pyld2zero - Zero curve given par yield curve

Syntax

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

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) 13 = BUS/252
`InputCompounding`	(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, InputCompounding) 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');
InputCompounding = 1;
Compounding = 12;

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

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 - Zero curve given par yield curve

Syntax

Arguments

Description

Examples

See Also