disc2zero (Financial Toolbox)

Zero curve given a discount curve.

Syntax

[zr, cd] = disc2zero(dr, cd, sd, ocomp, obasis)
[zr, cd] = disc2zero(dr, cd, sd, ocomp)
[zr, cd] = disc2zero(dr, cd, sd)

Arguments

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 factors in dr. 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 discount rates in dr.

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.

Description

[zr, cd] = disc2zero(dr, cd, sd, ocomp, obasis)

returns a zero curve given a discount 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. The zero rates are the yields to maturity on theoretical zero-coupon bonds.

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 discount factors dr over a set of maturity dates cd, and a settlement date sd:

dr = [0.9996
      0.9947
      0.9896
      0.9866
      0.9826
      0.9786
      0.9745
      0.9665
      0.9552
      0.9466];
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 output zero curve, on an actual/365 basis.

ocomp = 365;
obasis = 3;

Execute the function

[zr, cd] = disc2zero(dr, cd, sd, ocomp, obasis)

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

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