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# optstockbyls

Price European, Bermudan, or American vanilla options using Longstaff-Schwartz model

## Syntax

• Price = optstockbyls(RateSpec,StockSpec,OptSpec,StrikeSettle,
ExerciseDates)
example
• Price = optstockbyls(___,Name,Value)
• [Price,Path,Times,Z] = optstockbyls(RateSpec,StockSpec,OptSpec,StrikeSettle,
ExerciseDates)
example
• [Price,Path,Times,Z] = optstockbyls(___,Name,Value)

## Description

example

Price = optstockbyls(RateSpec,StockSpec,OptSpec,StrikeSettle,
ExerciseDates)
returns vanilla option prices using the Longstaff-Schwartz model. 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.

Price = optstockbyls(___,Name,Value) returns vanilla option prices using the Longstaff-Schwartz model using optional name-value pair arguments. 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.

example

[Price,Path,Times,Z] = optstockbyls(RateSpec,StockSpec,OptSpec,StrikeSettle,
ExerciseDates)
returns vanilla option prices using the Longstaff-Schwartz model. 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.

[Price,Path,Times,Z] = optstockbyls(___,Name,Value) returns vanilla option prices using the Longstaff-Schwartz model using optional name-value pair arguments. 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.

## Examples

expand all

### Compute the Price of a Vanilla Option

Define the RateSpec.

```StartDates = 'Jan-1-2013';
EndDates = 'Jan-1-2015';
Rates = 0.05;
RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates, ...
'EndDates', EndDates, 'Rates', Rates)
```
```RateSpec =

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 =

FinObj: 'StockSpec'
Sigma: 0.1000
AssetPrice: 100
DividendType: []
DividendAmounts: 0
ExDividendDates: []

```

Define the vanilla option.

```OptSpec = 'put';
Settle = 'Jan-1-2013';
ExerciseDates = 'Jan-1-2015';
Strike = 105;
```

Compute the vanilla option price using the Longstaff-Schwartz model.

```Antithetic = true;
Price = optstockbyls(RateSpec, StockSpec, OptSpec, Strike, Settle, ...
ExerciseDates, 'Antithetic', Antithetic)
```
```Price =

3.2292

```

## Input Arguments

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### RateSpec — Interest-rate term structurestructure

Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

### StockSpec — Stock specification for underlying assetstructure

Stock specification for underlying asset, specified using StockSpec obtained from stockspec. For information on the stock specification, see stockspec.

stockspec can handle other types of underlying assets. For example, stocks, stock indices, and commodities.

Data Types: struct

### OptSpec — Definition of option string with value 'call' or 'put'

Definition of option, specified as 'call' or 'put' using a string.

Data Types: char

### Strike — Option strike price valuesnonnegative 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 datedate string | nonnegative scalar integer

Settlement date or trade date for the vanilla option, specified as a date string or nonnegative scalar integer.

Data Types: char

### ExerciseDates — Option exercise datesdate string | nonnegative integer

Option exercise dates, specified as a date string or nonnegative scalar integer:

• For a European option, use a 1-by-1 vector of dates. For a European option, there is only one ExerciseDates 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 if ExerciseDates is a 1-by-1 vector of serial date numbers or cell array of strings, the option can be exercised between Settle and the single listed ExerciseDates.

Data Types: char

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: Price = optstockbyls(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'AmericanOpt','1','NumTrials','2000')

### 'AmericanOpt' — Option type0 European or Bermuda (default) | scalar with values [0,1]

Option type, specified as positive integer scalar flags with values:

• 0 — European or Bermuda

• 1 — American

Data Types: single | double

### 'NumTrials' — Simulation trials1000 (default) | scalar

Simulation trials, specified as a scalar number of independent sample paths.

Data Types: double

### 'NumPeriods' — Simulation periods per trial100 (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 variatesTBD (default) | scalar | nonnegative integer

Dependent random variates used to generate the Brownian motion vector (i.e., Wiener processes) that drive the simulation, specified as a NumPeriods-by-2-by-NumTrials 3-D time series array.

Data Types: single | double

### 'Antithetic' — Indicator for antithetic samplingfalse (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

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### Price — Expected price of vanilla optionscalar

Expected price of the vanilla option, returned as a 1-by-1 scalar.

### Path — Simulated paths of correlated state variablesvector

Simulated paths of correlated state variables, returned as a (NumPeriods + 1)-by-2-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 pathsvector

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.

## See Also

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