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
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: [1×1 struct]
TimeSpec: [1×1 struct]
RateSpec: [1×1 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: {[3×1 double] [3×3 double] [3×5 double] [3×7 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
Stock tree structure for a standard trinomial tree, specified
by using stttree
.
Data Types: struct
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
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
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.
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.
Option type, specified as an NINST
-by-1
matrix of flags
with values:
0
— European1
— American
Data Types: double
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 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 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
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
Expected prices for barrier options at time 0, returned as a NINST
-by-1
matrix.
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
A Barrier is a type of exotic option whose existence or payoff depends on the price of the underlying asset reaching a certain barrier level during the option's life.
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 R2015bAlthough 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.
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)