bondbycir
Price bond from Cox-Ingersoll-Ross interest-rate tree
Syntax
Description
[
adds additional name-value pair arguments.Price
,PriceTree
]
= bondbycir(___,Name,Value
)
Examples
Price a Bond Using a CIR Interest-Rate Tree
Define the CouponRate
for a bond.
CouponRate = 0.035;
Create a RateSpec
using the intenvset
function.
Rates = [0.035; 0.042147; 0.047345; 0.052707]; Dates = [datetime(2017,1,1) ; datetime(2018,1,1) ; datetime(2019,1,1) ; datetime(2020,1,1) ; datetime(2021,1,1)]; ValuationDate = datetime(2017,1,1); EndDates = Dates(2:end)'; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate, 'StartDates', ValuationDate, 'EndDates',EndDates,'Rates', Rates, 'Compounding', Compounding);
Create a CIR
tree.
NumPeriods = length(EndDates); Alpha = 0.03; Theta = 0.02; Sigma = 0.1; Settle = datetime(2017,1,1); Maturity = datetime(2021,1,1); CIRTimeSpec = cirtimespec(ValuationDate, Maturity, NumPeriods); CIRVolSpec = cirvolspec(Sigma, Alpha, Theta); CIRT = cirtree(CIRVolSpec, RateSpec, CIRTimeSpec)
CIRT = struct with fields:
FinObj: 'CIRFwdTree'
VolSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2 3]
dObs: [736696 737061 737426 737791]
FwdTree: {[1.0350] [1.0790 1.0500 1.0298] [1.1275 1.0887 1.0594 1.0390 1.0270] [1.1905 1.1406 1.1014 1.0718 1.0512 1.0390 1.0350]}
Connect: {[3x1 double] [3x3 double] [3x5 double]}
Probs: {[3x1 double] [3x3 double] [3x5 double]}
Price the bond.
[Price,PriceTree] = bondbycir(CIRT,CouponRate,Settle,Maturity)
Price = 94.0880
PriceTree = struct with fields:
FinObj: 'CIRPriceTree'
tObs: [0 1 2 3 4]
dObs: [736696 737061 737426 737791 738157]
PTree: {[94.0880] [86.8351 93.6116 98.7823] [83.9957 89.8068 94.6078 98.1958 100.4146] [87.0721 90.8422 94.0486 96.6208 98.5012 99.6471 100.0320] [100 100 100 100 100 100 100]}
AITree: {[0] [0 0 0] [0 0 0 0 0] [0 0 0 0 0 0 0] [0 0 0 0 0 0 0]}
Connect: {[3x1 double] [3x3 double] [3x5 double]}
Input Arguments
CIRTree
— Interest-rate structure
structure
Interest-rate tree structure, created by cirtree
.
Data Types: struct
CouponRate
— Bond coupon rate
positive decimal value
Bond coupon rate, specified as an NINST
-by-1
decimal annual rate or NINST
-by-1
cell array,
where each element is a NumDates
-by-2
cell
array. The first column of the NumDates
-by-2
cell array is dates and the second column is associated rates. The date indicates the
last day that the coupon rate is valid.
Data Types: double
| cell
Settle
— Settlement date
datetime array | string array | date character vector
Settlement date, specified either as a scalar or
NINST
-by-1
vector using a datetime array, string
array, or date character vectors.
To support existing code, bondbycir
also
accepts serial date numbers as inputs, but they are not recommended.
The Settle
date for every bond is set to the
ValuationDate
of the CIR tree. The bond argument
Settle
is ignored.
Maturity
— Maturity date
datetime array | string array | date character vector
Maturity date, specified as a NINST
-by-1
vector using a datetime array, string array, or date character vectors representing the
maturity date for each bond.
To support existing code, bondbycir
also
accepts serial date numbers as inputs, but they are not recommended.
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: [Price,PriceTree] =
bondbycir(CIRTree,CouponRate,Settle,Maturity,'Period',4,'Face',10000)
Period
— Coupons per year
2
per year (default) | vector
Coupons per year, specified as the comma-separated pair consisting of
'Period'
and an NINST
-by-1
vector. Values for Period
are 1
,
2
, 3
, 4
,
6
, and 12
.
Data Types: double
Basis
— Day-count basis
0
(actual/actual) (default) | integer from 0
to 13
Day-count basis of the instrument, specified as the comma-separated pair
consisting of 'Basis'
and a
NINST
-by-1
vector.
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 for generating dates when Maturity
is end-of-month date for month having 30 or fewer days
1
(in effect) (default) | nonnegative integer [0,1]
End-of-month rule flag for generating dates when Maturity
is
an end-of-month date for a month having 30 or fewer days, specified as the
comma-separated pair consisting of 'EndMonthRule'
and a nonnegative
integer [0
, 1
] using a
NINST
-by-1
vector.
0
= Ignore rule, meaning that a payment date is always the same numerical day of the month.1
= Set rule on, meaning that a 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
NINST
-by-1
vector using a datetime array,
string array, or date character vectors.
To support existing code, bondbycir
also
accepts serial date numbers as inputs, but they are not recommended.
FirstCouponDate
— Irregular first coupon date
datetime array | string array | date character vector
Irregular first coupon date, specified as the comma-separated pair consisting of
'FirstCouponDate'
and a
NINST
-by-1
vector using a datetime array,
string array, or date character vectors.
To support existing code, bondbycir
also
accepts serial date numbers as inputs, but they are not recommended.
When FirstCouponDate
and LastCouponDate
are both specified, FirstCouponDate
takes precedence in
determining the coupon payment structure. If you do not specify a
FirstCouponDate
, the cash flow payment dates are determined
from other inputs.
