optstockbyfd
Calculate vanilla option prices using finite difference method
Syntax
Description
[
calculates
vanilla option prices using the finite difference method. Price
,PriceGrid
,AssetPrices
,Times
]
= optstockbyfd(RateSpec
,StockSpec
,OptSpec
,Strike
,Settle
,ExerciseDates
)
[
adds optional name-value pair arguments. Price
,PriceGrid
,AssetPrices
,Times
]
= optstockbyfd(___,Name,Value
)
Examples
Price a Vanilla Call Option Using Finite Difference Method
Create a RateSpec
.
AssetPrice = 50; Strike = 45; Rate = 0.035; Volatility = 0.30; Settle = '01-Jan-2015'; Maturity = '01-Jan-2016'; 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 of a European vanilla call option using the finite difference method.
ExerciseDates = 'may-1-2015'; OptSpec = 'Call'; Price = optstockbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)
Price = 6.7352
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 values 'call'
or
'put'
.
Data Types: char
| string
Strike
— Option strike price value
nonnegative scalar | nonnegative vector
Option strike price value, specified as a nonnegative scalar or vector.
For a European option, use a scalar of strike price.
For a Bermuda option, use a
1
-by-NSTRIKES
vector of strike prices.For an American option, use a scalar of strike price.
Data Types: single
| double
Settle
— Settlement or trade date
serial date number | date character vector | datetime object
Settlement 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 dates
serial date number | date character vector | datetime object
Option exercise dates, specified as a serial date number, a date character vector, or a datetime object:
For a European option, use a
1
-by-1
vector of dates, specified as a nonnegative scalar integer, a date character vector, or a datetime object. For a Bermuda option, use a1
-by-NSTRIKES
vector of dates, specified as a nonnegative scalar integer, date character vector, or datetime object.For an American option, use a
1
-by-2
cell array of date character vectors. 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 a1
-by-1
vector of serial date numbers or a cell array of date character vectors, the option can be exercised betweenSettle
and the single listed date inExerciseDates
.
Data Types: double
| char
| cell
| datetime
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 =
optstockbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'AssetGridSize',1000)
AssetGridSize
— Size of asset grid used for finite difference grid
400
(default) | positive scalar
Size of the asset grid used for a finite difference grid, specified as the comma-separated
pair consisting of 'AssetGridSize'
and a positive
scalar.
Data Types: double
AssetPriceMax
— Maximum price for price grid boundary
if unspecified, StockSpec
values
are calculated using asset distributions at maturity (default) | positive scalar
Maximum price for price grid boundary, specified as the comma-separated pair consisting of
'AssetPriceMax'
as a positive scalar.
Data Types: single
| double
TimeGridSize
— Size of time grid used for finite difference grid
100
(default) | positive scalar
Size of the time grid used for a finite difference grid, specified as the comma-separated pair
consisting of 'TimeGridSize'
and a positive
scalar.
Data Types: double
AmericanOpt
— Option type
0
(European/Bermuda) (default) | scalar with values [0,1]
Option type, specified as the comma-separated pair consisting of
'AmericanOpt'
and
NINST
-by-1
positive integer
scalar flags with values:
0
— European/Bermuda1
— American
Data Types: double
Output Arguments
Price
— Expected prices for vanilla options
scalar
Expected prices for vanilla options, returned as a 1
-by-1
matrix.
PriceGrid
— Grid containing prices calculated by finite difference method
grid
Grid containing prices calculated by the finite difference method,
returned as a grid that is two-dimensional with size PriceGridSize*length(Times)
.
The number of columns does not have to be equal to the TimeGridSize
,
because ex-dividend 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
vector
Times corresponding to second dimension of the PriceGrid
,
returned as a vector.
More About
Vanilla Option
A vanilla option is a category of options that includes only the most standard components.
A vanilla option has an expiration date and straightforward strike price. American-style options and European-style options are both categorized as vanilla options.
The payoff for a vanilla option is as follows:
For a call:
For a put:
where:
St is the price of the underlying asset at time t.
K is the strike price.
For more information, see Vanilla Option.
References
[1] Haug, E. G., J. Haug, and A. Lewis. "Back to basics: a new approach to the discrete dividend problem." Vol. 9, Wilmott magazine, 2003, pp. 37–47.
[2] Wu, L. and Y. K. Kwok. "A front-fixing finite difference method for the valuation of American options." Journal of Financial Engineering. Vol. 6.4, 1997, pp. 83–97.
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