barrierbybls

Price European barrier options using Black-Scholes option pricing model

Syntax

Price = barrierbybls(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,BarrierSpec,Barrier)

Price = barrierbybls(___,Name,Value)

Description

Price = barrierbybls(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,BarrierSpec,Barrier) calculates European barrier option prices using the Black-Scholes option pricing model.

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 = barrierbybls(___,Name,Value) adds optional name-value pair arguments.

Examples

Price an European Barrier Down Out Call Option

Compute the price of an European barrier down out call option using the following data:

Rates = 0.035;
Settle = datetime(2015,1,1);
Maturity = datetime(2016,1,1);
Compounding = -1;
Basis = 1;

Define a RateSpec.

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates', Maturity, ...
'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis)

RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9656
            Rates: 0.0350
         EndTimes: 1
       StartTimes: 0
         EndDates: 736330
       StartDates: 735965
    ValuationDate: 735965
            Basis: 1
     EndMonthRule: 1

Define a StockSpec.

AssetPrice = 50;
Volatility = 0.30;
StockSpec = stockspec(Volatility, AssetPrice)

StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.3000
         AssetPrice: 50
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Calculate the price of an European barrier down out call option using the Black-Scholes option pricing model.

Strike = 50;
OptSpec = 'call';
Barrier = 45;
BarrierSpec = 'DO';

Price = barrierbybls(RateSpec, StockSpec, OptSpec, Strike, Settle,...
Maturity,  BarrierSpec, Barrier)

Price = 
4.4285

Price European Barrier Down Out and Down In Call Options

Compute the price of European down out and down in call options using the following data:

Rates = 0.035;
Settle = datetime(2015,1,1);
Maturity = datetime(2016,1,1);
Compounding = -1;
Basis = 1;

Define a RateSpec.

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates', Maturity, ...
'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis)

RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9656
            Rates: 0.0350
         EndTimes: 1
       StartTimes: 0
         EndDates: 736330
       StartDates: 735965
    ValuationDate: 735965
            Basis: 1
     EndMonthRule: 1

Define a StockSpec.

AssetPrice = 50;
Volatility = 0.30;
StockSpec = stockspec(Volatility, AssetPrice)

StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.3000
         AssetPrice: 50
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Calculate the price of European barrier down out and down in call options using the Black-Scholes Option Pricing model.

Strike = 50;
OptSpec = 'Call';
Barrier = 45;
BarrierSpec = {'DO';'DI'};

Price = barrierbybls(RateSpec, StockSpec, OptSpec, Strike, Settle, Maturity,  BarrierSpec, Barrier)

Price = 2×1

    4.4285
    2.3301

Input Arguments

RateSpec — Interest-rate term structure

structure

Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

StockSpec — Stock specification for underlying asset

structure

Stock specification for the underlying asset. For information on the stock specification, see stockspec.

stockspec handles several types of underlying assets. For example, for physical commodities the price is StockSpec.Asset, the volatility is StockSpec.Sigma, and the convenience yield is StockSpec.DividendAmounts.

Data Types: struct

OptSpec — Definition of option

character vector with values 'call' or 'put' | string array with values "call" or "put"

Definition of the option as 'call' or 'put', specified as an NINST-by-1 cell array of character vectors or string array with values 'call' or 'put' or "call" or "put".

Data Types: char | cell | string

Strike — Option strike price value

numeric

Option strike price value, specified as an NINST-by-1 matrix of numeric values, where each row is the schedule for one option.

Data Types: double

Settle — Settlement or trade date

datetime array | string array | date character vector

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

To support existing code, barrierbybls 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 an NINST-by-1 vector using a datetime array, string array, or date character vectors.

Note

For a European option, there is only one ExerciseDates on the option expiry date which is the maturity of the instrument.

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

BarrierSpec — Barrier option type

character vector with values: 'UI', 'UO', 'DI', 'DO'

Barrier option type, specified as 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 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.

• '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 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 = barrierbybls(RateSpec,StockSpec,OptSpec,Strike,Settle,Maturity,BarrierSpec,Barrier,Rebate,1000)

Rebate — Rebate value

0 (default) | numeric

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

Output Arguments

Price — Expected prices for barrier options

matrix

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

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] Hull, J. Options, Futures and Other Derivatives Fourth Edition. Prentice Hall, 2000, pp. 646–649.

[2] Aitsahlia, F., L. Imhof, and T.L. Lai. “Pricing and hedging of American knock-in options.” The Journal of Derivatives. Vol. 11.3, 2004, pp. 44–50.

[3] Rubinstein M. and E. Reiner. “Breaking down the barriers.” Risk. Vol. 4(8), 1991, pp. 28–35.

Version History

Introduced in R2016b

R2022b: Serial date numbers not recommended

Although barrierbybls 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.