Financial Toolbox™

zero2pyld

Par yield curve given zero curve

Syntax

[ParRates, CurveDates] = zero2pyld(ZeroRates, CurveDates, Settle, 
Compounding, Basis, OutputCompounding)

Arguments

`ZeroRates`	A number of bonds (`NUMBONDS`) by 1 vector of annualized zero rates, as decimal fractions. In aggregate, the rates constitute an implied zero curve for the investment horizon represented by `CurveDates`.
`CurveDates`	A `NUMBONDS`-by-1 vector of maturity dates (as serial date numbers) that correspond to the zero rates.
`Settle`	A serial date number that is the common settlement date for the zero rates.
`Compounding`	(Optional) Scalar value representing the periodicity in which the output par rates are compounded when annualized. Allowed values are:
	`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
`Basis`	(Optional) Day-count basis used to annualize the implied zero rates. 0 = actual/actual (default) 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 (ISMA) 9 = actual/360 (ISMA) 10 = actual/365 (ISMA) 11 = 30/360E (ISMA) 12 = actual/365 (ISDA)
`OutputCompounding`	(Optional) Scalar value representing the periodicity in which the input zero rates were compounded when annualized. The default is the value for `Compounding`.

Description

[ParRates, CurveDates] = zero2pyld(ZeroRates, CurveDates, Settle, Compounding, Basis, OutputCompounding) returns a par yield curve given a zero curve and its maturity dates.

`ParRates`	A `NUMBONDS`-by-1 vector of annualized par yields, as decimal fractions. (Par yields = coupon rates.) In aggregate, the yield rates in `ParRates` constitute a par yield curve for the investment horizon represented by `CurveDates`.
`CurveDates`	A `NUMBONDS`-by-1 vector of maturity dates (as serial date numbers) that correspond to the par yield rates. This vector is the same as the input vector `CurveDates`.

Examples

Given

A zero curve over a set of maturity dates and
A settlement date
Annual compounding for the input zero curve and monthly compounding for the output par rates

compute a par yield curve.

ZeroRates = [0.0457
             0.0487
             0.0506
             0.0507
             0.0505
             0.0504
             0.0506
             0.0516
             0.0539
             0.0530];

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 = 1;
OutputCompounding = 12;

[ParRates, CurveDates] = zero2pyld(ZeroRates, CurveDates,...  
Settle, Compounding, [] , OutputCompounding)

ParRates =

    0.0479
    0.0511
    0.0530
    0.0531
    0.0526
    0.0524
    0.0525
    0.0534
    0.0555
    0.0543

CurveDates =

      730796
      730831
      730866
      730887
      730914
      730943
      730971
      731027
      731098
      731167

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

zero2pyld

Syntax

Arguments

Description

Examples

See Also