Financial Toolbox™

disc2zero

Zero curve given discount curve

Syntax

[ZeroRates, CurveDates] = disc2zero(DiscRates, CurveDates, Settle, 
Compounding, Basis)

Arguments

`DiscRates`	Column vector of discount factors, as decimal fractions. In aggregate, the factors in `DiscRates` constitute a discount curve for the investment horizon represented by `CurveDates`.
`CurveDates`	Column vector of maturity dates (as serial date numbers) that correspond to the discount factors in `DiscRates`.
`Settle`	Serial date number that is the common settlement date for the discount rates in `DiscRates`.
`Compounding`	(Optional) Output compounding. A scalar that sets the compounding frequency per year for annualizing the output zero rates. 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 for annualizing the output 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

[ZeroRates, CurveDates] = disc2zero(DiscRates, CurveDates, Settle, Compounding, Basis) returns a zero curve given a discount curve and its maturity dates.

`ZeroRates`	Column vector of decimal fractions. In aggregate, the rates in `ZeroRates` constitute a zero curve for the investment horizon represented by `CurveDates`. The zero rates are the yields to maturity on theoretical zero-coupon bonds.
`CurveDates`	Column vector of maturity dates (as serial date numbers) that correspond to the zero rates. This vector is the same as the input vector `CurveDates`.

Examples

Given discount factors DiscRates over a set of maturity dates CurveDates, and a settlement date Settle

DiscRates = [0.9996
             0.9947
             0.9896
             0.9866
             0.9826
             0.9786
             0.9745
             0.9665
             0.9552
             0.9466];

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');

Set daily compounding for the output zero curve, on an actual/365 basis.

Compounding = 365;
Basis = 3;

Execute the function

[ZeroRates, CurveDates] = disc2zero(DiscRates, CurveDates,... 
Settle, Compounding, Basis)

which returns the zero curve ZeroRates at the maturity dates CurveDates.

ZeroRates =
    0.0487
    0.0510
    0.0523
    0.0524
    0.0530
    0.0526
    0.0530
    0.0532
    0.0549
    0.0536

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

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

disc2zero

Syntax

Arguments

Description

Examples

See Also