bndkrdur
Bond key rate duration given zero curve
Syntax
Description
computes the key rate durations for one or more bonds given a zero curve and a
set of key rates.KeyRateDuration
= bndkrdur(ZeroData
,CouponRate
,Settle
,Maturity
)
adds optional name-value pair arguments. KeyRateDuration
= bndkrdur(___,Name,Value
)
Examples
Find the Bond Key Rate Duration Given the Zero Curve
This example shows how to compute the key rate duration of a bond for key rate times of 2, 5, 10, and 30 years.
ZeroRates = [0.0476 .0466 .0465 .0468 .0473 .0478 ... .0493 .0539 .0572 .0553 .0530]'; ZeroDates = daysadd('31-Dec-1998',[30 360 360*2 360*3 360*5 ... 360*7 360*10 360*15 360*20 360*25 360*30],1); ZeroData = [ZeroDates ZeroRates]; krdur = bndkrdur(ZeroData,.0525,'12/31/1998',... '11/15/2028','KeyRates',[2 5 10 30])
krdur = 1×4
0.2986 0.8791 4.1353 9.5814
Find the Bond Key Rate Duration Given the Zero Curve Using datetime Inputs
This example shows how to use datetime
inputs for Settle
and Maturity
and also use a table for ZeroData
to compute the key rate duration of a bond for key rate times of 2, 5, 10, and 30 years.
ZeroRates = [0.0476 .0466 .0465 .0468 .0473 .0478 ... .0493 .0539 .0572 .0553 .0530]'; ZeroDates = daysadd('31-Dec-1998',[30 360 360*2 360*3 360*5 ... 360*7 360*10 360*15 360*20 360*25 360*30],1); ZeroData = table(datetime(ZeroDates,'ConvertFrom','datenum','Locale','en_US'), ZeroRates); krdur = bndkrdur(ZeroData,.0525,datetime('12/31/1998','Locale','en_US'),... datetime('11/15/2028','Locale','en_US'),'KeyRates',[2 5 10 30])
krdur = 1×4
0.2986 0.8791 4.1353 9.5814
Input Arguments
ZeroData
— Zero curve
matrix | table
Zero Curve, specified as a
numRates
-by-2
matrix or a
numRates
-by-2
table.
If ZeroData
is represented as a
numRates
-by-2
matrix, the
first column is a MATLAB® serial date number and the second column is the
accompanying zero rates.
If ZeroData
is a table, the first column can be a
datetime array, string array, or date character vectors. The second column
must be numeric data corresponding to the zero rates.
Data Types: double
| datetime
| char
| string
| table
CouponRate
— Annual percentage rate used to determine coupons payable on a bond
decimal
Annual percentage rate used to determine the coupons payable on a
bond, specified as decimal value using a scalar or a
NUMBONDS
-by-1
vector.
Data Types: double
Settle
— Settlement date for all bonds and zero curve
datetime scalar | string scalar | date character vector
Settlement date for all bonds and zero curve, specified as a scalar
datetime, string, or date character vector. Settle
must
be the same settlement date for all the bonds and the zero curve.
To support existing code, bndkrdur
also
accepts serial date numbers as inputs, but they are not recommended.
Data Types: char
| string
| datetime
Maturity
— Maturity date for bonds
datetime array | string array | date character vector
Maturity date for bonds, specified as a scalar or a
NUMBONDS
-by-1
vector using a
datetime array, string array, or date character vectors.
To support existing code, bndkrdur
also
accepts serial date numbers as inputs, but they are not recommended.
Data Types: char
| string
| datetime
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: KeyRateDuration =
bndkrdur(ZeroData,.0525,'12/31/1998','11/15/2028','KeyRates',[2 5 10
30])
InterpMethod
— Interpolation method used to obtain points from zero curve
'linear'
(default) |
'cubic'
, 'pchip'
Interpolation method used to obtain points from the zero curve,
specified as the comma-separated pair consisting of
'InterpMethod'
and a character vector using one
of the following values:
'linear'
(default)'cubic'
'pchip'
Data Types: char
ShiftValue
— Value that zero curve is shifted up and down to compute duration
.01
(100 basis points) (default) | numeric
Value that zero curve is shifted up and down to compute duration,
specified as the comma-separated pair consisting of
'ShiftValue'
and a scalar numeric value.
Data Types: double
KeyRates
— Rates to perform the duration calculation
set to each of the zero dates (default) | numeric
Rates to perform the duration calculation, specified as the
comma-separated pair consisting of 'KeyRates'
and a
time to maturity using a scalar or a
NUMBONDS
-by-1
vector.
Data Types: double
CurveCompounding
— Compounding frequency of curve
2 (default) | integer with value of 1
, 2
,
3
, 4
,
6
, or 12
Compounding frequency of the curve, specified as the
comma-separated pair consisting of 'CurveCompounding'
and a scalar using one of the following values:
1
— Annual compounding2
— Semiannual compounding3
— Compounding three times per year4
— Quarterly compounding6
— Bimonthly compounding12
— Monthly compounding
.
Data Types: double
CurveBasis
— Basis of the curve
0
(default) | numeric values: 0
,1
,
2
, 3
,
4
, 6
, 7
,
8
, 9
,
10
, 11
,
12
, 13
Basis of the curve, specified as the comma-separated pair
consisting of 'CurveBasis'
and a scalar using one of
the following values:
0 = actual/actual
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 (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.
