asianbyitt

Price Asian options using implied trinomial tree (ITT)

Syntax

Price = asianbyitt(ITTTree,OptSpec,Strike,Settle,ExerciseDates)

Price = asianbyitt(___,AmericanOpt,AvgType,AvgPrice,AvgDate)

Description

Price = asianbyitt(ITTTree,OptSpec,Strike,Settle,ExerciseDates) prices Asian options using an implied trinomial tree (ITT).

Price = asianbyitt(___,AmericanOpt,AvgType,AvgPrice,AvgDate) adds optional arguments for AmericanOpt, AvgType, AvgPrice, and AvgDate.

Examples

Price a Floating-Strike Asian Option Using an ITT Equity Tree

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

load deriv.mat;

OptSpec = 'put';
Strike = NaN;
Settle = datetime(2006,1,1);
ExerciseDates = datetime(2007,1,1);

Price = asianbyitt(ITTTree, OptSpec, Strike, Settle, ExerciseDates)

Price = 1.0778

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 character vector or a cell array of character vectors.

Data Types: char | cell

Strike — Option strike price value

matrix of nonnegative integers

Option strike price value, specified with a nonnegative integer using a NINST-by-1 matrix of strike price values.

To compute the value of a floating-strike Asian option, Strike must be specified as NaN. Floating-strike Asian options are also known as average strike options.

Data Types: double

Settle — Settlement date or trade date

datetime array | string array | date character vector

Settlement date or trade date for the Asian option, specified as a NINST-by-1 matrix of settlement or trade dates using a datetime array, string array, or date character vectors.

Note

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

To support existing code, asianbyitt 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 vector:

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

• For an American option, use a NINST-by-2 vector of exercise date boundaries. The option can be exercised on any tree 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.

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

AmericanOpt — Option type

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

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

• 0 — European

• 1 — American

Data Types: double

AvgType — Average types

arithmetic (default) | character vector with values of arithmetic or geometric

Average types, specified as arithmetic for arithmetic average, or geometric for geometric average.

Data Types: char

AvgPrice — Average price of underlying asset at Settle

scalar numeric

Average price of underlying asset at Settle, specified as a scalar numeric.

Note

Use this argument when AvgDate < Settle.

Data Types: double

AvgDate — Date averaging period begins

datetime scalar | string scalar | date character vector

Date averaging period begins, specified as a scalar datetime, string, or date character vector.

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

Output Arguments

Price — Expected prices for Asian options at time 0

vector

Expected prices for Asian options at time 0, returned as a NINST-by-1 vector. Pricing of Asian options is done using Hull-White (1993). Therefore, for these options there are no unique prices on the tree nodes except for the root node.

More About

Asian Option

An Asian option is a path-dependent option with a payoff linked to the average value of the underlying asset during the life (or some part of the life) of the option.

Asian options are similar to lookback options in that there are two types of Asian options: fixed (average price option) and floating (average strike option). Fixed Asian options have a specified strike, while floating Asian options have a strike equal to the average value of the underlying asset over the life of the option. For more information, see Asian Option.

References

[1] Hull, J., and A. White. “Efficient Procedures for Valuing European and American Path-Dependent Options.” Journal of Derivatives. Vol. 1, pp. 21–31.

Version History

Introduced in R2007a

R2022b: Serial date numbers not recommended

Although asianbyitt 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.