barrierbystt
Price barrier options using standard trinomial tree
Syntax
Description
[
prices barrier options using a standard trinomial (STT) tree.Price
,PriceTree
]
= barrierbystt(STTTree
,OptSpec
,Strike
,Settle
,ExerciseDates
,AmericanOpt
,BarrierSpec
,Barrier
)
Note
Alternatively, you can use the Barrier
object to price Barrier options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
Examples
Price a Barrier Option Using the Standard Trinomial Tree Model
Create a RateSpec
.
StartDates = datetime(2009,1,1); EndDates = datetime(2013,1,1); Rates = 0.035; Basis = 1; Compounding = -1; RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates,... 'EndDates', EndDates, 'Rates', Rates,'Compounding', Compounding, 'Basis', Basis)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: -1
Disc: 0.8694
Rates: 0.0350
EndTimes: 4
StartTimes: 0
EndDates: 735235
StartDates: 733774
ValuationDate: 733774
Basis: 1
EndMonthRule: 1
Create a StockSpec
.
AssetPrice = 85; Sigma = 0.15; StockSpec = stockspec(Sigma, AssetPrice)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.1500
AssetPrice: 85
DividendType: []
DividendAmounts: 0
ExDividendDates: []
Create an STTTree
.
NumPeriods = 4; TimeSpec = stttimespec(StartDates, EndDates, 4); STTTree = stttree(StockSpec, RateSpec, TimeSpec)
STTTree = struct with fields:
FinObj: 'STStockTree'
StockSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2 3 4]
dObs: [733774 734139 734504 734869 735235]
STree: {[85] [110.2179 85 65.5520] [142.9174 110.2179 85 65.5520 50.5537] [185.3182 142.9174 110.2179 85 65.5520 50.5537 38.9870] [240.2985 185.3182 142.9174 110.2179 85 65.5520 50.5537 38.9870 30.0668]}
Probs: {[3x1 double] [3x3 double] [3x5 double] [3x7 double]}
Define the barrier option and compute the price.
Settle = datetime(2009,1,1); ExerciseDates = datetime(2012,1,1); OptSpec = 'call'; Strike = 105; AmericanOpt = 1; BarrierSpec = 'UI'; Barrier = 115; Price= barrierbystt(STTTree, OptSpec, Strike, Settle, ExerciseDates,... AmericanOpt, BarrierSpec, Barrier)
Price = 3.7977
Input Arguments
STTTree
— Stock tree structure for standard trinomial tree
structure
Stock tree structure for a standard trinomial tree, specified
by using stttree
.
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 'call'
or 'put'
using
a character vector or a NINST
-by-1
cell
array of character vectors for 'call'
or 'put'
.
Data Types: char
| cell
Strike
— European or American option strike price value
nonnegative numeric
European or American option strike price value, specified with a nonnegative integer using a
NINST
-by-1
matrix of nonnegative numeric values. Each row is
the schedule for one option. To compute the value
of a floating-strike barrier option,
Strike
should be specified as
NaN
. Floating-strike barrier
options are also known as average strike
options.
Data Types: double
Settle
— Settlement date or trade date
datetime array | string array | date character vector
Settlement date or trade date for the barrier option, specified as a
NINST
-by-1
vector of settlement or
trade dates using a datetime array, string array, or date character vectors.
Note
The Settle
date for every barrier option is set
to the ValuationDate
of the stock tree. The
barrier argument, Settle
, is ignored.
To support existing code, barrierbystt
also
accepts serial date numbers as inputs, but they are not recommended.
ExerciseDates
— Option exercise dates
datetime array | string array | date character vector
Option exercise dates, specified as a datetime array, string array, or date character vectors:
For a European option, use a
NINST
-by-1
matrix of exercise dates. Each row is the schedule for one option. For a European option, there is only oneExerciseDates
on the option expiry date.For an American option, use a
NINST
-by-2
vector of exercise date boundaries. The option can be exercised on any tree 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
cell array of character vectors, the option can be exercised betweenValuationDate
of the stock tree and the single listedExerciseDates
.
To support existing code, barrierbystt
also
accepts serial date numbers as inputs, but they are not recommended.
