barrierbyitt
Price barrier options using implied trinomial tree (ITT)
Syntax
Description
Examples
Price a Barrier Option Using an ITT Tree
This example shows how to price a barrier option using an ITT tree by loading the file deriv.mat, which provides ITTTree. The ITTTree structure contains the stock specification and time information needed to price the option.
load deriv.mat; OptSpec = 'Call'; Strike = 85; Settle = datetime(2006,1,1); ExerciseDates = datetime(2008,12,31); AmericanOpt = 1; BarrierSpec = 'UI'; Barrier = 115; Price = barrierbyitt(ITTTree,OptSpec,Strike,Settle,ExerciseDates,AmericanOpt,... BarrierSpec,Barrier)
Price = 2.4074
Input Arguments
ITTTree
— Stock tree structure
structure
Stock tree structure, specified by using itttree
.
Data Types: struct
OptSpec
— Definition of option
character vector with values 'call'
or 'put'
| cell array of character vectors with values 'call'
or 'put'
Definition of an option as 'call'
or 'put'
,
specified as a NINST
-by-1
cell
array of character vector values.
Data Types: char
| cell
Strike
— Option strike price value
numeric
Option strike price value for a European or an American Option, specified as
NINST
-by-1
matrix of numeric values. Each row is the
schedule for one option.
Data Types: double
Settle
— Settlement or trade date
datetime array | string array | date character vector
Settlement or trade date for the barrier option, specified as a
NINST
-by-1
vector using a datetime array, string array,
or date character vectors. The Settle
date for every barrier is set to the
ValuationDate
of the stock tree. The barrier argument
Settle
is ignored.
To support existing code, barrierbyitt
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 dates. Each row is the schedule for one option. For a European option, there is only oneExerciseDates
on the option expiry date which is the maturity of the instrument.For an American option, use a
NINST
-by-2
vector of exercise date boundaries. For each instrument, 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 anNINST
-by-1
, the option can be exercised betweenValuationDate
of the stock tree and the single listed date inExerciseDates
.
To support existing code, barrierbyitt
also
accepts serial date numbers as inputs, but they are not recommended.
AmericanOpt
— Option type
option type values 0
or 1
Option type, specified as NINST
-by-1
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 a 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 level
numeric
Barrier level, specified as an NINST
-by-1
matrix of
numeric values.
Data Types: double
Rebate
— Rebate value
0
(default) | numeric
(Optional) Rebate value, specified as 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
(Optional) Derivatives pricing options, specified as structure
that is created with derivset
.
Data Types: struct
Output Arguments
Price
— Expected prices for barrier options at time 0
vector
Expected prices for barrier options at time 0, returned as a NINST
-by-1
vector.
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 R2007aR2022b: Serial date numbers not recommended
Although barrierbyitt
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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