zero2fwd (Financial Toolbox)

Forward curve given a zero curve.

Syntax

[fr, cd] = zero2fwd(zr, cd, sd, ocomp, obasis, icomp, ibasis)
[fr, cd] = zero2fwd(zr, cd, sd, ocomp, obasis, icomp)
[fr, cd] = zero2fwd(zr, cd, sd, ocomp, obasis)
[fr, cd] = zero2fwd(zr, cd, sd, ocomp)
[fr, cd] = zero2fwd(zr, cd, sd)

Arguments

zr: Zero rates. An N-by-1 vector of annualized zero rates, as decimal fractions. In aggregate, the rates in zr constitute an implied zero 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 zero rates in zr. 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 zero rates in zr.

ocomp: Output compounding. A scalar that sets the compounding frequency per year for annualizing the output forward rates in fr. 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
365 = daily compounding
-1 = continuous compounding

obasis: Output day-count basis for annualizing the forward rates in fr.
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 zero rates in zr. Allowed values are the same as for ocomp. Default = ocomp.

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

Description

[fr, cd] = zero2fwd(zr, cd, sd, ocomp, obasis, icomp, ibasis)

returns an implied forward rate curve given a zero curve and its maturity dates.

fr: Forward rates. An N-by-1 vector of decimal fractions. In aggregate, the rates in fr constitute a forward curve over the dates in cd.

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

Example

Given a zero curve zr over a set of maturity dates cd, and a settlement date sd:

zr = [0.0458
      0.0502
      0.0518
      0.0519
      0.0524
      0.0519
      0.0523
      0.0525
      0.0541
      0.0529];
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 annual compounding for the forward curve, on an actual/actual basis. The zero curve was compounded daily on an actual/365 basis.

ocomp = 1;
obasis = 0;
icomp = 365;
ibasis = 3;

Execute the function

[fr, cd] = zero2fwd(zr, cd, sd, ocomp, obasis, icomp, ibasis)

which returns the forward rate curve fr at the maturity dates cd:

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