optstocksensbybaw
Calculate American options prices and sensitivities using Barone-Adesi and Whaley option pricing model
Syntax
Description
Examples
Compute an American Option Price and Sensitivities Using the Barone-Adesi and Whaley Option Pricing Model
Consider an American call option with an exercise price of $120. The option expires on Jan 1, 2018. The stock has a volatility of 14% per annum, and the annualized continuously compounded risk-free rate is 4% per annum as of Jan 1, 2016. Using this data, calculate the price of the American call, assuming the price of the stock is $125 and pays a dividend of 2%.
StartDate = datetime(2016,1,1); EndDate = datetime(2018,1,1); Basis = 1; Compounding = -1; Rates = 0.04;
Define the RateSpec
.
RateSpec = intenvset('ValuationDate',StartDate,'StartDate',StartDate,'EndDate',EndDate, ... 'Rates',Rates,'Basis',Basis,'Compounding',Compounding)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: -1
Disc: 0.9231
Rates: 0.0400
EndTimes: 2
StartTimes: 0
EndDates: 737061
StartDates: 736330
ValuationDate: 736330
Basis: 1
EndMonthRule: 1
Define the StockSpec
.
Dividend = 0.02;
AssetPrice = 125;
Volatility = 0.14;
StockSpec = stockspec(Volatility,AssetPrice,'Continuous',Dividend)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.1400
AssetPrice: 125
DividendType: {'continuous'}
DividendAmounts: 0.0200
ExDividendDates: []
Define the American option.
OptSpec = 'call';
Strike = 120;
Settle = datetime(2016,1,1);
Maturity = datetime(2018,1,1);
Compute the price and sensitivities for the American option.
OutSpec = {'price';'delta';'theta'}; [Price,Delta,Theta] = optstocksensbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'OutSpec',OutSpec)
Price = 14.5180
Delta = 0.6672
Theta = -3.1861
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
Settle
— Settlement date
datetime array | string array | date character vector
Settlement date for the American option, specified as a
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, optstocksensbybaw
also
accepts serial date numbers as inputs, but they are not recommended.
Maturity
— Maturity date
datetime array | string array | date character vector
Maturity date for the American option, specified as a
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, optstocksensbybaw
also
accepts serial date numbers as inputs, but they are not recommended.
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 NINST
-by-1
cell array of character vectors
or string arrays with values 'call'
or
'put'
.
Data Types: char
| string
Strike
— American option strike price value
nonnegative scalar | nonnegative vector
American option strike price value, specified as a nonnegative
scalar or NINST
-by-1
matrix
of strike price values. Each row is the schedule for one option.
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,Delta,Theta] = optstocksensbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'OutSpec',OutSpec)
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 comma-separated pair consisting
of 'OutSpec'
and a NOUT
- by-1
or
a 1
-by-NOUT
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
Output Arguments
PriceSens
— Expected prices or sensitivities for American options
matrix
Expected prices or sensitivities for American options, returned
as a NINST
-by-1
matrix.
Note
All sensitivities are evaluated by computing a discrete approximation of the partial derivative. This means that the option is revalued with a fractional change for each relevant parameter. The change in the option value divided by the increment is the approximated sensitivity value.
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] Barone-Aclesi, G. and Robert E. Whaley. “Efficient Analytic Approximation of American Option Values.” The Journal of Finance. Volume 42, Issue 2 (June 1987), 301–320.
[2] Haug, E. The Complete Guide to Option Pricing Formulas. Second Edition. McGraw-Hill Education, January 2007.
Version History
Introduced in R2017aR2022b: Serial date numbers not recommended
Although optstocksensbybaw
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.
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