zero2disc (Financial Toolbox)

Discount curve given a zero curve.

Syntax

[dr, cd] = zero2disc(zr, cd, sd, icomp, ibasis)
[dr, cd] = zero2disc(zr, cd, sd, icomp)
[dr, cd] = zero2disc(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; i.e., the settlement date for the bonds from which the zero curve was bootstrapped.

icomp: Input compounding. A scalar that indicates the compounding frequency per year used for annualizing the input 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

ibasis: Input day-count basis used for annualizing the input zero rates in zr.
0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.

Description

[dr, cd] = zero2disc(zr, cd, sd, icomp, ibasis)

returns a discount curve given a zero curve and its maturity dates.

dr: Discount factors. An N-by-1 vector of discount factors, as decimal fractions. In aggregate, the factors in dr constitute a discount 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 discount rates in dr. 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 = [0.0464
      0.0509
      0.0524
      0.0525
      0.0531
      0.0525
      0.0530
      0.0531
      0.0549
      0.0536];
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');

The zero curve was compounded daily on an actual/365 basis.

icomp = 365;
ibasis = 3;

Execute the function:

[dr, cd] = zero2disc(zr, cd, sd, icomp, ibasis)

which returns the discount curve dr at the maturity dates cd:

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