fwd2zero (Financial Toolbox)

Zero curve given a forward curve.

Syntax

[zr, cd] = fwd2zero(fr, cd, sd, ocomp, obasis, icomp, ibasis)
[zr, cd] = fwd2zero(fr, cd, sd, ocomp, obasis, icomp)
[zr, cd] = fwd2zero(fr, cd, sd, ocomp, obasis)
[zr, cd] = fwd2zero(fr, cd, sd, ocomp)
[zr, cd] = fwd2zero(fr, cd, sd)

Arguments

fr: Forward rates. An N-by-1 vector of annualized implied forward rates, as decimal fractions. In aggregate, the rates in fr constitute an implied forward 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 forward rates in fr. 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 forward rates in fr.

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
365 = daily compounding
-1 = continuous 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 forward rates in fr. Allowed values are the same as for ocomp. Default = ocomp.

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

Description

[zr, cd] = fwd2zero(fr, cd, sd, ocomp, obasis, icomp, ibasis)

returns a zero curve given an implied forward 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) that correspond 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 an implied forward curve fr over a set of maturity dates cd, and a settlement date sd:

fr = [0.0469
      0.0519
      0.0549
      0.0535
      0.0558
      0.0508
      0.0560
      0.0545
      0.0615
      0.0486];
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 daily compounding for the zero curve, on an actual/365 basis. The forward curve was compounded annually on an actual/actual basis.

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

Execute the function

[zr, cd] = fwd2zero(fr, cd, sd, ocomp, obasis, icomp, ibasis)

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

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