optemfloatbybk
Price embedded option on floating-rate note for Black-Karasinski interest-rate tree
Syntax
Description
[
prices embedded options on floating-rate notes from a Black-Karasinski interest rate tree.
Price
,PriceTree
]
= optemfloatbybk(BKTree
,Spread
,Settle
,Maturity
,OptSpec
,Strike
,ExerciseDates
)optemfloatbybk
computes prices of vanilla floating-rate notes with
embedded options.
Note
Alternatively, you can use the OptionEmbeddedFloatBond
object to price embedded floating-rate bond option
instruments. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
[
adds optional name-value pair arguments. Price
,PriceTree
]
= optemfloatbybk(___,Name,Value
)
Examples
Price European Callable Embedded Option for Floating-Rate Note
Define the interest-rate term structure.
Rates = [0.03;0.034;0.038;0.04]; 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;
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: 734869
ValuationDate: 734869
Basis: 0
EndMonthRule: 1
Build the BK tree.
VolDates = [datetime(2013,1,1) ; datetime(2014,1,1) ; datetime(2015,1,1) ; datetime(2016,1,1)]; VolCurve = 0.01; AlphaDates = datetime(2016,1,1); AlphaCurve = 0.1; BKVolSpec = bkvolspec(RateSpec.ValuationDate, VolDates, VolCurve,... AlphaDates, AlphaCurve); BKTimeSpec = bktimespec(RateSpec.ValuationDate, VolDates, Compounding); BKT = bktree(BKVolSpec, RateSpec, BKTimeSpec)
BKT = struct with fields:
FinObj: 'BKFwdTree'
VolSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2 3]
dObs: [734869 735235 735600 735965]
CFlowT: {[4x1 double] [3x1 double] [2x1 double] [4]}
Probs: {[3x1 double] [3x3 double] [3x5 double]}
Connect: {[2] [2 3 4] [2 3 4 5 6]}
FwdTree: {[1.0300] [1.0387 1.0380 1.0373] [1.0477 1.0469 1.0460 1.0452 1.0444] [1.0485 1.0477 1.0468 1.0460 1.0452 1.0444 1.0436]}
The floater instrument has a spread of 15, a period of one year, and matures and is callable on Jan-1-2015.
Spread = 15;
Settle = datetime(2012,1,1);
Maturity = datetime(2015,1,1);
Period = 1;
OptSpec = {'call'};
Strike =101;
ExerciseDates = datetime(2015,1,1);
Compute the price of the floater with the embedded call.
Price= optemfloatbybk(BKT, Spread, Settle, Maturity,...
OptSpec, Strike, ExerciseDates)
Price = 100.4201
Input Arguments
BKTree
— Interest-rate tree structure
binomial tree structure
Interest-rate tree specified as a structure by using bktree
.
Data Types: struct
Spread
— Number of basis points over the reference rate
nonnegative integer | vector of nonnegative integers
Number of basis points over the reference rate specified as
a vector of nonnegative integers for the number of instruments (NINST
)-by-1
).
Data Types: single
| double
Settle
— Settlement dates of floating-rate note
ValuationDate
of BDT Tree (default) | datetime array | string array | date character vector
Settlement dates of floating-rate note specified a
NINST
-by-1
vector using a datetime array, string
array, or date character vectors.
Note
The Settle
date for every floating-rate note with an embedded
option is set to the ValuationDate
of the BK tree. The
floating-rate note argument Settle
is ignored.
To support existing code, optemfloatbybk
also
accepts serial date numbers as inputs, but they are not recommended.
Maturity
— Floating-rate note maturity date
datetime array | string array | date character vector
Floating-rate note maturity date specified as a
NINST
-by-1
vector using a datetime array, string
array, or date character vectors.
To support existing code, optemfloatbybk
also
accepts serial date numbers as inputs, but they are not recommended.
OptSpec
— Definition of option
character vector | cell array of character vectors
Definition of option as 'call'
or 'put'
specified
as a NINST
-by-1
cell array of
character vectors for 'call'
or 'put'
.
Data Types: cell
| char
Strike
— Option strike price values
nonnegative integer | vector of nonnegative integers
Option strike price values specified nonnegative integers using
as NINST
-by-NSTRIKES
vector
of strike price values.
