fwd2zero

Zero curve given forward 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] = fwd2zero(ForwardRates,CurveDates,Settle)

[ZeroRates,CurveDates] = fwd2zero(___,Name,Value)

Description

[ZeroRates,CurveDates] = fwd2zero(ForwardRates,CurveDates,Settle) returns a zero curve given an implied forward rate curve and its maturity dates. If both inputs for CurveDates and Settle are serial date numbers or date character vectors, CurveDates is returned as serial date numbers. However, if either of the inputs for CurveDates and Settle are a datetime array, CurveDates is returned as a datetime array.

[ZeroRates,CurveDates] = fwd2zero(___,Name,Value) adds optional name-value pair arguments

Examples

Compute the Zero Curve Given the Forward Curve

This example shows how to compute the zero curve, given an implied forward rate curve over a set of maturity dates, a settlement date, and a compounding rate.

ForwardRates = [0.0469
                0.0519
                0.0549
                0.0535
                0.0558
                0.0508
                0.0560
                0.0545
                0.0615
                0.0486];

CurveDates = [datenum('06-Nov-2000')
              datenum('11-Dec-2000')
              datenum('15-Jan-2001')
              datenum('05-Feb-2001')
              datenum('04-Mar-2001')
              datenum('02-Apr-2001')
              datenum('30-Apr-2001')
              datenum('25-Jun-2001')
              datenum('04-Sep-2001')
              datenum('12-Nov-2001')];

Settle = datenum('03-Nov-2000');

InputCompounding = 1;
InputBasis = 2;
OutputCompounding = 1;
OutputBasis = 2;

Execute the function fwd2zero to return the zero-rate curve ZeroRates at the maturity dates CurveDates.

[ZeroRates, CurveDates] = fwd2zero(ForwardRates, CurveDates,...
Settle,'InputCompounding',1,'InputBasis',2,'OutputCompounding',1,'OutputBasis',2)

ZeroRates = 10×1

    0.0469
    0.0515
    0.0531
    0.0532
    0.0538
    0.0532
    0.0536
    0.0539
    0.0556
    0.0543

CurveDates = 10×1

      730796
      730831
      730866
      730887
      730914
      730943
      730971
      731027
      731098
      731167

Compute the Zero Curve Given the Forward Curve Using datetime Inputs

This example shows how to use datetime inputs compute the zero curve, given an implied forward rate curve over a set of maturity dates, a settlement date, and a compounding rate.

ForwardRates = [0.0469
                0.0519
                0.0549
                0.0535
                0.0558
                0.0508
                0.0560
                0.0545
                0.0615
                0.0486];

CurveDates = [datenum('06-Nov-2000')
              datenum('11-Dec-2000')
              datenum('15-Jan-2001')
              datenum('05-Feb-2001')
              datenum('04-Mar-2001')
              datenum('02-Apr-2001')
              datenum('30-Apr-2001')
              datenum('25-Jun-2001')
              datenum('04-Sep-2001')
              datenum('12-Nov-2001')];

Settle = datenum('03-Nov-2000');

InputCompounding = 1;
InputBasis = 2;
OutputCompounding = 1;
OutputBasis = 2;CurveDates = datetime(CurveDates,'ConvertFrom','datenum','Locale','en_US');
Settle = datetime(Settle,'ConvertFrom','datenum','Locale','en_US');
[ZeroRates, CurveDates] = fwd2zero(ForwardRates, CurveDates,...
Settle,'InputCompounding',1,'InputBasis',2,'OutputCompounding',1,'OutputBasis',2)

ZeroRates = 10×1

    0.0469
    0.0515
    0.0531
    0.0532
    0.0538
    0.0532
    0.0536
    0.0539
    0.0556
    0.0543

CurveDates = 10x1 datetime array
   06-Nov-2000 00:00:00
   11-Dec-2000 00:00:00
   15-Jan-2001 00:00:00
   05-Feb-2001 00:00:00
   04-Mar-2001 00:00:00
   02-Apr-2001 00:00:00
   30-Apr-2001 00:00:00
   25-Jun-2001 00:00:00
   04-Sep-2001 00:00:00
   12-Nov-2001 00:00:00

Input Arguments

ForwardRates — Annualized implied forward rates

decimal fraction

Annualized implied forward rates, specified as a (NUMBONDS)-by-1 vector using decimal fractions. In aggregate, the rates in ForwardRates constitute an implied forward curve for the investment horizon represented by CurveDates. The first element pertains to forward rates from the settlement date to the first curve date.

Data Types: double

CurveDates — Maturity dates

serial date number | date character vector | datetime

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

Data Types: double | datetime | char

Settle — Common settlement date for ForwardRates

serial date number | date character vector | datetime

Common settlement date for ForwardRates, 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] = fwd2zero(ForwardRates,CurveDates,Settle,'InputCompounding',3,'InputBasis',5,'OutputCompounding',4,'OutputBasis',5)

'InputCompounding' — Compounding frequency of input forward rates

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

Compounding frequency of input forward rates, specified with 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 InputCompounding is not specified, then InputCompounding is assigned the value specified for OutputCompounding. If either InputCompounding or OutputCompounding are not specified, the default is 2

Data Types: double

'InputBasis' — Day-count basis of input forward rates

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

Day count basis of input forward rates, specified as a numeric value. Allowed values are:

• 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

'OutputCompounding' — Compounding frequency of output zero rates

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

Compounding frequency of output zero rates, specified with 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 not specified, then OutputCompounding is assigned the value specified for InputCompounding. If either InputCompounding or OutputCompounding are not specified, the default is 2 (semiannual) for both.

Data Types: double

'OutputBasis' — Day-count basis of output zero rates

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

Day count basis of output zero rates, specified as a numeric value. Allowed values are:

• 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

Output Arguments

ZeroRates — Zero curve for investment horizon represented by CurveDates

numeric

Zero curve for the investment horizon represented by CurveDates, returned as a NUMBONDS-by-1 vector of decimal fractions. In aggregate, the rates in ZeroRates constitute a zero curve for the investment horizon represented by CurveDates.

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 the zero rates in ZeroRates. This vector is the same as the input vector CurveDates, but is sorted by ascending maturity.

If both inputs for CurveDates and Settle are serial date numbers or date character vectors, CurveDates is returned as serial date numbers. However, if either of the inputs for CurveDates and Settle are a datetime array, CurveDates is returned as a datetime array.