Financial Toolbox

prbyzero

Price bonds in a portfolio by a 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, 3, 4, 6, and 12. Default = 2.
	Basis	(Optional) Day-count basis of the bond. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.
	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.

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 semi-annual compounding for the zero curve, on an actual/365 basis. Derive the zero curve within 50 iterations.

• OutputCompounding = 2;
  OutputBasis = 3;
  MaxIterations = 50;
  

Execute zbtprice

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

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.

See Also

tr2bonds, zbtprice

portvrisk

prdisc