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asianbycrr - Price Asian option from CRR binomial tree

Syntax

Price = asianbycrr(CRRTree, OptSpec, Strike, Settle, ExerciseDates, AmericanOpt, AvgType, AvgPrice, AvgDate)

Arguments

`CRRTree`	Stock tree structure created by `crrtree`.
`OptSpec`	`NINST`-by-`1` list of string values `'Call'` or `'Put'`.
`Strike`	`NINST`-by-`1` vector of strike price values. Each row is 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, 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. Default = `Settle`.

Description

Price = asianbycrr(CRRTree, 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.

Asian options are priced using Hull-White (1993). Consequently, for these options only the root node contains a unique price.

Examples

Price a floating-strike Asian option using a CRR binomial tree.

Load the file deriv.mat, which provides CRRTree. The CRRTree 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-2003';
ExerciseDates = '01-Jan-2004';

Use asianbycrr to compute the price of the option.

Price = asianbycrr(CRRTree, OptSpec, Strike, Settle, ... 
ExerciseDates)

Price = 

 1.2177

References

Hull, J., and A. White, "Efficient Procedures for Valuing European and American Path-Dependent Options," Journal of Derivatives, Volume 1, pp. 21-31.