optstockbyitt

Price options on stocks using implied trinomial tree (ITT)

Syntax

[Price,PriceTree] = optstockbyitt(ITTTree,OptSpec,Strike,Settle,ExerciseDates)

[Price,PriceTree] = optstockbyitt(___,AmericanOpt)

Description

[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).

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

Examples

Price an American Stock Option Using an ITT Equity Tree

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.

load deriv.mat

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

Price a Bermudan Stock Option Using an ITT Equity Tree

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.

load deriv.mat;

% 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

ITTTree — Stock tree structure

structure

Stock tree structure, specified by using itttree.

Data Types: struct

OptSpec — Definition of option

character vector with value 'call' or 'put' | cell array of character vectors with values 'call' or 'put'

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

Data Types: char | cell

Strike — Option strike price values

nonnegative integer

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

Settle — Settlement date or trade date

datetime array | string array | date character vector

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.

ExerciseDates — Option exercise dates

datetime array | string array | date character vector

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.

AmericanOpt — Option type

0 European or Bermuda (default) | integer with values of 0 or 1

(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

Price — Expected price of option at time 0

vector

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

PriceTree — Structure containing trees of vectors of instrument prices for each node

structure

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.

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: $$\max (St-K,0)$$

• For a put: $$\max (K-St,0)$$

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] Chriss, Neil A., E. Derman, and I. Kani. “Implied trinomial trees of the volatility smile.” Journal of Derivatives. 1996.

Version History

Introduced in R2007a

R2022b: Serial date numbers not recommended

Although optstockbyitt 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.