barrierbyitt

Price barrier options using implied trinomial tree (ITT)

Syntax

[Price,PriceTree] = barrierbyitt(ITTTree,OptSpec,Strike,Settle,AmericanOpt,ExerciseDates,BarrierSpec,Barrier)

[Price,PriceTree] = barrierbyitt(___,Rebate,Options)

Description

[Price,PriceTree] = barrierbyitt(ITTTree,OptSpec,Strike,Settle,AmericanOpt,ExerciseDates,BarrierSpec,Barrier) calculates prices for barrier options using implied trinomial tree (ITT).

[Price,PriceTree] = barrierbyitt(___,Rebate,Options) adds optional arguments for Rebate and Options.

Examples

Price a Barrier Option Using an ITT Tree

This example shows how to price a barrier option using an ITT 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 = 'Call';
Strike =  85;
Settle = '01-Jan-2006';
ExerciseDates = '31-Dec-2008';
AmericanOpt = 1;
BarrierSpec = 'UI';
Barrier =  115;

Price = barrierbyitt(ITTTree,OptSpec,Strike,Settle,ExerciseDates,AmericanOpt,...
BarrierSpec,Barrier)

Price = 2.4074

Input Arguments

ITTTree — Stock tree structure

structure

Stock tree structure, specified by using itttree.

Data Types: struct

OptSpec — Definition of option

character vector with values 'call' or 'put' | cell array of character vectors with values 'call' or 'put'

Definition of an option as 'call' or 'put', specified as a NINST-by-1 cell array of character vector values.

Data Types: char | cell

Strike — Option strike price value

numeric

Option strike price value for a European or an American Option, specified as NINST-by-1 matrix of numeric values. Each row is the schedule for one option.

Data Types: double

Settle — Settlement or trade date

serial date number | date character vector

Settlement or trade date for the barrier option, specified as a NINST-by-1 matrix of serial date numbers or date character vectors. The Settle date for every barrier is set to the ValuationDate of the stock tree. The barrier argument Settle is ignored.

Data Types: double | char

ExerciseDates — Option exercise dates

serial date number | date character vector

Option exercise dates, specified as a serial date number or a date character vector:

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

• For an American option, use a NINST-by-2 vector of exercise date boundaries. For each instrument, the option can be exercised on any date between or including the pair of dates on that row. If only one non-NaN date is listed, or if ExerciseDates is an NINST-by-1, the option can be exercised between ValuationDate of the stock tree and the single listed date in ExerciseDates.

Data Types: double | char | cell

AmericanOpt — Option type

option type values 0 or 1

Option type, specified as NINST-by-1 flags with values:

• 0 — European

• 1 — American

Data Types: double

BarrierSpec — Barrier option type

character vector with values: 'UI', 'UO', 'DI', 'DO' | cell array of character vectors with values: 'UI', 'UO', 'DI', 'DO'

Barrier option type, specified as a character vector or a cell array of character vectors with the following values:

• 'UI' — Up Knock-in

  This option becomes effective when the price of the underlying asset passes above the barrier level. It gives the option holder the right, but not the obligation, to buy or sell (call/put) the underlying security at the strike price if the underlying asset goes above the barrier level during the life of the option. Note, barrierbyfd does not support American knock-in barrier options.

• 'UO' — Up Knock-out

  This option gives the option holder the right, but not the obligation, to buy or sell (call/put) the underlying security at the strike price as long as the underlying asset does not go above the barrier level during the life of the option. This option terminates when the price of the underlying asset passes above the barrier level. Usually, with an up-and-out option, the rebate is paid if the spot price of the underlying reaches or exceeds the barrier level.

• 'DI' — Down Knock-in

  This option becomes effective when the price of the underlying stock passes below the barrier level. It gives the option holder the right, but not the obligation, to buy or sell (call/put) the underlying security at the strike price if the underlying security goes below the barrier level during the life of the option. With a down-and-in option, the rebate is paid if the spot price of the underlying does not reach the barrier level during the life of the option. Note, barrierbyfd does not support American knock-in barrier options.

• 'DO' — Down Knock-up

  This option gives the option holder the right, but not the obligation, to buy or sell (call/put) the underlying asset at the strike price as long as the underlying asset does not go below the barrier level during the life of the option. This option terminates when the price of the underlying security passes below the barrier level. Usually the option holder receives a rebate amount if the option expires worthless.

Option	Barrier Type	Payoff if Barrier Crossed	Payoff if Barrier not Crossed
Call/Put	Down Knock-out	Worthless	Standard Call/Put
Call/Put	Down Knock-in	Call/Put	Worthless
Call/Put	Up Knock-out	Worthless	Standard Call/Put
Call/Put	Up Knock-in	Standard Call/Put	Worthless

Data Types: char | cell

Barrier — Barrier level

numeric

Barrier level, specified as an NINST-by-1 matrix of numeric values.

Data Types: double

Rebate — Rebate value

0 (default) | numeric

(Optional) Rebate value, specified as a NINST-by-1 matrix of numeric values. For Knock-in options, the Rebate is paid at expiry. For Knock-out options, the Rebate is paid when the Barrier is reached.

Data Types: double

Options — Derivatives pricing options

structure

(Optional) Derivatives pricing options, specified as structure that is created with derivset.

Data Types: struct

Output Arguments

Price — Expected prices for barrier options at time 0

vector

Expected prices for barrier options at time 0, returned as a NINST-by-1 vector.

PriceTree — Structure with vector of barrier option prices at each node

tree structure

Structure with a vector of barrier option prices at each node, returned as a tree structure.

PriceTree is a MATLAB^® structure of trees containing vectors of instrument prices and a vector of observation times for each node.

PriceTree.PTree contains the prices.

PriceTree.tObs contains the observation times.

PriceTree.dObs contains the observation dates.

More About

Barrier Option

A Barrier option has not only a strike price but also a barrier level and sometimes a rebate.

A rebate is a fixed amount that is paid if the option cannot be exercised because the barrier level has been reached or not reached. The payoff for this type of option depends on whether the underlying asset crosses the predetermined trigger value (barrier level), indicated by Barrier, during the life of the option. For more information, see Barrier Option.

References

[1] 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.