optstockbyls
Price European, Bermudan, or American vanilla options using Monte Carlo simulations
Syntax
Description
returns vanilla option prices using the Longstaff-Schwartz model.
Price
= optstockbyls(RateSpec
,StockSpec
,OptSpec
,Strike
,Settle
,ExerciseDates
)optstockbyls
computes prices of European, Bermudan, and American
vanilla options.
For American and Bermudan options, the Longstaff-Schwartz least squares method is used to calculate the early exercise premium.
Note
Alternatively, you can use the Vanilla
object to price
vanilla options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
adds
optional name-value pair arguments.Price
= optstockbyls(___,Name,Value
)
Examples
Compute the Price of European Vanilla Option
Define the RateSpec
.
StartDates = datetime(2013,1,1); EndDates = datetime(2015,1,1); Rates = 0.05; RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates, ... 'EndDates', EndDates, 'Rates', Rates)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 2
Disc: 0.9060
Rates: 0.0500
EndTimes: 4
StartTimes: 0
EndDates: 735965
StartDates: 735235
ValuationDate: 735235
Basis: 0
EndMonthRule: 1
Define the StockSpec
for the asset.
AssetPrice = 100; Sigma = 0.1; StockSpec = stockspec(Sigma, AssetPrice)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.1000
AssetPrice: 100
DividendType: []
DividendAmounts: 0
ExDividendDates: []
Define the European vanilla option.
OptSpec = 'put';
Settle = datetime(2013,1,1);
ExerciseDates = datetime(2015,1,1);
Strike = 105;
Compute the European vanilla option price using the Longstaff-Schwartz model.
Antithetic = true; Price = optstockbyls(RateSpec, StockSpec, OptSpec, Strike, Settle, ... ExerciseDates, 'Antithetic', Antithetic)
Price = 3.2292
Compute the Price of Bermudan Vanilla Option
Define the RateSpec
.
StartDates = datetime(2013,1,1); EndDates = datetime(2015,1,1); Rates = 0.05; RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates, ... 'EndDates', EndDates, 'Rates', Rates)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 2
Disc: 0.9060
Rates: 0.0500
EndTimes: 4
StartTimes: 0
EndDates: 735965
StartDates: 735235
ValuationDate: 735235
Basis: 0
EndMonthRule: 1
Define the StockSpec
for the asset.
AssetPrice = 100; Sigma = 0.1; StockSpec = stockspec(Sigma, AssetPrice)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.1000
AssetPrice: 100
DividendType: []
DividendAmounts: 0
ExDividendDates: []
Define the Bermudan vanilla option.
OptSpec = 'put';
Settle = datetime(2013,1,1);
Strike = [105,106];
ExerciseDates = {datetime(2014,1,1),datetime(2015,1,1)};
Compute the Bermudan vanilla option price using the Longstaff-Schwartz model.
Price = optstockbyls(RateSpec, StockSpec, OptSpec, Strike, Settle, ExerciseDates)
Price = 4.5126
Input Arguments
StockSpec
— Stock specification for underlying asset
structure
OptSpec
— Definition of option
character vector with value 'call'
or
'put'
Definition of option, specified as 'call'
or
'put'
using a character vector.
Data Types: char
Strike
— Option strike price values
nonnegative scalar integer
Option strike price value, specified with nonnegative scalar integer:
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 date or trade date
datetime scalar | string scalar | date character vector
Settlement date or trade date for the vanilla option, specified as a scalar datetime, string, or date character vector.
To support existing code, optstockbyls
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 as follows:
For a European option, use a
1
-by-1
vector of dates. For a European option, there is only oneExerciseDates
on the option expiry date.For a Bermuda option, use a
1
-by-NSTRIKES
vector of dates.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, or ifExerciseDates
is a1
-by-1
cell array of character vectors, the option can be exercised betweenSettle
and the single listedExerciseDates
.
To support existing code, optstockbyls
also
accepts serial date numbers as inputs, but they are not recommended.
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 =
optstockbyls(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'AmericanOpt','1','NumTrials','2000')
AmericanOpt
— Option type
0
European or Bermuda (default) | scalar with values [0,1]
Option type, specified as the comma-separated pair consisting of
'AmericanOpt'
and positive integer scalar flags with values:
0
— European or Bermuda1
— American
Note
For American and Bermudan 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
NumTrials
— Simulation trials
1000
(default) | scalar
Simulation trials, specified as a scalar number of independent sample paths.
Data Types: double
NumPeriods
— Simulation periods per trial
100
(default) | scalar
Simulation periods per trial, specified as a scalar number.
NumPeriods
is considered only when pricing European vanilla
options. For American and Bermuda vanilla options, NumPeriod
is
equal to the number of Exercise
days during the life of the
option.
Data Types: double
Z
— Dependent random variates
scalar | nonnegative integer
Dependent random variates used to generate the Brownian motion vector (that is,
Wiener processes) that drive the simulation, specified as a be
NumPeriods
-by-1
-by-NumTrials
3-D time series array.
Data Types: double
Antithetic
— Indicator for antithetic sampling
false
(default) | logical flag with value of true
or
false
Indicator for antithetic sampling, specified with a value of
true
or false
.
Data Types: logical
Output Arguments
Price
— Expected price of vanilla option
scalar
Expected price of the vanilla option, returned as a
1
-by-1
scalar.
Path
— 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. 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
— Dependent random variates
vector
Dependent random variates, if Z
is specified as an optional input
argument, the same value is returned. Otherwise, Z
contains the
random variates generated internally.
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.
Version History
Introduced in R2013bR2022b: Serial date numbers not recommended
Although optstockbyls
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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