Financial Derivatives Toolbox™

asianbyitt - Price Asian options using implied trinomial tree (ITT)

Syntax

Price = asianbyitt(ITTTree, OptSpec, Strike, Settle, ExerciseDates, AmericanOpt, AvgType, AvgPrice, AvgDate)

Arguments

`ITTTree`	Stock tree structure created by `itttree`.
`OptSpec`	`NINST`-by-`1` list of string values `'call'` or `'put'`.
`Strike`	`NINST`-by-`1` vector of strike price values. Each row represents the schedule for one option.
`Settle`	`NINST`-by-`1` vector of `Settle` dates. The settle date for every Asian option is set to the valuation date of the stock tree. The Asian argument `Settle` is ignored.
`ExerciseDates`	For a European option (`AmericanOpt = 0`): `NINST`-by-`1` vector of exercise dates. Each row is the schedule for one option. For a European option, there is only one exercise date which is the option expiry date. For an American option (`AmericanOpt = 1`): `NINST`-by-`2` vector of exercise date boundaries. For each instrument, 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 `NINST`-by-`1`, the option can be exercised between the valuation date of the stock tree and the single listed exercise date.
`AmericanOpt`	(Optional) If `AmericanOpt = 0`, `NaN`, or is unspecified, the option is a European option. If `AmericanOpt = 1`, the option is an American option.
`AvgType`	(Optional) String = `'arithmetic'` for arithmetic average (default) or `'geometric'` for geometric average.
`AvgPrice`	(Optional) Scalar representing the average price of the underlying asset at `Settle`. This argument is used when `AvgDate < Settle`. Default is the current stock price.
`AvgDate`	(Optional) Scalar representing the date on which the averaging period begins.

Description

Price = asianbyitt(ITTTree, OptSpec, Strike, Settle, ExerciseDates, AmericanOpt, AvgType, AvgPrice, AvgDate)calculates the value of fixed- and floating-strike Asian options. To compute the value of a floating-strike Asian option, specify Strike as NaN. Fixed-strike Asian options are also known as average price options. Floating-strike Asian options are also known as average strike options.

Price is a NINST-by-1 vector of expected prices at time 0.

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

Examples

Price a floating-strike Asian option using an ITT equity tree.

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

load deriv.mat;

Set the required values. Other arguments will use defaults.

OptSpec = 'put';
Strike = NaN;
Settle = '01-Jan-2006';
ExerciseDates = '01-Jan-2007';

Use asianbyitt to compute the price of the option.

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

Price = 

 1.0778

References