Data Types: double
Period
— Number of coupon payments per year
2
(default) | numeric with values 0
, 1
,
2
, 3
,
4
, 6
or
12
Number of coupon payments per year, specified as the
comma-separated pair consisting of 'Period'
and a
scalar or a NUMBONDS
-by-1
vector
using the values: 0
, 1
,
2
, 3
, 4
,
6
, or 12
.
Data Types: double
Basis
— Day-count basis of instrument
0
(default) | numeric values: 0
,1
,
2
, 3
,
4
, 6
, 7
,
8
, 9
,
10
, 11
,
12
, 13
Day-count of the instrument, specified as the comma-separated pair
consisting of 'Basis'
and a scalar or a
NUMBONDS
-by-1
vector using a
supported value:
0 = actual/actual
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 (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.
Data Types: double
EndMonthRule
— End-of-month rule flag
1
(in effect) (default) | nonnegative integer 0
or
1
End-of-month rule flag, specified as the comma-separated pair
consisting of 'EndMonthRule'
and a scalar or a
NUMBONDS
-by-1
vector. 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 coupon payment date is always the same numerical day of the month.1
= Set rule on, meaning that a bond coupon payment date is always the last actual day of the month.
Data Types: logical
IssueDate
— Bond issue date
datetime array | string array | date character vector
Bond Issue date, specified as the comma-separated pair consisting
of 'IssueDate'
and a scalar or a
NUMBONDS
-by-1
vector using a
datetime array, string array, or date character vectors.
If you do not specify an IssueDate
, the cash
flow payment dates are determined from other inputs.
To support existing code, bndkrdur
also
accepts serial date numbers as inputs, but they are not recommended.
Data Types: char
| string
| datetime
FirstCouponDate
— Irregular or normal first coupon date
datetime array | string array | date character vector
Irregular or normal first coupon date, specified as the
comma-separated pair consisting of 'FirstCouponDate'
and a scalar or a NUMBONDS
-by-1
vector using a datetime array, string array, or date character vectors.
If you do not specify a FirstCouponDate
, the
cash flow payment dates are determined from other inputs.
To support existing code, bndkrdur
also
accepts serial date numbers as inputs, but they are not recommended.
Data Types: char
| string
| datetime
LastCouponDate
— Irregular or normal last coupon date
datetime array | string array | date character vector
Irregular or normal last coupon date, specified as the
comma-separated pair consisting of 'LastCouponDate'
and a scalar or a NUMBONDS
-by-1
vector using a datetime array, string array, or date character vectors.
If you do not specify a LastCouponDate
, the
cash flow payment dates are determined from other inputs.
To support existing code, bndkrdur
also
accepts serial date numbers as inputs, but they are not recommended.
Data Types: char
| string
| datetime
StartDate
— Forward starting date of payments
datetime array | string array | date character vector
Forward starting date of payments, specified as the
comma-separated pair consisting of 'StartDate'
and a
scalar or a NUMBONDS
-by-1
vector
using a datetime array, string array, or date character vectors. The
StartDate
is when a bond actually starts (the
date from which a bond cash flow is considered). To make an instrument
forward-starting, specify this date as a future date.
If you do not specify a StartDate
, the
effective start date is the Settle
date.
To support existing code, bndkrdur
also
accepts serial date numbers as inputs, but they are not recommended.
Data Types: char
| string
| datetime
Face
— Face value of bond
100
(default) | numeric
Face value of the bond, specified as the comma-separated pair
consisting of 'Face'
and a scalar or a
NUMBONDS
-by-1
vector.
Data Types: double
Output Arguments
KeyRateDuration
— Key rate durations
matrix
Key rate durations, returned as a
numBonds
-by-numRates
matrix.
Algorithms
bndkrdur
computes the key rate durations for one or more bonds
given a zero curve and a set of key rates. By default, the key rates are each of the
zero curve rates. For each key rate, the duration is computed by shifting the zero
curve up and down by a specified amount (ShiftValue
) at that
particular key rate, computing the present value of the bond in each case with the
new zero curves, and then evaluating the following:
Note
The shift to the curve is computed by shifting the particular key rate by the
ShiftValue
and then interpolating the values of the
curve in the interval between the previous and next key rates. For the first key
rate, any curve values before the date are equal to the
ShiftValue
; likewise, for the last key rate, any curve
values after the date are equal to the ShiftValue
.
References
[1] Golub, B., Tilman, L. Risk Management: Approaches for Fixed Income Markets. Wiley, 2000.
[2] Tuckman, B. Fixed Income Securities: Tools for Today's Markets. Wiley, 2002.
Version History
Introduced before R2006aR2022b: Serial date numbers not recommended
Although bndkrdur
supports serial date numbers,
datetime
values are recommended instead. The
datetime
data type provides flexible date and time
formats, storage out to nanosecond precision, and properties to account for time
zones and daylight saving time.
To convert serial date numbers or text to datetime
values, use the datetime
function. For example:
t = datetime(738427.656845093,"ConvertFrom","datenum"); y = year(t)
y = 2021
There are no plans to remove support for serial date number inputs.
See Also
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