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# 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/3603 = actual/3654 = 30/360 (BMA)5 = 30/360 (ISDA)6 = 30/360 (European)7 = actual/365 (Japanese)8 = actual/actual (ICMA)9 = actual/360 (ICMA)10 = actual/365 (ICMA)11 = 30/360E (ICMA) 12 = actual/actual (ISDA)13 = BUS/252For more information, see basis.

## 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

expand all

### Compute a Discount Curve Given a Zero Curve and Maturity Dates

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 is compounded daily on an actual/365 basis.`
```Compounding = 365;
Basis = 3;
```

Execute the function zero2disc which returns the discount curve DiscRates at the maturity dates CurveDates.

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