pyld2zero (Financial Toolbox)

Zero curve given a par yield curve.

Syntax

[zr, cd] = pyld2zero(pr,cd,sd,ocomp,obasis,icomp,ibasis,maxiter)
[zr, cd] = pyld2zero(pr,cd,sd,ocomp,obasis,icomp,ibasis)
[zr, cd] = pyld2zero(pr,cd,sd,ocomp,obasis,icomp)
[zr, cd] = pyld2zero(pr,cd,sd,ocomp,obasis)
[zr, cd] = pyld2zero(pr,cd,sd,ocomp)
[zr, cd] = pyld2zero(pr,cd,sd)

Arguments

pr: Par yield rates. An N-by-1 vector of annualized par yields, as decimal fractions. (Par yields = coupon rates.) In aggregate, the yield rates in pr constitute a par yield curve for the investment horizon represented by cd.

cd: Curve dates. An N-by-1 vector of maturity dates (as serial date numbers) that correspond to the par rates in pr. Use datenum to convert date strings to serial date numbers.

sd: Settlement date. A serial date number that is the common settlement date for the par rates in pr.

ocomp: Output compounding. A scalar that sets the compounding frequency per year for annualizing the output zero rates in zr. Allowed values are:

1: = annual compounding
2 = semi-annual compounding (default)
3 = compounding three times per year
4 = quarterly compounding
6 = bimonthly compounding
12 = monthly compounding

obasis: Output day-count basis for annualizing the output zero rates in zr.
0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.

icomp: Input compounding. A scalar that indicates the compounding frequency per year used for annualizing the input par rates in pr. Allowed values are the same as for ocomp. Default = ocomp.

ibasis: Input day-count basis used for annualizing the input par rates in pr. Allowed values are the same as for obasis. Default = obasis.

maxiter: Maximum number of iterations for deriving the zero rates in zr. A scalar. Default = 200.

Description

[zr, cd] = pyld2zero(pr,cd,sd,ocomp,obasis,icomp,ibasis,maxiter)

returns a zero curve given a par yield curve and its maturity dates.

zr: Zero rates. An N-by-1 vector of decimal fractions. In aggregate, the rates in zr constitute a zero curve for the investment horizon represented by cd.

cd: Curve dates. An N-by-1 vector of maturity dates (as serial date numbers) corresponding to the zero rates in zr. This vector is the same as the input vector cd. Use datestr to convert serial date numbers to date strings.

Example

Given a par yield curve pr over a set of maturity dates cd, and a settlement date sd:

pr = [0.0479
      0.0522
      0.0540
      0.0540
      0.0536
      0.0532
      0.0532
      0.0539
      0.0558
      0.0543];
cd = [datenum('06-Nov-1997')
      datenum('11-Dec-1997')
      datenum('15-Jan-1998')
      datenum('05-Feb-1998')
      datenum('04-Mar-1998')
      datenum('02-Apr-1998')
      datenum('30-Apr-1998')
      datenum('25-Jun-1998')
      datenum('04-Sep-1998')
      datenum('12-Nov-1998')];
sd = datenum('03-Nov-1997');

Set monthly compounding for the zero curve, on an actual/365 basis. The par yield curve was compounded annually on an actual/actual basis. Derive the zero curve within 50 iterations.

ocomp = 12;
obasis = 3;
icomp = 1;
ibasis = 0;
maxiter = 50;

Execute the function

[zr, cd] = pyld2zero(pr,cd,sd,ocomp,obasis,icomp,ibasis,maxiter)

which returns the zero curve zr at the maturity dates cd:

(For readability, pr and zr are shown only to the basis point. However, MATLAB computed them at full precision. If you enter pr as shown, zr may differ due to rounding.)