310 0.0331
max(abs(OriginalParRates - ParRatesOut))% Roundtrip error
ans = 1.2750e-16

Input Arguments

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Annualized par yields (coupon rates), specified as aNUMBONDS-by-1vector using decimal fractions. In aggregate, the rates constitute an implied zero curve for the investment horizon represented byCurveDates.

Data Types:double

Maturity dates which correspond to the inputParRates, specified as aNUMBONDS-by-1vector using serial date numbers, date character vectors, or datetime arrays.

Data Types:double|datetime|char

Common settlement date for inputParRates, specified as serial date numbers, date character vectors, or datetime arrays.

Data Types:double|datetime|char

Name-Value Pair Arguments

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

Example:[ZeroRates,CurveDates] = pyld2zero(ParRates,CurveDates,Settle,'OutputCompounding',3,'OutputBasis',5,'InputCompounding',4,'InputBasis',5)

Compounding frequency of outputZeroRates, specified using the allowed values:

  • 0— Simple interest (no compounding)

  • 1— Annual compounding

  • 2— Semiannual compounding (default)

  • 3— Compounding three times per year

  • 4— Quarterly compounding

  • 6— Bimonthly compounding

  • 12— Monthly compounding

  • 365— Daily compounding

  • -1— Continuous compounding

Note

  • IfOutputCompoundingis set to0(simple),-1(continuous), or365(daily), theInputCompoundingmust also be specified using a valid value.

  • IfOutputCompoundingis not specified, thenOutputCompoundingis assigned the value specified forInputCompounding.

  • If eitherOutputCompoundingorInputCompoundingare not specified, the default is2(semiannual) for both.

Data Types:double

Day count basis of outputZeroRates, specified using allowed 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, seeBasis.

Note

IfOutputBasisis not specified, thenOutputBasisis assigned the value specified forInputBasis. If eitherInputBasisorOutputBasisare not specified, the default is0(actual/actual) for both.

Data Types:double

Compounding frequency of inputParRates, specified using allowed values:

  • 1— Annual compounding

  • 2— Semiannual compounding (default)

  • 3— Compounding three times per year

  • 4— Quarterly compounding

  • 6— Bimonthly compounding

  • 12— Monthly compounding

Note

  • IfOutputCompoundingis1,2,3,4,6, or12andInputCompoundingis not specified, the value ofOutputCompoundingis used.

  • IfOutputCompoundingis0(simple),-1(continuous), or365(daily), a validInputCompoundingvalue must also be specified.

  • If eitherInputCompoundingorOutputCompoundingare not specified, the default is2(semiannual) for both.

Data Types:double

Day count basis of the inputParRates, specified using allowed 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, seeBasis.

Note

IfInputBasisis not specified, thenInputBasisis assigned the value specified forOutputBasis. If eitherInputBasisorOutputbasisare not specified, the default is0(actual/actual) for both.

Data Types:double

Output Arguments

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Zero rates, returned as aNUMBONDS-by-1numeric vector. In aggregate, the rates inZeroRatesconstitute a zero curve for the investment horizon represented byCurveDates.ZeroRatesare ordered by ascending maturity.

Maturity dates that correspond to theZeroRates, returned as aNUMBONDS-by-1vector of maturity dates that correspond to each par rate contained inZeroRates.CurveDatesare ordered by ascending maturity.

If either input forCurveDatesorSettleis a datetime array,CurveDatesis returned as a datetime array. Otherwise,CurveDatesare returned as a serial date numbers.

See Also

|||||||||(Financial Instruments Toolbox)

Topics

Introduced before R2006a

Financial Toolbox Documentation

万博1manbetx

A Practical Guide to Modeling Financial Risk with MATLAB

A Practical Guide to Modeling Financial Risk with MATLAB

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