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# barrierbycrr

Price barrier option from Cox-Ross-Rubinstein binomial tree

## Description

example

[Price,PriceTree] = barrierbycrr(CRRTree,OptSpec,Strike,Settle,AmericanOpt,ExerciseDates,BarrierSpec,Barrier) calculates prices for barrier options using a Cox-Ross-Rubinstein binomial tree.

Note

Alternatively, you can use the Barrier object to price Barrier options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

example

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

## Examples

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This example shows how to price a barrier option using a CRR binomial tree by loading 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;

OptSpec = 'Call';
Strike = 105;
Settle = datetime(2003,1,1);
ExerciseDates = datetime(2006,1,1);
AmericanOpt = 1;
BarrierSpec = 'UI';
Barrier = 102;

Price = barrierbycrr(CRRTree, OptSpec, Strike, Settle, ...
ExerciseDates, AmericanOpt, BarrierSpec, Barrier)
Price = 12.1272

## Input Arguments

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Stock tree structure, specified by using crrtree.

Data Types: struct

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

Data Types: char | cell

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

Data Types: double

Settlement or trade date for the barrier option, specified as a NINST-by-1 vector using a datetime array, string array, 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.

To support existing code, barrierbycrr also accepts serial date numbers as inputs, but they are not recommended.

Option exercise dates, specified as a datetime array, string array, or date character vector:

• For a European option, use a 1-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 1-by-2 vector of exercise date boundaries. 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 a NINST-by-1, the option can be exercised between ValuationDate of the stock tree and the single listed date in ExerciseDates.

To support existing code, barrierbycrr also accepts serial date numbers as inputs, but they are not recommended.

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

• 0 — European

• 1 — American

Data Types: double

Barrier option type, specified as a character vector or an NINST-by-1 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.

• 'UO' — Up Knock-out

This option gives the option holder the right, but not the obligation, to buy/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.

OptionBarrier TypePayoff if Barrier CrossedPayoff if Barrier not Crossed
Call/PutDown Knock-outWorthlessStandard Call/Put
Call/PutDown Knock-inCall/PutWorthless
Call/PutUp Knock-outWorthlessStandard Call/Put
Call/PutUp Knock-inStandard Call/PutWorthless

Data Types: char | cell

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

Data Types: double

(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

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

Data Types: struct

## Output Arguments

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

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

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### 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.

## Version History

Introduced before R2006a

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