AmericanOpt
— Option type
scalar with values [0,1]
Option type, specified as an NINST
-by-1
matrix of flags
with values:
0
— European1
— American
Data Types: double
BarrierSpec
— Barrier option type
character vector with values: 'UI'
, 'UO'
, 'DI'
, 'DO'
| cell array of character vectors with values: 'UI'
, 'UO'
, 'DI'
, 'DO'
Barrier option type, specified as a character vector or an
NINST
-by-1
cell array of character vectors with the following
values:
'UI'
— Up Knock-inThis option becomes effective when the price of the underlying asset passes above the barrier level. It gives the option holder the right, but not the obligation, to buy or sell (call/put) the underlying security at the strike price if the underlying asset goes above the barrier level during the life of the option. Note,
barrierbyfd
does not support American knock-in barrier options.'UO'
— Up Knock-outThis option gives the option holder the right, but not the obligation, to buy or sell (call/put) the underlying security at the strike price as long as the underlying asset does not go above the barrier level during the life of the option. This option terminates when the price of the underlying asset passes above the barrier level. Usually, with an up-and-out option, the rebate is paid if the spot price of the underlying reaches or exceeds the barrier level.
'DI'
— Down Knock-inThis option becomes effective when the price of the underlying stock passes below the barrier level. It gives the option holder the right, but not the obligation, to buy or sell (call/put) the underlying security at the strike price if the underlying security goes below the barrier level during the life of the option. With a down-and-in option, the rebate is paid if the spot price of the underlying does not reach the barrier level during the life of the option. Note,
barrierbyfd
does not support American knock-in barrier options.'DO'
— Down Knock-upThis option gives the option holder the right, but not the obligation, to buy or sell (call/put) the underlying asset at the strike price as long as the underlying asset does not go below the barrier level during the life of the option. This option terminates when the price of the underlying security passes below the barrier level. Usually the option holder receives a rebate amount if the option expires worthless.
Option | Barrier Type | Payoff if Barrier Crossed | Payoff if Barrier not Crossed |
---|---|---|---|
Call/Put | Down Knock-out | Worthless | Standard Call/Put |
Call/Put | Down Knock-in | Call/Put | Worthless |
Call/Put | Up Knock-out | Worthless | Standard Call/Put |
Call/Put | Up Knock-in | Standard Call/Put | Worthless |
Data Types: char
| cell
Barrier
— Barrier levels
numeric
Barrier levels, specified as an NINST
-by-1
matrix of
numeric values.
Data Types: double
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 = barrierbystt(STTTree,OptSpec,Strike,Settle,ExerciseDates,1,'UI',115,'Rebate',25)
Rebate
— Rebate values
0
(default) | numeric
Rebate values, specified as the comma-separated pair consisting of 'Rebate'
and a NINST
-by-1
matrix of numeric
values. For Knock-in options, the Rebate
is paid at
expiry. For Knock-out options, the Rebate
is paid
when the Barrier
is reached.
Data Types: double
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 for barrier options at time 0
matrix
Expected prices for barrier options at time 0, returned as a NINST
-by-1
matrix.
PriceTree
— Structure with vector of barrier option prices at each node
tree structure
Structure with a vector of barrier option prices at each node, returned as a tree structure.
PriceTree
is a MATLAB® structure of trees
containing vectors of instrument prices and a vector of observation
times for each node.
PriceTree.PTree
contains the prices.
PriceTree.tObs
contains the observation times.
PriceTree.dObs
contains the observation dates.
More About
Barrier Option
A Barrier option has not only a strike price but also a barrier level and sometimes a rebate.
A rebate is a fixed amount that is paid if the option cannot be exercised because
the barrier level has been reached or not reached. The payoff for this type of
option depends on whether the underlying asset crosses the predetermined trigger
value (barrier level), indicated by Barrier
, during the life of
the option. For more information, see Barrier Option.
References
[1] Derman, E., I. Kani, D. Ergener and I. Bardhan. “Enhanced Numerical Methods for Options with Barriers.” Financial Analysts Journal. (Nov.-Dec.), 1995, pp. 65–74.
Version History
Introduced in R2015bR2022b: Serial date numbers not recommended
Although barrierbystt
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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