LastCouponDate
— Irregular last coupon date
datetime array | string array | date character vector
Irregular last coupon date, specified as the comma-separated pair consisting of
'LastCouponDate'
and a
NINST
-by-1
vector using a datetime array,
string array, or date character vectors.
To support existing code, bondbycir
also
accepts serial date numbers as inputs, but they are not recommended.
In the absence of a specified FirstCouponDate
, a specified
LastCouponDate
determines the coupon structure of the bond. The
coupon structure of a bond is truncated at the LastCouponDate
,
regardless of where it falls, and is followed only by the bond's maturity cash flow
date. If you do not specify a LastCouponDate
, the cash flow
payment dates are determined from other inputs.
StartDate
— Forward starting date of payments
Settle
date (default) | datetime array | string array | date character vector
Forward starting date of payments (the date from which a bond cash flow is
considered), specified as the comma-separated pair consisting of
'StartDate'
and a
NINST
-by-1
vector using a datetime array,
string array, or date character vectors.
To support existing code, bondbycir
also
accepts serial date numbers as inputs, but they are not recommended.
If you do not specify StartDate
, the effective start date is
the Settle
date.
Face
— Face value
100
(default) | nonnegative value | cell array of nonnegative values
Face or par value, specified as the comma-separated pair consisting of
'Face'
and a NINST
-by-1
vector of nonnegative face values or a
NINST
-by-1
cell array of face values or face
value schedules. For the latter case, each element of the cell array is a
NumDates
-by-2
cell array, where the first
column is dates and the second column is its associated face value. The date indicates
the last day that the face value is valid.
Data Types: cell
| double
AdjustCashFlowsBasis
— Flag to adjust cash flows based on actual period day count
false
(default) | value of 0
(false) or 1
(true)
Flag to adjust cash flows based on actual period day count, specified as the
comma-separated pair consisting of 'AdjustCashFlowsBasis'
and a
NINST
-by-1
vector of logicals with values of
0
(false) or 1
(true).
Data Types: logical
BusinessDayConvention
— Business day conventions
actual
(default) | character vector | cell array of character vectors
Business day conventions, specified as the comma-separated pair consisting of
'BusinessDayConvention'
and a character vector or a
N
-by-1
(or
NINST
-by-2
if
BusinessDayConvention
is different for each leg) cell array of
character vectors of business day conventions. The selection for business day
convention determines how nonbusiness days are treated. Nonbusiness days are defined
as weekends plus any other date that businesses are not open (e.g. statutory
holidays). Values are:
actual
— Nonbusiness days are effectively ignored. Cash flows that fall on nonbusiness days are assumed to be distributed on the actual date.follow
— Cash flows that fall on a non-business day are assumed to be distributed on the following business day.modifiedfollow
— Cash flows that fall on a non-business day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.previous
— Cash flows that fall on a non-business day are assumed to be distributed on the previous business day.modifiedprevious
— Cash flows that fall on a non-business day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.
Data Types: char
| cell
Holidays
— Holidays used in computing business days
if not specified, the default is to use
holidays.m
(default) | MATLAB® dates
Holidays used in computing business days, specified as the comma-separated pair
consisting of 'Holidays'
and MATLAB dates using a NHolidays
-by-1
vector.
Data Types: datetime
Output Arguments
Price
— Expected bond prices at time 0
vector
Expected bond prices at time 0, returned as a
NINST
-by-1
vector.
PriceTree
— Tree structure of instrument prices
structure
Tree structure of instrument prices, returned as a MATLAB structure of trees containing vectors of instrument prices and accrued
interest, and a vector of observation times for each node. Within
PriceTree
:
PriceTree.tObs
contains the observation times.PriceTree.dObs
contains the observation dates.PriceTree.PTree
contains the clean prices.PriceTree.AITree
contains the accrued interest.
More About
Vanilla Bond
A vanilla coupon bond is a security representing an obligation to repay a borrowed amount at a designated time and to make periodic interest payments until that time.
The issuer of a bond makes the periodic interest payments until the bond matures. At maturity, the issuer pays to the holder of the bond the principal amount owed (face value) and the last interest payment.
Stepped Coupon Bond
A step-up and step-down bond is a debt security with a predetermined coupon structure over time.
With these instruments, coupons increase (step up) or decrease (step down) at specific times during the life of the bond.
Bond with an Amortization Schedule
An amortized bond is treated as an asset, with the discount amount being amortized to interest expense over the life of the bond.
References
[1] Cox, J., Ingersoll, J.,and S. Ross. "A Theory of the Term Structure of Interest Rates." Econometrica. Vol. 53, 1985.
[2] Brigo, D. and F. Mercurio. Interest Rate Models - Theory and Practice. Springer Finance, 2006.
[3] Hirsa, A. Computational Methods in Finance. CRC Press, 2012.
[4] Nawalka, S., Soto, G., and N. Beliaeva. Dynamic Term Structure Modeling. Wiley, 2007.
[5] Nelson, D. and K. Ramaswamy. "Simple Binomial Processes as Diffusion Approximations in Financial Models." The Review of Financial Studies. Vol 3. 1990, pp. 393–430.
Version History
Introduced in R2018aR2022b: Serial date numbers not recommended
Although bondbycir
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
capbycir
| cfbycir
| fixedbycir
| floatbycir
| floorbycir
| oasbycir
| optbndbycir
| optfloatbycir
| optembndbycir
| optemfloatbycir
| rangefloatbycir
| swapbycir
| swaptionbycir
| instbond
MATLAB 명령
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