barrierbybls
Price European barrier options using Black-Scholes option pricing model
Syntax
Description
calculates European barrier option prices using the Black-Scholes option pricing model.Price
= barrierbybls(RateSpec
,StockSpec
,OptSpec
,Strike
,Settle
,ExerciseDates
,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.
adds optional name-value pair arguments. Price
= barrierbybls(___,Name,Value
)
Examples
Price an European Barrier Down Out Call Option
Compute the price of an European barrier down out call option using the following data:
Rates = 0.035; Settle = datetime(2015,1,1); Maturity = datetime(2016,1,1); 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: 0.9656
Rates: 0.0350
EndTimes: 1
StartTimes: 0
EndDates: 736330
StartDates: 735965
ValuationDate: 735965
Basis: 1
EndMonthRule: 1
Define a StockSpec
.
AssetPrice = 50; Volatility = 0.30; StockSpec = stockspec(Volatility, AssetPrice)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.3000
AssetPrice: 50
DividendType: []
DividendAmounts: 0
ExDividendDates: []
Calculate the price of an European barrier down out call option using the Black-Scholes option pricing model.
Strike = 50; OptSpec = 'call'; Barrier = 45; BarrierSpec = 'DO'; Price = barrierbybls(RateSpec, StockSpec, OptSpec, Strike, Settle,... Maturity, BarrierSpec, Barrier)
Price = 4.4285
Price European Barrier Down Out and Down In Call Options
Compute the price of European down out and down in call options using the following data:
Rates = 0.035; Settle = datetime(2015,1,1); Maturity = datetime(2016,1,1); 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: 0.9656
Rates: 0.0350
EndTimes: 1
StartTimes: 0
EndDates: 736330
StartDates: 735965
ValuationDate: 735965
Basis: 1
EndMonthRule: 1
Define a StockSpec
.
AssetPrice = 50; Volatility = 0.30; StockSpec = stockspec(Volatility, AssetPrice)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.3000
AssetPrice: 50
DividendType: []
DividendAmounts: 0
ExDividendDates: []
Calculate the price of European barrier down out and down in call options using the Black-Scholes Option Pricing model.
Strike = 50; OptSpec = 'Call'; Barrier = 45; BarrierSpec = {'DO';'DI'}; Price = barrierbybls(RateSpec, StockSpec, OptSpec, Strike, Settle, Maturity, BarrierSpec, Barrier)
Price = 2×1
4.4285
2.3301
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 an
NINST
-by-1
cell array of character vectors or string array with
values 'call'
or
'put'
or
"call"
or
"put"
.
Data Types: char
| cell
| string
Strike
— Option strike price value
numeric
Option strike price value, specified as an NINST
-by-1
matrix of numeric values, where 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 an
NINST
-by-1
vector using a datetime array, string
array, or date character vectors.
To support existing code, barrierbybls
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 an NINST
-by-1
vector
using a datetime array, string array, or date character vectors.
Note
For a European option, there is only one ExerciseDates
on the
option expiry date which is the maturity of the instrument.
To support existing code, barrierbybls
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 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.
'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
| cell
Barrier
— Barrier level
numeric
Barrier level, specified as
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 = barrierbybls(RateSpec,StockSpec,OptSpec,Strike,Settle,Maturity,BarrierSpec,Barrier,Rebate,1000)
Rebate
— Rebate value
0
(default) | numeric
Rebate value, specified as the comma-separated pair consisting of 'Rebate'
and
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
Output Arguments
Price
— Expected prices for barrier options
matrix
Expected prices for barrier options at time 0, returned as a NINST
-by-1
matrix.
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 barrierbybls
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
| barrierbyls
| barriersensbybls
| barriersensbyls
| Barrier
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