disc2zero

Zero curve given discount 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 optional name-value pair inputs: Compounding and Basis.

Syntax

[ZeroRates,CurveDates] = disc2zero(DiscRates,CurveDates,Settle)

[ZeroRates,CurveDates] = disc2zero(___,Name,Value)

Description

[ZeroRates,CurveDates] = disc2zero(DiscRates,CurveDates,Settle) returns a zero curve given a discount curve and its maturity dates. If either inputs for CurveDates or Settle are datetime arrays, the output CurveDates is returned as datetime arrays.

[ZeroRates,CurveDates] = disc2zero(___,Name,Value) adds optional name-value pair arguments

Examples

Determine the Zero Curve Given a Discount Curve and Maturity Dates

Given the following discount factors DiscRates over a set of maturity dates CurveDates, and a settlement date Settle:

DiscRates = [0.9996
             0.9947
             0.9896
             0.9866
             0.9826
             0.9786
             0.9745
             0.9665
             0.9552
             0.9466];

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');

Set daily compounding for the output zero curve, on an actual/365 basis.

Compounding = 365;
Basis = 3;

Execute the function disc2zero which returns the zero curve ZeroRates at the maturity dates CurveDates.

[ZeroRates, CurveDates] = disc2zero(DiscRates, CurveDates,... 
Settle, Compounding, Basis)

ZeroRates = 10×1

    0.0487
    0.0510
    0.0523
    0.0524
    0.0530
    0.0526
    0.0530
    0.0532
    0.0549
    0.0536

CurveDates = 10×1

      730796
      730831
      730866
      730887
      730914
      730943
      730971
      731027
      731098
      731167

For readability, DiscRates and ZeroRates are shown here only to the basis point. However, MATLAB® software computed them at full precision. If you enter DiscRates as shown, ZeroRates may differ due to rounding.

Determine the Zero Curve Given a Discount Curve and Maturity Dates Using datetime Inputs

Given the following discount factors, DiscRates, over a set of maturity dates, CurveDates, and a settlement date, Settle, use datetime inputs to return the zero curve, ZeroRates, at the maturity dates, CurveDates.

DiscRates = [0.9996
             0.9947
             0.9896
             0.9866
             0.9826
             0.9786
             0.9745
             0.9665
             0.9552
             0.9466];

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');
Compounding = 365;
Basis = 3;

CurveDates = datetime(CurveDates,'ConvertFrom','datenum','Locale','en_US');
Settle = datetime(Settle,'ConvertFrom','datenum','Locale','en_US');

[ZeroRates, CurveDates] = disc2zero(DiscRates, CurveDates,...
Settle, Compounding, Basis)

ZeroRates = 10×1

    0.0487
    0.0510
    0.0523
    0.0524
    0.0530
    0.0526
    0.0530
    0.0532
    0.0549
    0.0536

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

Input Arguments

DiscRates — Discount factors

decimal fraction

Discount factors, specified as a column vector of decimal fractions. In aggregate, the factors in DiscRates constitute a discount curve for the investment horizon represented by CurveDates.

Data Types: double

CurveDates — Maturity dates

serial date number | date character vector | datetime

Maturity dates that correspond to the discount factors in DiscRates, specified as a column vector using serial date numbers, date character vectors, or datetime arrays.

Data Types: double | datetime | char

Settle — Common settlement date for discount rates in DiscRates

serial date number | date character vector | datetime

Common settlement date for the discount rates in DiscRates, 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] = disc2zero(DiscRates,CurveDates,Settle,'Compounding',6,'Basis',9)

'Compounding' — Rate at which output zero rates are compounded when annualized

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

Rate at which the output zero rates are compounded when annualized, specified as a numeric value. Allowed values are:

• 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

Data Types: double

'Basis' — Day-count basis used for annualizing output zero rates

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

Day-count basis used for annualizing the 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.

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 column vector of decimal fractions. The zero rates are the yields to maturity on theoretical zero-coupon bonds.

CurveDates — Maturity dates that correspond to ZeroRates

serial date number | date character vector | datetime

Maturity dates that correspond to the ZeroRates, returned as a column vector. This vector is the same as the input vector CurveDates, but the output is sorted by ascending maturity. If either inputs for CurveDates or Settle are datetime arrays, the output CurveDates is returned as datetime arrays.