Price bonds in portfolio by set of zero curves
computes the bond prices in a portfolio using a set of zero curves. BondPrices
= prbyzero(Bonds
,Settle
,ZeroRates
,ZeroDates
)
adds an optional argument for BondPrices
= prbyzero(___,Compounding
)Compounding
.
This example uses the function 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 the function 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 the function zbtprice
which returns the zero curve at the maturity dates.
[ZeroRates, ZeroDates] = zbtprice(Bonds, Prices, Settle,...
OutputCompounding)
ZeroRates = 11×1
0.0616
0.0609
0.0658
0.0590
0.0647
0.0655
0.0606
0.0601
0.0642
0.0621
⋮
ZeroDates = 11×1
729907
730364
730439
730500
730667
730668
730971
731032
731033
731321
⋮
Execute the function prbyzero
.
BondPrices = prbyzero(Bonds, Settle, ZeroRates, ZeroDates)
BondPrices = 12×1
99.3750
98.7980
106.8270
96.8750
103.6249
101.1250
103.1250
99.3637
101.0000
101.2500
⋮
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.
This example uses the function 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 the function prbyzero
with datetime
inputs 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'); OutputCompounding = 2; [ZeroRates, ZeroDates] = zbtprice(Bonds, Prices, Settle, OutputCompounding); dates = datetime(Bonds(:,1),'ConvertFrom','datenum','Locale','en_US'); data = Bonds(:,2:end); t=[table(dates) array2table(data)]; BondPrices = prbyzero(t, datetime(Settle,'ConvertFrom','datenum','Locale','en_US'),... ZeroRates, datetime(ZeroDates,'ConvertFrom','datenum','Locale','en_US'))
BondPrices = 12×1
99.3750
98.7980
106.8270
96.8750
103.6249
101.1250
103.1250
99.3637
101.0000
101.2500
⋮
Bonds
— Coupon bond information to compute pricesCoupon bond information to compute prices, specified as a 6-column
table or a NumBonds
-by-6
matrix of
bond information where the table columns or matrix columns contains:
Maturity
(Required) Maturity date of
the bond, as a serial date number. Use datenum
to
convert date character vectors to serial date numbers. If
the input Bonds
is a table, the
Maturity
dates can be serial date
numbers, date character vectors, or datetime arrays.
CouponRate
(Required) 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
bond. A vector of integers.
0 = actual/actual (default)
1 = 30/360 (SIA)
2 = actual/360
3 = actual/365
4 = 30/360 (BMA)
5 = 30/360 (ISDA)
6 = 30/360 (European)
7 = actual/365 (Japanese)
8 = actual/actual (ICMA)
9 = actual/360 (ICMA)
10 = actual/365 (ICMA)
11 = 30/360E (ICMA)
12 = actual/365 (ISDA)
13 = BUS/252
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
:
Note
If Bonds
is a table, the table
columns have the same meaning as when a matrix is used,
but the Maturity
dates can be serial
date numbers, date character vectors, or datetime
arrays.
If Bonds
is a matrix, it is a
NUMBONDS
-by-6
matrix of bonds where each row describes one bond. The
first two columns are required; the remaining columns
are optional but must be added in order. All rows in
Bonds
must have the same number
of columns. The columns are Maturity
,
CouponRate
,
Face
, Period
,
Basis
, and
EndMonthRule
.
.
Data Types: double
| table
Settle
— Settlement dateSettlement date, specified as serial date numbers, date character vectors, or datetime arrays.
Data Types: double
| datetime
| char
ZeroRates
— Observed zero ratesObserved zero rates, specified as
NUMDATES
-by-NUMCURVES
matrix
of decimal fractions. Each column represents a rate curve. Each row
represents an observation date.
Data Types: double
| datetime
| char
ZeroDates
— Observed dates for ZeroRates
Observed dates for ZeroRates
, specified as a
NUMDATES
-by-1
column using
serial date numbers, date character vectors, or datetime arrays.
Data Types: double
| datetime
| char
Compounding
— Compounding frequency of input ZeroRates
when annualized2
(default) | numeric values: 1
, 2
,
3
, 4
, 6
,
12
,(Optional) Compounding frequency of input ZeroRates
when annualized, specified using the allowed values:
1
— Annual compounding
2
— Semiannual compounding
(default)
3
— Compounding three times per
year
4
— Quarterly compounding
6
— Bimonthly compounding
12
— Monthly compounding
Data Types: double
BondPrices
— Clean bond pricesClean bond prices, returned as a
NUMBONDS
-by-NUMCURVES
matrix.
Each column is derived from the corresponding zero curve in
ZeroRates
.
In addition, you can use the Financial Instruments Toolbox™ method getZeroRates
(Financial Instruments Toolbox) 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 (Financial Instruments Toolbox).
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