optembndbyhjm
Price bonds with embedded options by Heath-Jarrow-Morton interest-rate tree
Syntax
Description
[
calculates price for bonds with embedded options
from a Heath-Jarrow-Morton interest-rate tree and
returns exercise probabilities in
Price
,PriceTree
]
= optembndbyhjm(HJMTree
,CouponRate
,Settle
,Maturity
,OptSpec
,Strike
,ExerciseDates
)PriceTree
.
optembndbyhjm
computes prices of
vanilla bonds with embedded options, stepped
coupon bonds with embedded options, amortizing
bonds with embedded options, and sinking fund
bonds with call embedded option. For more
information, see More About.
[
adds optional name-value pair arguments.Price
,PriceTree
]
= optembndbyhjm(___,Name,Value
)
Examples
Price a Callable Bond Using an HJM Interest-Rate Tree Model
Create a HJMTree
with the following data:
Rates = [0.05;0.06;0.07]; Compounding = 1; StartDates = [datetime(2007,1,1) ; datetime(2008,1,1) ; datetime(2009,1,1)]; EndDates = [datetime(2008,1,1) ; datetime(2009,1,1) ; datetime(2010,1,1)]; ValuationDate = datetime(2007,1,1);
Create a RateSpec
.
RateSpec = intenvset('Rates', Rates, 'StartDates', ValuationDate, 'EndDates', ... EndDates, 'Compounding', Compounding, 'ValuationDate', ValuationDate)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 1
Disc: [3x1 double]
Rates: [3x1 double]
EndTimes: [3x1 double]
StartTimes: [3x1 double]
EndDates: [3x1 double]
StartDates: 733043
ValuationDate: 733043
Basis: 0
EndMonthRule: 1
Create a VolSpec
.
VolSpec = hjmvolspec('Constant', 0.01)
VolSpec = struct with fields:
FinObj: 'HJMVolSpec'
FactorModels: {'Constant'}
FactorArgs: {{1x1 cell}}
SigmaShift: 0
NumFactors: 1
NumBranch: 2
PBranch: [0.5000 0.5000]
Fact2Branch: [-1 1]
Create a TimeSpec
.
TimeSpec = hjmtimespec(ValuationDate, EndDates, Compounding)
TimeSpec = struct with fields:
FinObj: 'HJMTimeSpec'
ValuationDate: 733043
Maturity: [3x1 double]
Compounding: 1
Basis: 0
EndMonthRule: 1
Build the HJMTree
.
HJMTree = hjmtree(VolSpec, RateSpec, TimeSpec)
HJMTree = struct with fields:
FinObj: 'HJMFwdTree'
VolSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2]
dObs: [733043 733408 733774]
TFwd: {[3x1 double] [2x1 double] [2]}
CFlowT: {[3x1 double] [2x1 double] [3]}
FwdTree: {[3x1 double] [2x1x2 double] [1x2x2 double]}
To compute the price of an American callable bond that pays a 6% annual coupon and matures and is callable on January 1, 2010.
BondSettlement = datetime(2007,1,1); BondMaturity = datetime(2010,1,1); CouponRate = 0.06; Period = 1; OptSpec = 'call'; Strike = [98]; ExerciseDates = datetime(2010,1,1); AmericanOpt = 1; [PriceCallBond,PT] = optembndbyhjm(HJMTree, CouponRate, BondSettlement, BondMaturity,... OptSpec, Strike, ExerciseDates, 'Period', 1,'AmericanOp',1)
PriceCallBond = 95.9492
PT = struct with fields:
FinObj: 'HJMPriceTree'
tObs: [0 1 2 3]
PBush: {[95.9492] [1x1x2 double] [1x2x2 double] [98 98 98 98]}
ProbBush: {[1] [1x1x2 double] [1x2x2 double] [0.2500 0.2500 0.2500 0.2500]}
ExBush: {[0] [1x1x2 double] [1x2x2 double] [1 1 1 1]}
ExProbBush: {[0] [1x1x2 double] [1x2x2 double] [0.2500 0.2500 0.2500 0.2500]}
ExProbsByBushLevel: [0 0 0 1]
Obtain Callable Bond Exercise Information Using a HJM Interest-Rate Tree Model
Create a HJMTree
with the following data:
Rates = [0.05;0.06;0.07];
Compounding = 1;
StartDates = [datetime(2007,1,1) ; datetime(2008,1,1) ; datetime(2009,1,1)];
EndDates = [datetime(2008,1,1) ; datetime(2009,1,1) ; datetime(2010,1,1)];
ValuationDate = 'jan-1-2007';
Create a RateSpec
.
