Financial Toolbox™

zero2disc - Discount curve given zero curve

Syntax

[DiscRates, CurveDates] = zero2disc(ZeroRates, CurveDates, Settle, 
Compounding, Basis)

Arguments

`ZeroRates`	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`	`NUMBONDS`-by-1 vector of maturity dates (as serial date numbers) that correspond to the zero rates.
`Settle`	Serial date number that is the common settlement date for the zero rates; that is, the settlement date for the bonds from which the zero curve was bootstrapped.
`Compounding`	(Optional) Scalar that indicates the compounding frequency per year used for annualizing the input zero rates in `ZeroRates`. Allowed values are:
	`1`	Annual compounding
	`2`	Semiannual compounding (default)
	`3`	Compounding three times per year
	`4`	Quarterly compounding
	`6`	Bimonthly compounding
	`12`	Monthly compounding
	`365`	Daily compounding
	`-1`	Continuous compounding
`Basis`	(Optional) Day-count basis used for annualizing the input zero rates. 0 = actual/actual (default) 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (PSA) 5 = 30/360 (ISDA) 6 = 30/360 (European) 7 = actual/365 (Japanese) 8 = actual/actual (ISMA) 9 = actual/360 (ISMA) 10 = actual/365 (ISMA) 11 = 30/360E (ISMA) 12 = actual/365 (ISDA)

Description

[DiscRates, CurveDates] = zero2disc(ZeroRates, CurveDates, Settle, Compounding, Basis) 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, Compounding, Basis)

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^® software computed them at full precision. If you enter ZeroRates as shown, DiscRates may differ due to rounding.

zero2disc - Discount curve given zero curve

Syntax

Arguments

Description

Examples

See Also