Financial Toolbox

zero2fwd

Forward curve given a zero curve

Syntax

• [ForwardRates, CurveDates] = zero2fwd(ZeroRates, CurveDates, 
  Settle, OutputCompounding, OutputBasis, 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.
OutputCompounding	(Optional) Output compounding. A scalar that sets the compounding frequency per year for annualizing the output forward 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 forward rates. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.
InputCompounding	(Optional) A scalar that indicates the compounding frequency per year used for annualizing the input zero rates. Allowed values are the same as for OutputCompounding. Default = OutputCompounding.
InputBasis	(Optional) Input day-count basis used for annualizing the input zero rates. Allowed values are the same as for OutputBasis. Default = OutputBasis.

Description

[ForwardRates, CurveDates] = zero2fwd(ZeroRates, CurveDates, Settle, OutputCompounding, OutputBasis, InputCompounding, InputBasis) returns an implied forward rate curve given a zero curve and its maturity dates.

ForwardRates	A NUMBONDS-by-1 vector of decimal fractions. In aggregate, the rates in ForwardRates constitute a forward curve over the dates in CurveDates.
CurveDates	A NUMBONDS-by-1 vector of maturity dates (as serial date numbers) that correspond to the forward rates in. 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 = [0.0458
               0.0502
               0.0518
               0.0519
               0.0524
               0.0519
               0.0523
               0.0525
               0.0541
               0.0529];
  
  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 annual compounding for the forward curve, on an actual/actual basis. The zero curve was compounded daily on an actual/365 basis.

• OutputCompounding = 1;
  OutputBasis = 0;
  InputCompounding = 365;
  InputBasis = 3;
  

Execute the function

• [ForwardRates, CurveDates] = zero2fwd(ZeroRates, CurveDates,... 
  Settle, OutputCompounding, OutputBasis, InputCompounding,... 
  InputBasis)
  

which returns the forward rate curve ForwardRates at the maturity dates CurveDates.

• ForwardRates =
  
        0.0469
        0.0519
        0.0550
        0.0536
        0.0556
        0.0511
        0.0559
        0.0546
        0.0612
        0.0487
  
  CurveDates =
  
        730796
        730831
        730866
        730887
        730914
        730943
        730971
        731027
        731098
        731167
  

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

See Also

fwd2zero and other functions for Term Structure of Interest Rates

zero2disc

zero2pyld