Data Types: single
| double
ExerciseDates
— Exercise date for option (European, Bermuda, or American)
datetime array | string array | date character vector
Exercise date for option (European, Bermuda, or American) specified as a
NINST
-by-NSTRIKES
or
NINST
-by-2
vector using a datetime array, string
array, or date character vectors.
To support existing code, optemfloatbybk
also
accepts serial date numbers as inputs, but they are not recommended.
If a European or Bermuda option, the
ExerciseDates
is a1
-by-1
(European) or1
-by-NSTRIKES
(Bermuda) vector of exercise dates. For a European option, there is only oneExerciseDate
on the option expiry date.If an American option, then
ExerciseDates
is a1
-by-2
vector of exercise date boundaries. The option exercises on any date between or including the pair of dates on that row. If there is only one non-NaN
date, or ifExerciseDates
is1
-by-1
, the option exercises between theSettle
date and the single listedExerciseDate
.
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] =
optemfloatbybk(BKTree,Spread,Settle,Maturity,OptSpec,Strike,ExerciseDates,'AmericanOpt',1,'FloatReset',6,'Basis',8)
AmericanOpt
— Option type
scalar | vector of positive integers[0,1]
Option type, specified as the comma-separated pair consisting of
'AmericanOpt'
and
NINST
-by-1
positive integer scalar flags with
values:
0
— European/Bermuda1
— American
Data Types: double
FloatReset
— Frequency of payments per year
1
(default) | positive integer from the set[1,2,3,4,6,12]
| vector of positive integers from the set
[1,2,3,4,6,12]
Frequency of payments per year, specified as the comma-separated pair consisting
of 'FloatReset'
and positive integers for the values
[1,2,3,4,6,12]
in a
NINST
-by-1
vector.
Note
Payments on floating-rate notes (FRNs) are determined by the effective interest-rate between reset dates. If the reset period for an FRN spans more than one tree level, calculating the payment becomes impossible due to the recombining nature of the tree. That is, the tree path connecting the two consecutive reset dates cannot be uniquely determined because there will be more than one possible path for connecting the two payment dates.
Data Types: double
Basis
— Day-count basis of the instrument
0
(actual/actual) (default) | positive integers of the set [1...13]
| vector of positive integers of the set [1...13]
Day-count basis of the instrument, specified as the comma-separated pair consisting of
'Basis'
and a positive integer using a
NINST
-by-1
vector. The
Basis
value represents the basis used when annualizing the input
forward-rate tree.
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 [0,1]
End-of-month rule flag, specified as the comma-separated pair consisting of
'EndMonthRule'
and a nonnegative integer [0
,
1
] 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
Principal
— Principal values
100
(default) | vector of nonnegative values | cell array of nonnegative values
Principal values, specified as the comma-separated pair consisting of
'Principal'
and nonnegative values using a
NINST
-by-1
vector or
NINST
-by-1
cell array of notional principal
amounts. When using a NINST
-by-1
cell array,
each element is a NumDates
-by-2
cell array where
the first column is dates and the second column is associated principal amount. The
date indicates the last day that the principal value is valid.
Data Types: double
| cell
Options
— Structure containing derivatives pricing options
structure
Structure containing derivatives pricing options, specified as the comma-separated pair
consisting of 'Options'
and a structure obtained from using
derivset
.
Data Types: struct
Output Arguments
Price
— Expected prices of the floating-rate note option at time 0
scalar | vector
Expected prices of the floating-rate note option at time 0 are
returned as a scalar or an NINST
-by-1
vector.
PriceTree
— Structure of trees containing vectors of option prices at each node
tree structure
Structure of trees containing vectors of instrument prices and accrued interest and a vector of observation times for each node returned as:
PriceTree.PTree
contains option prices.PriceTree.tObs
contains the observation times.
More About
Floating-Rate Note with Embedded Options
A floating-rate note with an embedded option enables floating-rate notes to have early redemption features.
A FRN with an embedded option gives investors or issuers the option to retire the outstanding principal prior to maturity. An embedded call option gives the right to retire the note prior to the maturity date (callable floater), and an embedded put option gives the right to sell the note back at a specific price (puttable floater).
For more information, see Floating-Rate Note with Embedded Options.
Version History
Introduced in R2013aR2022b: Serial date numbers not recommended
Although optemfloatbybk
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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