RateSpec = intenvset('Rates', Rates, 'StartDates', ValuationDate, 'EndDates', ... EndDates, 'Compounding', Compounding, 'ValuationDate', ValuationDate);
Build the HJM tree with the following data.
VolSpec = hjmvolspec('Constant', 0.01);
TimeSpec = hjmtimespec(ValuationDate, EndDates, Compounding);
HJMTree = hjmtree(VolSpec, RateSpec, TimeSpec);
Define the callable bond instruments.
Settle = datetime(2007,1,1);
Maturity = [datetime(2009,1,1) ; datetime(2010,1,1)];
CouponRate = {{datetime(2009,1,1) .0325;datetime(2010,1,1) .0375}};
OptSpec='call';
Strike= [90;92];
ExerciseDates= [datetime(2009,1,1) ; datetime(2010,1,1)];
Price the instruments.
[Price, PriceTree]= optembndbyhjm(HJMTree, CouponRate, Settle, Maturity, OptSpec, Strike,... ExerciseDates, 'Period', 1,'AmericanOpt',1)
Price = 2×1
86.0874
84.1482
PriceTree = struct with fields:
FinObj: 'HJMPriceTree'
tObs: [0 1 2 3]
PBush: {[2x1 double] [2x1x2 double] [2x2x2 double] [2x4 double]}
ProbBush: {[1] [1x1x2 double] [1x2x2 double] [0.2500 0.2500 0.2500 0.2500]}
ExBush: {[2x1 double] [2x1x2 double] [2x2x2 double] [2x4 double]}
ExProbBush: {[2x1 double] [2x1x2 double] [2x2x2 double] [2x4 double]}
ExProbsByBushLevel: [2x4 double]
Examine the output PriceTree.ExBush
. PriceTree.ExBush
contains the exercise indicator arrays. Each element of the cell array is an array containing 1
's where an option is exercised and 0
's where it is not.
PriceTree.ExBush{4}
ans = 2×4
0 0 0 0
1 1 1 1
There is no exercise for instrument 1 and instrument 2 is exercised at all nodes.
PriceTree.ExBush{3}
ans = ans(:,:,1) = 1 1 0 0 ans(:,:,2) = 1 1 0 0
There is exercise for instrument 1 at all nodes and no exercise for instrument 2.
PriceTree.ExBush{2}
ans = ans(:,:,1) = 0 0 ans(:,:,2) = 0 0
There is no exercise for instrument 1 or instrument 2.
Next view the probability of reaching each node from the root node using PriceTree.ProbBush
.
PriceTree.ProbBush{2}
ans = ans(:,:,1) = 0.5000 ans(:,:,2) = 0.5000
PriceTree.ProbBush{3}
ans = ans(:,:,1) = 0.2500 0.2500 ans(:,:,2) = 0.2500 0.2500
PriceTree.ProbBush{4}
ans = 1×4
0.2500 0.2500 0.2500 0.2500
View the exercise probabilities using PriceTree.ExProbBush
. PriceTree.ExProbBush
contains the exercise probabilities. Each element in the cell array is an array containing 0
's where there is no exercise, or the probability of reaching that node where exercise happens.
PriceTree.ExProbBush{4}
ans = 2×4
0 0 0 0
0.2500 0.2500 0.2500 0.2500
PriceTree.ExProbBush{3}
ans = ans(:,:,1) = 0.2500 0.2500 0 0 ans(:,:,2) = 0.2500 0.2500 0 0
PriceTree.ExProbBush{2}
ans = ans(:,:,1) = 0 0 ans(:,:,2) = 0 0
View the exercise probabilities at each tree level using PriceTree.ExProbsByBushLevel
. PriceTree.ExProbsByBushLevel
is an array with each row holding the exercise probability for a given option at each tree observation time.
