Learn more about Financial Derivatives Toolbox

barrierbyeqp - Price barrier option from EQP binomial tree

Syntax

[Price, PriceTree] = barrierbyeqp(EQPTree, OptSpec, Strike, ExerciseDates, AmericanOpt, BarrierSpec, Barrier, Rebate, Options)

Arguments

`EQPTree`	Stock tree structure created by `eqptree`.
`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 barrier option is set to the valuation date of the stock tree. The barrier 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`	If `AmericanOpt = 0`, `NaN`, or is unspecified, the option is a European option. If `AmericanOpt = 1`, the option is an American option.
`BarrierSpec`	List of string values: `'UI'`: Up Knock In `'UO'`: Up Knock Out `'DI'`: Down Knock In `'DO'`: Down Knock Out
`Barrier`	Vector of barrier values.
`Rebate`	(Optional) `NINST`-by-`1` matrix of rebate values. Default = 0. For Knock-in options, the rebate is paid at expiry. For Knock-out options, the rebate is paid when the barrier is reached.
`Options`	(Optional) Derivatives pricing options structure created with `derivset`.

See instbarrier for a description of barrier contract arguments.

Description

[Price, PriceTree] = barrierbyeqp(EQPTree, OptSpec, Strike,ExerciseDates, AmericanOpt, BarrierSpec, Barrier, Rebate,Options) computes the price of barrier options using an equal probabilities binomial tree.

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

PriceTree is a tree structure with a vector of instrument prices at each node.

Examples

Price a barrier option using an EQP equity tree.

Load the file deriv.mat, which provides EQPTree. The EQPTree 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 = 105;
Settle = '01-Jan-2003';
ExerciseDates = '01-Jan-2006';
AmericanOpt = 1;
BarrierSpec = 'UI';
Barrier = 102;

Price = barrierbyeqp(EQPTree, OptSpec, Strike, Settle, ... 
ExerciseDates, AmericanOpt, BarrierSpec, Barrier)

Price =

 12.2632

References

Derman, E., I. Kani, D. Ergener and I. Bardhan, "Enhanced Numerical Methods for Options with Barriers," Financial Analysts Journal, (Nov. - Dec. 1995), pp. 65-74.