# optstockbyitt

Price options on stocks using implied trinomial tree (ITT)

## Description

example

[Price,PriceTree] = optstockbyitt(ITTTree,OptSpec,Strike,Settle,ExerciseDates) returns the price of a European, Bermuda, or American stock option from an implied trinomial tree (ITT).

example

[Price,PriceTree] = optstockbyitt(___,AmericanOpt) adds an optional argument for AmericanOpt.

## Examples

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This example shows how to price an American stock option using an ITT equity tree by loading the file deriv.mat, which provides the ITTTree. The ITTTree structure contains the stock specification and time information needed to price the American option.

OptSpec = 'Put';
Strike = 30;
Settle = datetime(2006,1,1);
ExerciseDates = datetime(2010,1,1);
AmericanOpt = 1;

Price = optstockbyitt(ITTTree, OptSpec, Strike, Settle,ExerciseDates, AmericanOpt)
Price = 0.1271

Load the file deriv.mat, which provides an ITTTree. The ITTTree structure contains the stock specification and time information needed to price the Bermudan option.

% Option
OptSpec = 'Put';
Strike = 30;
Settle = datetime(2006,1,1);
ExerciseDatesBerm= [datetime(2007,1,1) , datetime(2008,1,1) , datetime(2008,12,31) , datetime(2010,1,1)];

Price the Bermudan option.

Price = optstockbyitt(ITTTree, OptSpec, Strike, Settle, ExerciseDatesBerm)
Price =

0.1271

## Input Arguments

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Stock tree structure, specified by using itttree.

Data Types: struct

Definition of option, specified as 'call' or 'put' using a NINST-by-1 cell array of character vectors.

Data Types: char | cell

Option strike price value, specified with a NINST-by-1 or NINST-by-NSTRIKES depending on the option type:

• For a European option, use a NINST-by-1 vector of strike prices.

• For a Bermuda option, use aNINST-by-NSTRIKES matrix of strike prices. Each row is the schedule for one option. If an option has fewer than NSTRIKES exercise opportunities, the end of the row is padded with NaNs.

• For an American option, use a NINST-by-1 of strike prices.

Note

The interpretation of the Strike and ExerciseDates arguments depends upon the setting of the AmericanOpt argument. If AmericanOpt = 0, NaN, or is unspecified, the option is a European or Bermuda option. If AmericanOpt = 1, the option is an American option.

Data Types: double

Settlement date or trade date, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

Note

The Settle date for every option is set to the ValuationDate of the stock tree. The option argument Settle is ignored.

To support existing code, optstockbyitt also accepts serial date numbers as inputs, but they are not recommended.

Option exercise dates, specified as a NINST-by-1,NINST-by-2, or NINST-by-NSTRIKES vector using a datetime array, string array, or date character vectors, depending on the option type:

• For a European option, use a NINST-by-1 vector of dates. Each row is the schedule for one option. For a European option, there is only one ExerciseDates on the option expiry date.

• For a Bermuda option, use a NINST-by-NSTRIKES vector of dates. Each row is the schedule for one option.

• For an American option, use a NINST-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 NINST-by-1 vector, the option can be exercised between ValuationDate of the stock tree and the single listed ExerciseDates.

Note

The interpretation of the Strike and ExerciseDates arguments depends upon the setting of the AmericanOpt argument. If AmericanOpt = 0, NaN, or is unspecified, the option is a European or Bermuda option. If AmericanOpt = 1, the option is an American option.

To support existing code, optstockbyitt also accepts serial date numbers as inputs, but they are not recommended.

(Optional) Option type, specified as NINST-by-1 vector of integer flags with values:

• 0 — European or Bermuda

• 1 — American

Data Types: single | double

## Output Arguments

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Expected price of the vanilla option at time 0, returned as a NINST-by-1 vector.

Structure containing trees of vectors of instrument prices and a vector of observation times for each node. Values are:

• PriceTree.PTree contains the clean prices.

• PriceTree.tObs contains the observation times.

• PriceTree.dObs contains the observation dates.

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### 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: $\mathrm{max}\left(St-K,0\right)$

• For a put: $\mathrm{max}\left(K-St,0\right)$

where:

St is the price of the underlying asset at time t.

K is the strike price.