PriceTree.ExProbsByBushLevel
ans = 2×4
0 0 1 0
0 0 0 1
Price Single Stepped Callable Bonds Using an HJM Interest-Rate Tree Model
Price the following single stepped callable bonds using the following data: The data for the interest rate term structure is as follows:
Rates = [0.035; 0.042147; 0.047345; 0.052707]; ValuationDate = datetime(2010,1,1); StartDates = ValuationDate; EndDates = [datetime(2011,1,1) ; datetime(2012,1,1) ; datetime(2013,1,1) ; datetime(2014,1,1)]; Compounding = 1; % Create RateSpec RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding); % Instrument Settle = datetime(2010,1,1); Maturity = [datetime(2013,1,1) ; datetime(2014,1,1)]; CouponRate = {{datetime(2012,1,1) .0425;datetime(2014,1,1) .0750}}; OptSpec = 'call'; Strike = 100; ExerciseDates = datetime(2012,1,1); %Callable in two years % Build the tree with the following data Volatility = [.2; .19; .18; .17]; CurveTerm = [ 1; 2; 3; 4]; HJMTimeSpec = hjmtimespec(ValuationDate, EndDates); HJMVolSpec = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6); HJMT = hjmtree(HJMVolSpec, RS, HJMTimeSpec); % The first row corresponds to the price of the callable bond with maturity % of three years. The second row corresponds to the price of the callable % bond with maturity of four years. PHJM= optembndbyhjm(HJMT, CouponRate, Settle, Maturity ,OptSpec, Strike,... ExerciseDates, 'Period', 1)
PHJM = 2×1
100.0484
99.8009
Price a Sinking Fund Bond Using an HJM Interest-Rate Tree Model
A corporation issues a three year bond with a sinking fund obligation requiring the company to sink 1/3 of face value after the first year and 1/3 after the second year. The company has the option to buy the bonds in the market or call them at $99. The following data describes the details needed for pricing the sinking fund bond:
Rates = [0.035; 0.042147; 0.047345; 0.052707]; ValuationDate = datetime(2011,1,1); StartDates = ValuationDate; EndDates = [datetime(2012,1,1) ; datetime(2013,1,1) ; datetime(2014,1,1) ; datetime(2015,1,1)]; Compounding = 1;
Create the RateSpec
.
RateSpec = intenvset('ValuationDate', ValuationDate, 'StartDates',... StartDates, 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 1
Disc: [4x1 double]
Rates: [4x1 double]
EndTimes: [4x1 double]
StartTimes: [4x1 double]
EndDates: [4x1 double]
StartDates: 734504
ValuationDate: 734504
Basis: 0
EndMonthRule: 1
Build the HJM
tree.
Sigma = 0.1;
HJMTimeSpec = hjmtimespec(ValuationDate, EndDates, Compounding);
HJMVolSpec = hjmvolspec('Constant', Sigma);
HJMT = hjmtree(HJMVolSpec, RateSpec, HJMTimeSpec)
HJMT = struct with fields:
FinObj: 'HJMFwdTree'
VolSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2 3]
dObs: [734504 734869 735235 735600]
TFwd: {[4x1 double] [3x1 double] [2x1 double] [3]}
CFlowT: {[4x1 double] [3x1 double] [2x1 double] [4]}
FwdTree: {[4x1 double] [3x1x2 double] [2x2x2 double] [1x4x2 double]}
Define the sinking fund instrument. The bond has a coupon rate of 4.5%, a period of one year and matures in 1-Jan-2013. Face decreases 1/3 after the first year.
CouponRate = 0.045;
Settle = datetime(2011,1,1);
Maturity = datetime(2013,1,1);
Period = 1;
Face = { {datetime(2012,1,1) 100; ...
datetime(2013,1,1) 66.6666}};
Define the option provision.
OptSpec = 'call';
Strike = 99;
ExerciseDates = datetime(2012,1,1);
Price of non-sinking fund bond.
PNSF = bondbyhjm(HJMT, CouponRate, Settle, Maturity, Period)
PNSF = 100.5663
Price of the bond with the option sinking provision.
PriceSF = optembndbyhjm(HJMT, CouponRate, Settle, Maturity,... OptSpec, Strike, ExerciseDates, 'Period', Period, 'Face', Face)
PriceSF = 98.8736
Price an Amortizing Callable Bond Using an HJM Interest-Rate Tree Model
This example shows how to price an amortizing callable bond and a vanilla callable bond using an HJM lattice model.
Create a RateSpec
.
Rates = [0.035; 0.042147; 0.047345; 0.052707]; ValuationDate = datetime(2012,1,1); StartDates = ValuationDate; EndDates = [datetime(2013,1,1) ; datetime(2014,1,1) ; datetime(2015,1,1) ;datetime(2016,1,1)]; Compounding = 1; RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding);
Build a HJM tree.
