zero2disc (Financial Toolbox)

zero2disc
Discount curve given a zero curve

Syntax

[DiscRates, CurveDates] = zero2disc(ZeroRates, CurveDates, Settle, 
InputCompounding, InputBasis)

Arguments

ZeroRates
A number of bonds (NUMBONDS) by 1 vector of annualized zero rates, as decimal fractions. In aggregate, the rates constitute an implied zero curve for the investment horizon represented by CurveDates.

CurveDates
A NUMBONDS-by-1 vector of maturity dates (as serial date numbers) that correspond to the zero rates.

Settle
A serial date number that is the common settlement date for the zero rates; i.e., the settlement date for the bonds from which the zero curve was bootstrapped.

InputCompounding
(Optional) A scalar that indicates the compounding frequency per year used for annualizing the input zero rates in ZeroRates. 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

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

`ZeroRates`	A number of bonds (`NUMBONDS`) by 1 vector of annualized zero rates, as decimal fractions. In aggregate, the rates constitute an implied zero curve for the investment horizon represented by `CurveDates`.
`CurveDates`	A `NUMBONDS`-by-1 vector of maturity dates (as serial date numbers) that correspond to the zero rates.
`Settle`	A serial date number that is the common settlement date for the zero rates; i.e., the settlement date for the bonds from which the zero curve was bootstrapped.
`InputCompounding`	(Optional) A scalar that indicates the compounding frequency per year used for annualizing the input zero rates in `ZeroRates`. 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
`InputBasis`	(Optional) Input day-count basis used for annualizing the input zero rates. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.

Description
[DiscRates, CurveDates] = zero2disc(ZeroRates, CurveDates, Settle, InputCompounding, InputBasis) returns a discount curve given a zero curve and its maturity dates.


`DiscRates`	A `NUMBONDS`-by-1 vector of discount factors, as decimal fractions. In aggregate, the factors in constitute a discount curve for the investment horizon represented by `CurveDates`.
`CurveDates`	A `NUMBONDS`-by-1 vector of maturity dates (as serial date numbers) that correspond to the discount rates. This vector is the same as the input vector `CurveDates`.

Examples
Given a zero curve over a set of maturity dates and a settlement date

ZeroRates = [0.0464
             0.0509
             0.0524
             0.0525
             0.0531
             0.0525
             0.0530
             0.0531
             0.0549
             0.0536];

CurveDates = [datenum('06-Nov-2000')
              datenum('11-Dec-2000')
              datenum('15-Jan-2001')
              datenum('05-Feb-2001')
              datenum('04-Mar-2001')
              datenum('02-Apr-2001')
              datenum('30-Apr-2001')
              datenum('25-Jun-2001')
              datenum('04-Sep-2001')
              datenum('12-Nov-2001')];

Settle = datenum('03-Nov-2000');

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

InputCompounding = 365;
InputBasis = 3;

Execute the function

[DiscRates, CurveDates] = zero2disc(ZeroRates, CurveDates,... 
Settle, InputCompounding, InputBasis)

which returns the discount curve DiscRates at the maturity dates CurveDates.

DiscRates =
      0.9996
      0.9947
      0.9896
      0.9866
      0.9826
      0.9787
      0.9745
      0.9665
      0.9552
      0.9466

CurveDates =
      730796
      730831
      730866
      730887
      730914
      730943
      730971
      731027
      731098
      731167

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

See Also
disc2zero and other functions for Term Structure of Interest Rates

zbtyield zero2fwd