fwd2zero - Zero curve given forward curve

Syntax

[ZeroRates, CurveDates] = fwd2zero(ForwardRates, CurveDates, 
Settle, Compounding, Basis)

Arguments

`ForwardRates`	A number of bonds (`NUMBONDS`)-by-`1` vector of annualized implied forward rates, as decimal fractions. In aggregate, the rates in `ForwardRates` constitute an implied forward curve for the investment horizon represented by `CurveDates`. The first element pertains to forward rates from the settlement date to the first curve date.
`CurveDates`	A `NUMBONDS`-by-`1` vector of maturity dates (as serial date numbers) that correspond to the forward rates.
`Settle`	A serial date number that is the common settlement date for the forward rates.
`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) Output 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) 13 = BUS/252

Description

[ZeroRates, CurveDates] = fwd2zero(ForwardRates, CurveDates, Settle, Compounding, Basis) returns a zero curve given an implied forward rate curve and its maturity dates.

`ZeroRates`	A `NUMBONDS`-by-`1` vector of decimal fractions. In aggregate, the rates in `ZeroRates` constitute a 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 in `ZeroRates`. This vector is the same as the input vector `CurveDates`.

Examples

Given an implied forward rate curve over a set of maturity dates, a settlement date, and a compounding rate, compute the zero curve.

ForwardRates = [0.0469
                0.0519
                0.0549
                0.0535
                0.0558
                0.0508
                0.0560
                0.0545
                0.0615
                0.0486];

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');
Compounding = 1;

Execute the function

[ZeroRates, CurveDates] = fwd2zero(ForwardRates, CurveDates,... 
Settle, Compounding)

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

ZeroRates =

    0.0469
    0.0515
    0.0531
    0.0532
    0.0538
    0.0532
    0.0536
    0.0539
    0.0556
    0.0543

CurveDates =

      730796
      730831
      730866
      730887
      730914
      730943
      730971
      731027
      731098
      731167

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

fwd2zero - Zero curve given forward curve

Syntax

Arguments

Description

Examples

See Also