Financial Toolbox

disc2zero

Zero curve given a discount curve

Syntax

• [ZeroRates, CurveDates] = disc2zero(DiscRates, CurveDates, Settle, 
  OutputCompounding, OutputBasis)
  

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.
OutputCompounding	(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	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
OutputBasis	(Optional) Output day-count basis for annualizing the output zero rates. Allowed values are:
	0	actual/actual (default)
	1	30/360
	2	actual/360
	3	actual/365

Description

[ZeroRates, CurveDates] = disc2zero(DiscRates, CurveDates, Settle, OutputCompounding, OutputBasis) 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.

• OutputCompounding = 365;
  OutputBasis = 3;
  

Execute the function

• [ZeroRates, CurveDates] = disc2zero(DiscRates, CurveDates,... 
  Settle, OutputCompounding, OutputBasis)
  

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

See Also

zero2disc and other functions for Term Structure of Interest Rates

depstln

discrate