prbyzero - Price bonds in portfolio by set of zero curves

Syntax

BondPrices = prbyzero(Bonds, Settle, ZeroRates, ZeroDates)

Arguments

`Bonds`	Coupon bond information used to compute prices. A number of bonds (`NUMBONDS`)-by-`6` matrix where each row describes a bond. The first two columns are required; the rest are optional but must be added in order. All rows in `Bonds` must have the same number of columns. Columns are [`Maturity CouponRate Face Period Basis EndMonthRule`] where:
	`Maturity`	Maturity date as a serial date number or date string.
	`CouponRate`	Decimal number indicating the annual percentage rate used to determine the coupons payable on a bond.
	`Face`	(Optional) Face or par value of the bond. Default = 100.
	`Period`	(Optional) Coupons per year of the bond. Allowed values are 0, 1, 2 (default), 3, 4, 6, and 12.
	`Basis`	(Optional) Day-count basis of the instrument. A vector of integers. 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
	`EndMonthRule`	(Optional) End-of-month rule. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days. 0 = ignore rule, meaning that a bond's coupon payment date is always the same numerical day of the month. 1 = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month.
`Settle`	Serial date number of the settlement date.
`ZeroRates`	`NUMDATES`-by-`NUMCURVES` matrix of observed zero rates, as decimal fractions. Each column represents a rate curve. Each row represents an observation date.
`ZeroDates`	`NUMDATES`-by-`1` column of dates for observed zeros

Description

BondPrices = prbyzero(Bonds, Settle, ZeroRates, ZeroDates) computes the bond prices in a portfolio using a set of zero curves.

BondPrices is a NUMBONDS-by-NUMCURVES matrix of clean bond prices. Each column is derived from the corresponding zero curve in ZeroRates.

In addition, you can use the Fixed-Income Toolbox™ method getZeroRates for an IRDataCurve object with a Dates property to create a vector of dates and data acceptable for prbyzero. For more information, see Converting an IRDataCurve or IRFunctionCurve Object.

Examples

This example uses zbtprice to compute a zero curve given a portfolio of coupon bonds and their prices. It then reverses the process, using the zero curve as input to prbyzero to compute the prices.

Bonds = [datenum('6/1/1998') 0.0475 100 2 0 0; 
         datenum('7/1/2000') 0.06 100 2 0 0; 
         datenum('7/1/2000') 0.09375 100 6 1 0; 
         datenum('6/30/2001') 0.05125 100 1 3 1;
         datenum('4/15/2002') 0.07125 100 4 1 0;
         datenum('1/15/2000') 0.065 100 2 0 0; 
         datenum('9/1/1999') 0.08 100 3 3 0; 
         datenum('4/30/2001') 0.05875 100 2 0 0; 
         datenum('11/15/1999') 0.07125 100 2 0 0; 
         datenum('6/30/2000') 0.07 100 2 3 1; 
         datenum('7/1/2001') 0.0525 100 2 3 0; 
         datenum('4/30/2002') 0.07 100 2 0 0];

Prices = [ 99.375;
           99.875;
          105.75 ;
           96.875;
          103.625;
          101.125;
          103.125;
           99.375;
          101.0  ;
          101.25 ;
           96.375;
          102.75 ];

Settle = datenum('12/18/1997');

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

OutputCompounding = 2;

Execute zbtprice

[ZeroRates, ZeroDates] = zbtprice(Bonds, Prices, Settle,...
OutputCompounding)

which returns the zero curve at the maturity dates.

ZeroRates =

            0.0616
            0.0609
            0.0658
            0.0590
            0.0648
            0.0655
            0.0606
            0.0601
            0.0642
            0.0621
            0.0627

ZeroDates =

             729907
             730364
             730439
             730500
             730667
             730668
             730971
             731032
             731033
             731321
             731336

Now execute prbyzero

BondPrices = prbyzero(Bonds, Settle, ZeroRates, ZeroDates)

which returns

BondPrices =

             99.38
             98.80
            106.83
             96.88
            103.62
            101.13
            103.12
             99.36
            101.00
            101.25
             96.37
            102.74

In this example zbtprice and prbyzero do not exactly reverse each other. Many of the bonds have the end-of-month rule off (EndMonthRule = 0). The rule subtly affects the time factor computation. If you set the rule on (EndMonthRule = 1) everywhere in the Bonds matrix, then prbyzero returns the original prices, except when the two incompatible prices fall on the same maturity date.

prbyzero - Price bonds in portfolio by set of zero curves

Syntax

Arguments

Description

Examples

See Also