pyld2zero

Zero curve given par yield curve

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, and OutputBasis.

Syntax

[ZeroRates,CurveDates] = pyld2zero(ParRates,CurveDates,Settle)

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

Description

[ZeroRates,CurveDates] = pyld2zero(ParRates,CurveDates,Settle) returns a zero curve given a par yield curve and its maturity dates. If either input for CurveDates or Settle is a datetime array, CurveDates is returned as a datetime array. Otherwise, CurveDates is returned as a serial date number.

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

Examples

Compute Zero Curve Given Par Yield Curve

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 = 8×1

    0.0011
    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 = 8×1

    0.0011
    0.0030
    0.0064
    0.0144
    0.0207
    0.0261
    0.0329
    0.0355

Compute Zero Curve Given Par Yield Curve Using datetime Inputs

Use datetime inputs 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 = 8×1

    0.0011
    0.0030
    0.0064
    0.0144
    0.0207
    0.0261
    0.0329
    0.0356

Dates = 8x1 datetime
   01-Feb-2014
   01-Feb-2015
   01-Feb-2016
   01-Feb-2018
   01-Feb-2020
   01-Feb-2023
   01-Feb-2033
   01-Feb-2043

Demonstrate a Roundtrip From pyld2zero to zero2pyld

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

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 = 8×1

    0.0011
    0.0030
    0.0064
    0.0144
    0.0207
    0.0261
    0.0329
    0.0356

With the ZeroRates, use the zero2pyld function to return the ParRatesOut and determine the roundtrip error.

ParRatesOut = zero2pyld(ZeroRates, CurveDates, Settle, ...
'OutputCompounding', OutputCompounding, 'OutputBasis', OutputBasis, ...
'InputCompounding', InputCompounding, 'InputBasis', InputBasis)

ParRatesOut = 8×1

    0.0011
    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

ParRates — Annualized par yields

decimal fraction

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

Data Types: double

CurveDates — Maturity dates

serial date number | date character vector | datetime

Maturity dates which correspond to the input ParRates, specified as a NUMBONDS-by-1 vector using serial date numbers, date character vectors, or datetime arrays.

Data Types: double | datetime | char

Settle — Common settlement date for ZeroRates

serial date number | date character vector | datetime

Common settlement date for input ParRates, 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 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: [ZeroRates,CurveDates] = pyld2zero(ParRates,CurveDates,Settle,'OutputCompounding',3,'OutputBasis',5,'InputCompounding',4,'InputBasis',5)

'OutputCompounding' — Compounding frequency of output ZeroRates

2 (default) | numeric values: 0,1, 2, 3, 4, 6, 12, 365, -1

Compounding frequency of output ZeroRates, 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

• If OutputCompounding is set to 0 (simple), -1 (continuous), or 365 (daily), the InputCompounding must also be specified using a valid value.

• If OutputCompounding is not specified, then OutputCompounding is assigned the value specified for InputCompounding.

• If either OutputCompounding or InputCompounding are not specified, the default is 2 (semiannual) for both.

Data Types: double

'OutputBasis' — Day-count basis of output ZeroRates

0 (default) | numeric values: 0,1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13

Day count basis of output ZeroRates, 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, see Basis.

Note

If OutputBasis is not specified, then OutputBasis is assigned the value specified for InputBasis. If either InputBasis or OutputBasis are not specified, the default is 0 (actual/actual) for both.

Data Types: double

'InputCompounding' — Compounding frequency of input ParRates

2 (default) | numeric values: 0,1, 2, 3, 4, 6, 12, 365, -1

Compounding frequency of input ParRates, 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

• If OutputCompounding is 1, 2, 3, 4, 6, or 12 and InputCompounding is not specified, the value of OutputCompounding is used.

• If OutputCompounding is 0 (simple), -1 (continuous), or 365 (daily), a valid InputCompounding value must also be specified.

• If either InputCompounding or OutputCompounding are not specified, the default is 2 (semiannual) for both.

Data Types: double

'InputBasis' — Day-count basis of input ParRates

0 (default) | numeric values: 0,1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13

Day count basis of the input ParRates, 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, see Basis.

Note

If InputBasis is not specified, then InputBasis is assigned the value specified for OutputBasis. If either InputBasis or Outputbasis are not specified, the default is 0 (actual/actual) for both.

Data Types: double

Output Arguments

ZeroRates — Zero rates

numeric

Zero rates, returned as a NUMBONDS-by-1 numeric vector. In aggregate, the rates in ZeroRates constitute a zero curve for the investment horizon represented by CurveDates. ZeroRates are ordered by ascending maturity.

CurveDates — Maturity dates that correspond to ZeroRates

serial date number | date character vector | datetime

Maturity dates that correspond to the ZeroRates, returned as a NUMBONDS-by-1 vector of maturity dates that correspond to each par rate contained in ZeroRates. CurveDates are ordered by ascending maturity.

If either input for CurveDates or Settle is a datetime array, CurveDates is returned as a datetime array. Otherwise, CurveDates are returned as a serial date numbers.