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| R2012a Documentation → Financial Toolbox | |
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BondPrices = prbyzero(Bonds, Settle, ZeroRates, ZeroDates, Compounding)
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.
For more information, see basis. | |
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 | |
Compounding | Scalar value representing the rate at which the input zero rates were compounded when annualized. This argument determines the formula for the discount factors. Compounding values are: 1, 2, 3, 4, 6, 12. | |
BondPrices = prbyzero(Bonds, Settle, ZeroRates, ZeroDates, Compounding) 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.
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.
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