Financial Toolbox™

pyld2zero

Zero curve given par yield curve

Syntax

[ZeroRates, CurveDates] = pyld2zero(ParRates, CurveDates, Settle, 
Compounding, Basis, OutputCompounding)

Arguments

`ParRates`	Column vector of annualized implied par yield rates, as decimal fractions. (Par yields = coupon rates.) In aggregate, the yield rates in `ParRates` constitute an implied par yield curve for the investment horizon represented by `CurveDates`.
`CurveDates`	Column vector of maturity dates (as serial date numbers) that correspond to the par rates.
`Settle`	Serial date number that is the common settlement date for the par rates.
`Compounding`	(Optional) Scalar value representing the periodicity in which the output zero 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 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 par rates were compounded when annualized. The default is the value for `Compounding`.

Description

[ZeroRates, CurveDates] = pyld2zero(ParRates, CurveDates, Settle, Compounding, Basis, OutputCompounding) returns a zero curve given a par yield curve and its maturity dates.

`ZeroRates`	Column vector of decimal fractions. In aggregate, the rates in `ZeroRates` constitute a zero curve for the investment horizon represented by `CurveDates`.
`CurveDates`	Column vector of maturity dates (as serial date numbers) corresponding to the zero rates. This vector is the same as the input vector `CurveDates`.

Examples

Given

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

compute a zero yield curve.

ParRates = [0.0479
            0.0522
            0.0540
            0.0540
            0.0536
            0.0532
            0.0532
            0.0539
            0.0558
            0.0543];

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;

[ZeroRates, CurveDates] = pyld2zero(ParRates, CurveDates,... 
Settle, Compounding, [], OutputCompounding)

ZeroRates =

    0.0484
    0.0529
    0.0549
    0.0550
    0.0547
    0.0544
    0.0545
    0.0551
    0.0572
    0.0557

CurveDates =

      730796
      730831
      730866
      730887
      730914
      730943
      730971
      731027
      731098
      731167

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

pyld2zero

Syntax

Arguments

Description

Examples

See Also