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lookbackbyitt - Price lookback option using implied trinomial tree (ITT)

Syntax

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

Arguments

`ITTTree`	Stock tree structure created by `itttree`.
`OptSpec`	Number of instruments (`NINST`)-by-`1` cell array of strings `'call'` or `'put'`.
`Strike`	`NINST`-by-`1` vector of strike price values. Each row is the schedule for one option. To calculate the value of a floating-strike lookback option, specify `Strike` as `NaN`.
`Settle`	`NINST`-by-`1` vector of `Settle` dates. The settle date for every lookback option is set to the `ValuationDate` of the stock tree. The lookback 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.

Description

Price = lookbackbyitt(ITTTree, OptSpec, Strike, Settle, ExerciseDates, AmericanOpt) calculates the value of fixed- and floating-strike lookback options. Data arguments for lookbackbyitt are NINST-by-1 vectors, scalar, or empty. Fill unspecified entries in vectors with NaN. Only one data argument is required to create the instrument; the others may be omitted or passed as empty matrices [].

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

Note lookbackbyitt calculates values of fixed and floating strike lookback options. To compute the value of a floating strike lookback option, strike should be specified as NaN. Pricing of lookback options is done using Hull-White (1993). Consequently, for these options there are not unique prices on the tree nodes with the exception of the root node.

Examples

Price a lookback 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 = 'Call';
Strike = 85;
Settle = '01-Jan-2006';
ExerciseDates = '01-Jan-2008';

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

Price =

    0.5426

References

Hull, J., and A. White, "Efficient Procedures for Valuing European and American Path-Dependent Options," Journal of Derivatives, Fall 1993, pp. 21-31.