barrierbystt

Price barrier options using standard trinomial tree

Syntax

[Price,PriceTree] = barrierbystt(STTTree,OptSpec,Strike,Settle,ExerciseDates,AmericanOpt,BarrierSpec,Barrier)

[Price,PriceTree] = barrierbystt(___,Name,Value)

Description

[Price,PriceTree] = barrierbystt(STTTree,OptSpec,Strike,Settle,ExerciseDates,AmericanOpt,BarrierSpec,Barrier) prices barrier options using a standard trinomial (STT) 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.

[Price,PriceTree] = barrierbystt(___,Name,Value) prices barrier options using a standard trinomial (STT) tree with an optional name-value pair argument for Rebate and Options.

Examples

Price a Barrier Option Using the Standard Trinomial Tree Model

Create a RateSpec.

StartDates = datetime(2009,1,1); 
EndDates = datetime(2013,1,1); 
Rates = 0.035; 
Basis = 1; 
Compounding = -1;
RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates,...
'EndDates', EndDates, 'Rates', Rates,'Compounding', Compounding, 'Basis', Basis)

RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.8694
            Rates: 0.0350
         EndTimes: 4
       StartTimes: 0
         EndDates: 735235
       StartDates: 733774
    ValuationDate: 733774
            Basis: 1
     EndMonthRule: 1

Create a StockSpec.

AssetPrice = 85; 
Sigma = 0.15; 
StockSpec = stockspec(Sigma, AssetPrice)

StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1500
         AssetPrice: 85
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Create an STTTree.

NumPeriods = 4;
TimeSpec = stttimespec(StartDates, EndDates, 4);
STTTree = stttree(StockSpec, RateSpec, TimeSpec)

STTTree = struct with fields:
       FinObj: 'STStockTree'
    StockSpec: [1×1 struct]
     TimeSpec: [1×1 struct]
     RateSpec: [1×1 struct]
         tObs: [0 1 2 3 4]
         dObs: [733774 734139 734504 734869 735235]
        STree: {[85]  [110.2179 85 65.5520]  [142.9174 110.2179 85 65.5520 50.5537]  [185.3182 142.9174 110.2179 85 65.5520 50.5537 38.9870]  [240.2985 185.3182 142.9174 110.2179 85 65.5520 50.5537 38.9870 30.0668]}
        Probs: {[3×1 double]  [3×3 double]  [3×5 double]  [3×7 double]}

Define the barrier option and compute the price.

Settle = datetime(2009,1,1);
ExerciseDates = datetime(2012,1,1);
OptSpec =  'call';
Strike = 105;
AmericanOpt = 1;
BarrierSpec = 'UI';
Barrier = 115;

Price= barrierbystt(STTTree, OptSpec, Strike, Settle, ExerciseDates,...
AmericanOpt, BarrierSpec, Barrier)

Price = 
3.7977

Input Arguments

STTTree — Stock tree structure for standard trinomial tree

structure

Stock tree structure for a standard trinomial tree, specified by using stttree.

Data Types: struct

OptSpec — Definition of option

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

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

Data Types: char | cell

Strike — European or American option strike price value

nonnegative numeric

European or American option strike price value, specified with a nonnegative integer using a NINST-by-1 matrix of nonnegative numeric values. Each row is the schedule for one option. To compute the value of a floating-strike barrier option, Strike should be specified as NaN. Floating-strike barrier options are also known as average strike options.

Data Types: double

Settle — Settlement date or trade date

datetime array | string array | date character vector

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

Note

The Settle date for every barrier option is set to the ValuationDate of the stock tree. The barrier argument, Settle, is ignored.

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

ExerciseDates — Option exercise dates

datetime array | string array | date character vector

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

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

• For an American option, use a NINST-by-2 vector of exercise date boundaries. 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 a NINST-by-1 cell array of character vectors, the option can be exercised between ValuationDate of the stock tree and the single listed ExerciseDates.

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

AmericanOpt — Option type

scalar with values [0,1]

Option type, specified as an NINST-by-1 matrix of 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 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. 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 levels

numeric

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

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: Price = barrierbystt(STTTree,OptSpec,Strike,Settle,ExerciseDates,1,'UI',115,'Rebate',25)

Rebate — Rebate values

0 (default) | numeric

Rebate values, specified as the comma-separated pair consisting of 'Rebate' and 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

Derivatives pricing options, specified as the comma-separated pair consisting of 'Options' and a structure that is created with derivset.

Data Types: struct

Output Arguments

Price — Expected prices for barrier options at time 0

matrix

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

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 is a type of exotic option whose existence or payoff depends on the price of the underlying asset reaching a certain barrier level during the option's life.

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 in R2015b

R2022b: Serial date numbers not recommended

Although barrierbystt supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.