barrierbyls
Price European or American barrier options using Monte Carlo simulations
Syntax
Description
[
calculates barrier option prices on a single underlying asset using the Longstaff-Schwartz
model. Price
,Paths
,Times
,Z
]
= barrierbyls(RateSpec
,StockSpec
,OptSpec
,Strike
,Settle
,ExerciseDates
,BarrierSpec
,Barrier
)barrierbyls
computes prices of European and American barrier
options.
For American options, the Longstaff-Schwartz least squares method is used to calculate the early exercise premium.
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 an American Barrier Down In Put Option
Compute the price of an American down in put option using the following data:
Rates = 0.0325; Settle = datetime(2016,1,1); Maturity = datetime(2017,1,1); Compounding = -1; Basis = 1;
Define a RateSpec
.
RateSpec = intenvset('ValuationDate',Settle,'StartDates',Settle,'EndDates',Maturity, ... 'Rates',Rates,'Compounding',Compounding,'Basis',Basis)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: -1
Disc: 0.9680
Rates: 0.0325
EndTimes: 1
StartTimes: 0
EndDates: 736696
StartDates: 736330
ValuationDate: 736330
Basis: 1
EndMonthRule: 1
Define a StockSpec
.
AssetPrice = 40; Volatility = 0.20; StockSpec = stockspec(Volatility,AssetPrice)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.2000
AssetPrice: 40
DividendType: []
DividendAmounts: 0
ExDividendDates: []
Calculate the price of an American barrier down in put option.
Strike = 45; OptSpec = 'put'; Barrier = 35; BarrierSpec = 'DI'; AmericanOpt = 1; Price = barrierbyls(RateSpec,StockSpec,OptSpec,Strike,Settle,Maturity,BarrierSpec,... Barrier,'NumTrials',2000,'AmericanOpt',AmericanOpt)
Price = 4.7306
Input Arguments
StockSpec
— Stock specification for underlying asset
structure
Stock specification for the underlying asset. For information
on the stock specification, see stockspec
.
stockspec
handles several
types of underlying assets. For example, for physical commodities
the price is StockSpec.Asset
, the volatility is StockSpec.Sigma
,
and the convenience yield is StockSpec.DividendAmounts
.
Data Types: struct
OptSpec
— Definition of option
character vector with values 'call'
or
'put'
| string array with values "call"
or
"put"
Definition of the option as 'call'
or 'put'
, specified
as a character vector or string array with a value of "call"
or
"put"
.
Data Types: char
| string
Strike
— Option strike price value
scalar numeric
Option strike price value, specified as a scalar numeric.
Data Types: double
Settle
— Settlement or trade date
datetime scalar | string scalar | date character vector
Settlement or trade date for the barrier option, specified as a scalar datetime, string, or date character vector.
To support existing code, barrierbyls
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, there is only one
ExerciseDates
on the option expiry date which is the maturity of the instrument.For an American option, use a
1
-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, the option can be exercised betweenSettle
and the single listed date inExerciseDates
.
To support existing code, barrierbyls
also
accepts serial date numbers as inputs, but they are not recommended.
BarrierSpec
— Barrier option type
character vector with values: 'UI'
, 'UO'
, 'DI'
, 'DO'
Barrier option type, specified as a character vector 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.
'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.
'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
Barrier
— Barrier level
scalar numeric
Barrier level, specified as a scalar numeric.
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 = barrierbyls(RateSpec,StockSpec,OptSpec,Strike,Settle,Maturity,BarrierSpec,Barrier,Rebate,1000)
AmericanOpt
— Option type
0
(European) (default) | values [0,1]
Option type, specified as the comma-separated pair consisting of
'AnericanOpt'
and a
NINST
-by-1
positive integer scalar flags with
values:
0
— European1
— American
Note
For American options, the Longstaff-Schwartz least squares method is used to calculate the early exercise premium. For more information on the least squares method, see https://people.math.ethz.ch/%7Ehjfurrer/teaching/LongstaffSchwartzAmericanOptionsLeastSquareMonteCarlo.pdf.
Data Types: double
Rebate
— Rebate value
0
(default) | scalar numeric
Rebate value, specified as the comma-separated pair consisting of 'Rebate'
and a scalar numeric. 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
NumTrials
— Number of independent sample paths
1000
(default) | nonnegative integer
Number of independent sample paths (simulation trials), specified as the
comma-separated pair consisting of 'NumTrials'
and a scalar
nonnegative integer.
Data Types: double
NumPeriods
— Number of simulation periods per trial
100
(default) | nonnegative integer
Number of simulation periods per trial, specified as the comma-separated pair
consisting of 'NumPeriods'
and a scalar nonnegative integer.
Data Types: double
Z
— Time series array of dependent random variates
vector
Time series array of dependent random variates, specified as the comma-separated pair
consisting of 'Z'
and a
NumPeriods
-by-1
-by-NumTrials
3-D time series array. The Z
value generates the Brownian motion
vector (that is, Wiener processes) that drives the simulation.
Data Types: double
Antithetic
— Indicator for antithetic sampling
false
(default) | scalar logical flag with value of true
or false
Indicator for antithetic sampling, specified as the comma-separated pair consisting of
'Antithetic'
and a value of true
or
false
.
Data Types: logical
Output Arguments
Price
— Expected prices for barrier options
matrix
Expected prices for barrier options, returned as a NINST
-by-1
matrix.
Paths
— Simulated paths of correlated state variables
vector
Simulated paths of correlated state variables, returned as a NumPeriods
+ 1
-by-1
-by-NumTrials
3-D
time series array of simulated paths of correlated state variables.
Each row of Paths
is the transpose of the state
vector X(t) at time t for
a given trial.
Times
— Observation times associated with simulated paths
vector
Observation times associated with simulated paths, returned
as a NumPeriods + 1
-by-1
column
vector of observation times associated with the simulated paths. Each
element of Times
is associated with the corresponding
row of Paths
.
Z
— Time series array of dependent random variates
vector
Time series array of dependent random variates, returned as a
NumPeriods
-by-1
-by-NumTrials
3-D array when Z
is specified as an input argument. If the
Z
input argument is not specified, then the Z
output argument contains the random variates generated internally.
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] Hull, J. Options, Futures and Other Derivatives. Fourth Edition. Prentice Hall, 2000, pp. 646–649.
[2] Aitsahlia, F., L. Imhof, and T.L. Lai. “Pricing and hedging of American knock-in options.” The Journal of Derivatives. Vol. 11.3 , 2004, pp. 44–50.
[3] Rubinstein M. and E. Reiner. “Breaking down the barriers.” Risk. Vol. 4(8), 1991, pp. 28–35.
Version History
Introduced in R2016bR2022b: Serial date numbers not recommended
Although barrierbyls
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.
See Also
barrierbyfd
| barriersensbyfd
| barrierbybls
| barriersensbybls
| barriersensbyls
| Barrier
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