optbndbyhjm
Price bond option from Heath-Jarrow-Morton interest-rate tree
Syntax
Description
[
calculates
the price for a bond option from a Black-Karasinski interest-rate
tree.Price
,PriceTree
]
= optbndbyhjm(HJMTree
,OptSpec
,Strike
,ExerciseDates
,AmericanOpt
,CouponRate
,Settle
,Maturity
)
[
adds
optional arguments.Price
,PriceTree
]
= optbndbyhjm(___,Period
,Basis
,EndMonthRule
,IssueDate
,FirstCouponDate
,LastCouponDate
,StartDate
,Face
,Options
)
Examples
Price a European Call Option on a Bond
Using the HJM forward-rate tree in the deriv.mat
file,
price a European call option on a 4% bond with a strike of 96. The exercise date for the
option is Jan. 01, 2003. The settle date for the bond is Jan. 01, 2000, and the maturity
date is Jan. 01, 2004.
Load the file deriv.mat
, which provides HJMTree
.
The HJMTree
structure contains the time and forward-rate
information needed to price the bond.
load deriv.mat;
Use optbndbyhjm
to compute the price of the
'Call'
option.
[Price,PriceTree] = optbndbyhjm(HJMTree,'Call',96,datetime(2003,1,1), 0,0.04,datetime(2000,1,1),datetime(2004,1,1),1)
Price = 2.2035 PriceTree = struct with fields: FinObj: 'HJMPriceTree' tObs: [0 1 2 3 4] PBush: {[2.2035] [1×1×2 double] [1×2×2 double] [1×4×2 double] [0 0 0 0 0 0 0 0]} ExBush: {[0] [1×1×2 double] [1×2×2 double] [1×4×2 double] [0 0 0 0 0 0 0 0]}
Input Arguments
HJMTree
— Interest-rate tree structure
structure
Interest-rate tree structure, specified by using hjmtree
.
Data Types: struct
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, optbndbyhjm
also
accepts serial date numbers as inputs, but they are not recommended.
AmericanOpt
— Option type
0
European/Bermuda (default) | integer with values 0
or 1
(Optional) Option type, specified as NINST
-by-1
positive
integer flags with values:
0
— European/Bermuda1
— American
Data Types: double
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, optbndbyhjm
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, optbndbyhjm
also
accepts serial date numbers as inputs, but they are not recommended.
Period
— Coupons per year
2
per year (default) | vector
(Optional) Coupons per year, specified as an NINST
-by-1
vector.
Data Types: double
Basis
— Day-count basis
0
(actual/actual) (default) | integer from 0
to 13
(Optional) Day-count basis, specified as 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
(Optional) End-of-month rule flag is specified as 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
(Optional) Bond issue date, specified as an NINST
-by-1
vector using a datetime array, string array, or date character vectors.
To support existing code, optbndbyhjm
also
accepts serial date numbers as inputs, but they are not recommended.
FirstCouponDate
— Irregular first coupon date
datetime array | string array | date character vector
(Optional) Irregular first coupon date, specified as an
NINST
-by-1
vector using a datetime array, string
array, or date character vectors.
To support existing code, optbndbyhjm
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
(Optional) Irregular last coupon date, specified as a
NINST
-by-1
vector using a datetime array, string
array, or date character vectors.
To support existing code, optbndbyhjm
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
(Optional) Forward starting date of payments (the date from which a bond cash flow is
considered), specified as a NINST
-by-1
vector
using a datetime array, string array, or date character vectors.
To support existing code, optbndbyhjm
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
(Optional) Face or par value, specified as anNINST
-by-1
vector.
Data Types: double
Options
— Derivatives pricing options
structure
(Optional) Derivatives pricing options, specified as structure
that is created with derivset
.
Data Types: struct
Output Arguments
Price
— Expected prices of bond option at time 0
matrix
Expected price of the bond option at time 0
,
returned as a NINST
-by-1
matrix.
PriceTree
— Structure containing trees of vectors of instrument prices and accrued interest for each node
structure
Structure containing trees of vectors of instrument prices and accrued interest, and a vector of observation times for each node. Values are:
PriceTree.PBush
contains the clean prices.PriceTree.tObs
contains the observation times.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.
More About
Bond Option
A bond option gives the holder the right to sell a bond back to the issuer (put) or to redeem a bond from its current owner (call) at a specific price and on a specific date.
Financial Instruments Toolbox™ supports three types of put and call options on bonds:
American option: An option that you exercise any time until its expiration date.
European option: An option that you exercise only on its expiration date.
Bermuda option: A Bermuda option resembles a hybrid of American and European options. You can exercise it on predetermined dates only, usually monthly.
For more information, see Bond Options.
Version History
Introduced before R2006aR2022b: Serial date numbers not recommended
Although optbndbyhjm
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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