Calculate barrier option prices or sensitivities using finite difference method
[PriceSens,PriceGrid,AssetPrices,Times]
= barriersensbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,BarrierSpec,Barrier)
[PriceSens,PriceGrid,AssetPrices,Times]
= barriersensbyfd(___,Name,Value)
[
calculates European and American barrier option prices or sensitivities of a single
underlying asset using the finite difference method. PriceSens
,PriceGrid
,AssetPrices
,Times
]
= barriersensbyfd(RateSpec
,StockSpec
,OptSpec
,Strike
,Settle
,ExerciseDates
,BarrierSpec
,Barrier
)barrierbyfd
assumes that the barrier is continuously monitored.
[
adds optional namevalue pair arguments. PriceSens
,PriceGrid
,AssetPrices
,Times
]
= barriersensbyfd(___,Name,Value
)barriersesbyfd
assumes
that the barrier is continuously monitored.
Create a RateSpec
.
AssetPrice = 50; Strike = 45; Rate = 0.035; Volatility = 0.30; Settle = '01Jan2015'; Maturity = '01Jan2016'; Basis = 1; RateSpec = intenvset('ValuationDate',Settle,'StartDates',Settle,'EndDates',... Maturity,'Rates',Rate,'Compounding',1,'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
Create a StockSpec
.
StockSpec = stockspec(Volatility,AssetPrice)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.3000
AssetPrice: 50
DividendType: []
DividendAmounts: 0
ExDividendDates: []
Calculate the Price
, Delta
, and Theta
of a European Down and Out call option using the finite difference method.
Barrier = 40; BarrierSpec = 'DO'; OptSpec = 'Call'; OutSpec = {'price';'delta';'theta'}; [Price, Delta, Theta] = barriersensbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,... Maturity, BarrierSpec,Barrier,'Outspec',OutSpec)
Price = 8.5020
Delta = 0.8569
Theta = 1.8502
StockSpec
— Stock specification for underlying assetStock 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 'call'
or
'put'
 string array with values 'call'
or
'put'
Definition of an option as 'call'
or 'put'
, specified as
a character vector or string array with values "call"
or
"put"
.
Data Types: char
 string
Strike
— Option strike price valueOption strike price value, specified as a scalar numeric.
Data Types: double
Settle
— Settlement or trade dateSettlement or trade date for the barrier option, specified as a serial date number, a date character vector, or a datetime object.
Data Types: double
 char
 datetime
ExerciseDates
— Option exercise datesOption exercise dates, specified as a serial date number, a date character vector, or datetime object:
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
by2
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 nonNaN
date is listed, the option can be
exercised between Settle
and the single
listed date in ExerciseDates
.
Data Types: double
 char
 datetime
BarrierSpec
— Barrier option type'UI'
, 'UO'
, 'DI'
, 'DO'
Barrier option type, specified as a character vector with the following values:
'UI'
— Up Knockin
This 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
knockin barrier options.
'UO'
— Up Knockout
This 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 upandout option, the rebate is paid if the spot price of the underlying reaches or exceeds the barrier level.
'DI'
— Down Knockin
This 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 downandin 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
knockin barrier options.
'DO'
— Down Knockup
This 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 Knockout  Worthless  Standard Call/Put 
Call/Put  Down Knockin  Call/Put  Worthless 
Call/Put  Up Knockout  Worthless  Standard Call/Put 
Call/Put  Up Knockin  Standard Call/Put  Worthless 
Data Types: char
Barrier
— Barrier levelBarrier level, specified as a scalar numeric.
Data Types: double
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
PriceSens = barriersensbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,Maturity,BarrierSpec,Barrier,Rebate,1000,AmericanOpt,1)
'Rebate'
— Rebate value0
(default)  numericRebate value, specified as the commaseparated pair consisting of 'Rebate'
and a scalar numeric. For Knockin options, the
Rebate
is paid at expiry. For
Knockout
options, the Rebate
is paid when the Barrier
is reached.
Data Types: double
'OutSpec'
— Define outputs{'Price'}
(default)  character vector with values 'Price'
, 'Delta'
, 'Gamma'
, 'Vega'
, 'Lambda'
, 'Rho'
, 'Theta'
,
and 'All'
 cell array of character vectors with values 'Price'
, 'Delta'
, 'Gamma'
, 'Vega'
, 'Lambda'
, 'Rho'
, 'Theta'
,
and 'All'
Define outputs, specified as the commaseparated pair consisting of
'OutSpec'
and a NOUT

by1
or a
1
byNOUT
cell array of
character vectors with possible values of 'Price'
,
'Delta'
, 'Gamma'
,
'Vega'
, 'Lambda'
,
'Rho'
, 'Theta'
, and
'All'
.
OutSpec = {'All'}
specifies that the output
is Delta
, Gamma
, Vega
, Lambda
, Rho
, Theta
,
and Price
, in that order. This is the same as specifying OutSpec
to
include each sensitivity.
Example: OutSpec = {'delta','gamma','vega','lambda','rho','theta','price'}
Data Types: char
 cell
'AssetGridSize'
— Size of asset grid used for finite difference grid400
(default)  positive numericSize of the asset grid used for a finite difference grid, specified as the commaseparated
pair consisting of 'AssetGridSize'
and a scalar
positive numeric.
Data Types: double
'TimeGridSize'
— Size of time grid used for finite difference grid100
(default)  positive numericSize of the time grid used for a finite difference grid, specified as the commaseparated pair
consisting of 'TimeGridSize'
and a scalar positive
numeric.
Data Types: double
'AmericanOpt'
— Option type0
European (default)  integer with values 0
or
1
Option type, specified as the commaseparated pair consisting of
'AmericanOpt'
and a scalar flag with one of the
following values:
0
— European
1
— American
Data Types: logical
PriceSens
— Expected prices or sensitivities values for barrier optionsExpected prices or sensitivities (defined using OutSpec
)
for barrier options, returned as a NINST
by1
matrix.
PriceGrid
— Grid containing prices calculated by finite difference methodGrid containing prices calculated by the finite difference method,
returned as a twodimensional grid with size PriceGridSize*length(Times)
.
The number of columns does not have to be equal to the TimeGridSize
,
because exdividend dates in the StockSpec
are
added to the time grid. The price for t = 0
is
contained in PriceGrid(:, end)
.
Times
— Times corresponding to second dimension of PriceGrid
Times corresponding to the second dimension of the PriceGrid
,
returned as a vector.
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.
[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 knockin 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.
barrierbybls
 barrierbyfd
 barrierbyls
 barriersensbybls
 barriersensbyls
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