VolSpec = hjmvolspec('Constant', 0.01)
VolSpec = struct with fields:
FinObj: 'HJMVolSpec'
FactorModels: {'Constant'}
FactorArgs: {{1x1 cell}}
SigmaShift: 0
NumFactors: 1
NumBranch: 2
PBranch: [0.5000 0.5000]
Fact2Branch: [-1 1]
TimeSpec = hjmtimespec(ValuationDate, EndDates, Compounding)
TimeSpec = struct with fields:
FinObj: 'HJMTimeSpec'
ValuationDate: 734869
Maturity: [4x1 double]
Compounding: 1
Basis: 0
EndMonthRule: 1
HJMTree = hjmtree(VolSpec, RS, TimeSpec)
HJMTree = struct with fields:
FinObj: 'HJMFwdTree'
VolSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2 3]
dObs: [734869 735235 735600 735965]
TFwd: {[4x1 double] [3x1 double] [2x1 double] [3]}
CFlowT: {[4x1 double] [3x1 double] [2x1 double] [4]}
FwdTree: {[4x1 double] [3x1x2 double] [2x2x2 double] [1x4x2 double]}
Define the callable bond.
CouponRate = 0.05;
Settle = datetime(2012,1,1);
Maturity = datetime(2016,1,1);
Period = 1;
Face = {
{datetime(2014,1,1) 100;
datetime(2015,1,1) 70;
datetime(2016,1,1) 50};
};
OptSpec = 'call';
Strike = [97 95 93];
ExerciseDates = [datetime(2014,1,1) datetime(2015,1,1) datetime(2016,1,1)];
Price a callable amortizing bond using the HJM tree.
BondType = 'amortizing'; Pcallbonds = optembndbyhjm(HJMTree, CouponRate, Settle, Maturity ,OptSpec, Strike,... ExerciseDates, 'Period', 1,'Face',Face,'BondType', BondType)
Pcallbonds = 98.6000
Input Arguments
HJMTree
— Interest-rate tree structure
structure
Interest-rate tree structure, specified by using hjmtree
.
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 for the bond option, specified as a
NINST
-by-1
vector using a datetime array, string array, or
date character vectors.
Note
The Settle
date for every
bond is set to the
ValuationDate
of the HJM tree.
The bond argument Settle
is
ignored.
To support existing code, optembndbyhjm
also
accepts serial date numbers as inputs, but they are not recommended.
Maturity
— Maturity date
datetime array | string array | date character vector
Maturity date, specified as an NINST
-by-1
vector using a
datetime array, string array, or date character
vectors.
To support existing code, optembndbyhjm
also
accepts serial date numbers as inputs, but they are not recommended.
OptSpec
— Definition of option
character vector with value 'call'
or 'put'
| cell array of character vectors with values 'call'
or 'put'
Definition of option, specified as a NINST
-by-1
cell
array of character vectors.
Data Types: char
Strike
— Option strike price values
nonnegative integer
Option strike price value, specified as a NINST
-by-1
or NINST
-by-NSTRIKES
depending
on the type of option:
European option —
NINST
-by-1
vector of strike price values.Bermuda option —
NINST
by number of strikes (NSTRIKES
) matrix of strike price values. Each row is the schedule for one option. If an option has fewer thanNSTRIKES
exercise opportunities, the end of the row is padded withNaN
s.American option —
NINST
-by-1
vector of strike price values for each option.
Data Types: double
ExerciseDates
— Option exercise dates
datetime array | string array | date character vector
Option exercise dates, specified as a NINST
-by-1
,
NINST
-by-2
,
or
NINST
-by-NSTRIKES
vector using a datetime array, string array, or
date character vectors, depending on the type of
option:
For a European option, use a
NINST
-by-1
vector of dates. For a European option, there is only oneExerciseDates
on the option expiry date.For a Bermuda option, use a
NINST
-by-NSTRIKES
vector of dates.For an American option, use a
NINST
-by-2
vector of exercise date boundaries. The option can be exercised on any date between or including the pair of dates on that row. If only one non-NaN
date is listed, or ifExerciseDates
is aNINST
-by-1
vector, the option can be exercised betweenValuationDate
of the stock tree and the single listedExerciseDates
.
To support existing code, optembndbyhjm
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 = optembndbyhjm(HJMTree,CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates,'Period',1,'AmericanOp',1)
AmericanOpt
— Option type
0
European/Bermuda (default) | integer with values 0
or 1
Option type, specified as the comma-separated pair consisting of
'AmericanOpt'
and
NINST
-by-1
positive integer flags with values:
0
— European/Bermuda1
— American
Data Types: double
Period
— Coupons per year
2
per year (default) | vector
Coupons per year, specified as the comma-separated pair consisting of
'Period'
and a
NINST
-by-1
vector.
Data Types: double
Basis
— Day-count basis
0
(actual/actual) (default) | integer from 0
to 13
Day-count basis, specified as the comma-separated pair consisting of
'Basis'
and a
NINST
-by-1
vector of integers.
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 with values 0
or 1
End-of-month rule flag, specified as the comma-separated pair consisting of
'EndMonthRule'
and a
nonnegative integer using a
NINST
-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: double
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, optembndbyhjm
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, optembndbyhjm
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, optembndbyhjm
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
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, optembndbyhjm
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) | NINST
-by-1
vector | NINST
-by-1
cell array
Face or par value, specified as the
comma-separated pair consisting of
'Face'
and a
NINST
-by-1
vector or a
NINST
-by-1
cell array where each element is a
NumDates
-by-2
cell array where the first column is dates and the
second column is associated face value. The date
indicates the last day that the face value is valid.
Note
Instruments without a
Face
schedule are treated as
either vanilla bonds or stepped coupon bonds with
embedded options.
Data Types: double
BondType
— Type of underlying bond
'vanilla'
for scalar Face
values,
'callablesinking'
for scheduled
Face
values (default) | cell array of character vectors with values
'vanilla'
,'amortizing'
,
or 'callablesinking'
| string array with values
"vanilla"
,
"amortizing"
, or
"callablesinking"
Type of underlying bond, specified as the
comma-separated pair consisting of
'BondType'
and a
NINST
-by-1
cell array of character vectors or string array
specifying if the underlying is a vanilla bond, an
amortizing bond, or a callable sinking fund bond.
The supported types are:
'vanilla
' is a standard callable or puttable bond with a scalarFace
value and a single coupon or stepped coupons.'callablesinking'
is a bond with a schedule ofFace
values and a sinking fund call provision with a single or stepped coupons.'amortizing'
is an amortizing callable or puttable bond with a schedule ofFace
values with single or stepped coupons.
Data Types: char
| string
Options
— Derivatives pricing options
structure
Derivatives pricing options, specified as the comma-separated pair consisting of
'Options'
and a structure that
is created with derivset
.
Data Types: struct
Output Arguments
Price
— Expected prices of embedded option at time 0
matrix
Expected price of the embedded option at time 0
,
returned as a NINST
-by-1
matrix.
PriceTree
— Structure containing trees of vectors of instrument prices and exercise probabilities for each
node
structure
Structure containing trees of vectors of instrument prices, a vector of observation times for each node, and exercise probabilities. Values are:
PriceTree.ExBush
contains the exercise indicator arrays. Each element of the cell array is an array containing1
's where an option is exercised and0
's where it isn't.PriceTree.tObs
contains the observation times.PriceTree.ProbBush
contains the probability of reaching each node from root node.PriceTree.ExProbBush
contains the exercise probabilities. Each element in the cell array is an array containing0
's where there is no exercise, or the probability of reaching that node where exercise happens.PriceTree.ExProbsByBushLevel
is an array with each row holding the exercise probability for a given option at each tree observation time.
More About
Vanilla Bond with Embedded Option
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. A vanilla bond with an embedded option is where an option contract has an underlying asset of a vanilla bond.
Stepped Coupon Bond with Callable and Puttable Features
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. Stepped coupon bonds can have options features (call and puts).
Sinking Fund Bond with Call Embedded Option
A sinking fund bond is a coupon bond with a sinking fund provision.
This provision obligates the issuer to amortize portions of the principal prior to maturity, affecting bond prices since the time of the principal repayment changes. This means that investors receive the coupon and a portion of the principal paid back over time. These types of bonds reduce credit risk, since it lowers the probability of investors not receiving their principal payment at maturity.
The bond may have a sinking fund call option provision allowing the issuer to retire the sinking fund obligation either by purchasing the bonds to be redeemed from the market or by calling the bond via a sinking fund call, whichever is cheaper. If interest rates are high, then the issuer buys back the requirement amount of bonds from the market since bonds are cheap, but if interest rates are low (bond prices are high), then most likely the issuer is buying the bonds at the call price. Unlike a call feature, however, if a bond has a sinking fund call option provision, it is an obligation, not an option, for the issuer to buy back the increments of the issue as stated. Because of this, a sinking fund bond trades at a lower price than a non-sinking fund bond.
Amortizing Callable or Puttable Bond
Amortizing callable or puttable bonds work
under a scheduled Face
.
An amortizing callable bond gives the issuer the right to call
back the bond, but instead of paying the
Face
amount at maturity, it
repays part of the principal along with the coupon payments.
An amortizing puttable bond, repays part of the principal
along with the coupon payments and gives the bondholder the
right to sell the bond back to the issuer.
Version History
Introduced in R2008aR2022b: Serial date numbers not recommended
Although optembndbyhjm
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.
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