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dbltouchsensbybls

Calculate prices and sensitivities for double one-touch and double no-touch binary options using Black-Scholes option pricing model

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Syntax

PriceSens = dbltouchsensbybls(RateSpec,StockSpec,Settle,Maturity,BarrierSpec,Barrier,Payoff)
PriceSens = dbltouchsensbybls(___,Name,Value)

Description

example

PriceSens= dbltouchsensbybls(RateSpec,StockSpec,Settle,Maturity,BarrierSpec,Barrier,Payoff)calculates prices and sensitivities for double one-touch and double no-touch binary options using the Black-Scholes option pricing model.

example

PriceSens= dbltouchsensbybls(___,Name,Value)specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

Examples

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Open Live Script

Compute the price and sensitivities for a double no-touch option using the following data:

AssetPrice = 105; Rate = 0.1; Volatility = 0.2; Settle ='01-Jan-2018'; Maturity ='01-Jul-2018';

Define theRateSpecusingintenvset.

RateSpec = intenvset('ValuationDate', Settle,'StartDates', Settle,'EndDates',...Maturity,'Rates', Rate,'Compounding', -1);

Define theStockSpecusingstockspec.

DividendType ="Continuous"; DividendYield = Rate - 0.03; StockSpec = stockspec(Volatility, AssetPrice, DividendType, DividendYield);

Define the sensitivities.

OutSpec = {'price','delta','gamma'};

Calculate the price and sensitivities for a double no-touch binary option.

BarrierSpec ="DNT"; Barrier = [120 80]; Payoff = 10; [Price, Delta, Gamma] = dbltouchsensbybls(RateSpec, StockSpec, Settle, Maturity, BarrierSpec, Barrier, Payoff,'OutSpec',OutSpec)
Price = 5.6368
Delta = -0.2536
Gamma = -0.0275

Input Arguments

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Interest-rate term structure (annualized and continuously compounded), specified by theRateSpecobtained fromintenvset. For information on the interest-rate specification, seeintenvset.

Data Types:struct

Stock specification for the underlying asset, specified by theStockSpecobtained fromstockspec.

stockspechandles several types of underlying assets. For example, for physical commodities, the price isStockSpec.Asset, the volatility isStockSpec.Sigma, and the convenience yield isStockSpec.DividendAmounts.

Data Types:struct

Settlement or trade date for the double touch option, specified as anNINST-by-1matrix using serial date numbers, date character vectors, or datetime objects.

Data Types:double|char|datetime

Maturity date for the double touch option, specified as anNINST-by-1vector of serial date numbers or date character vectors.

Data Types:double|char|cell

Double barrier option type, specified as anNINST-by-1cell array of character vectors or string array with the following values:

  • 'DOT'— Double one-touch. The double one-touch option defines twoBarrierlevels. A double one-touch option provides aPayoffif the underlying asset ever touches either the upper or lowerBarrierlevels.

  • 'DNT'— Double no-touch. The double no-touch option defines twoBarrierlevels. A double no-touch option provides aPayoffif the underlying asset ever never touches either the upper or lowerBarrierlevels.

Data Types:char|cell|string

Double barrier value, specified as anNINST-by-2matrix of numeric values, where the first column is Upper Barrier(1)(UB) and the second column is Lower Barrier(2)(LB). Barrier(1) must be greater than Barrier(2).

Data Types:double

Payoff value, specified as anNINST-by-1matrix of numeric values, where each element is a1-by-2vector in which the first column is Barrier(1)(UB) and the second column is Barrier(2)(LB). Barrier(1) must be greater than Barrier(2).

Note

The payoff value is calculated for the point in time that theBarriervalue is reached. The payoff is either cash or nothing. If you specify a double no-touch option usingBarrierSpec, the payoff is at theMaturityof the option.

Data Types:double

Name-Value Arguments

Specify optional pairs of arguments asName1=Value1,...,NameN=ValueN,在那里Nameis the argument name andValueis 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 encloseNamein quotes.

Example:PriceSens = dbltouchsensbybls(RateSpec,StockSpec,OptSpec,Strike,Settle,Maturity,BarrierSpec,Barrier,'OutSpec','Delta')

Define outputs, specified as the comma-separated pair consisting of'OutSpec'and anNOUT- by-1or a1-by-NOUTcell array of character vectors with possible values of'Price','Delta','Gamma','Vega','Lambda','Rho',“θ”, and'All'.

OutSpec = {'All'}specifies that the output isDelta,Gamma,Vega,Lambda,Rho,Theta, andPrice, in that order. This is the same as specifyingOutSpecto include each sensitivity.

Example:OutSpec = {'delta','gamma','vega','lambda','rho','theta','price'}

Data Types:char|cell

Output Arguments

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Expected prices at time 0 or sensitivities (defined usingOutSpec) for double one-touch options, returned as anNINST-by-1matrix.

More About

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Double One-Touch and Double No-Touch Options

Double one-touchoptions and双no-touchoptions work the same way as one-touch options, except that there are two barriers.

A double one-touch or double no-touch option provides a payoff if the underlying spot either ever or never touches either the upper or lowerBarrierlevels. If neither barrier level is breached prior to expiration, the option expires worthless and the trader loses all the premium paid to the broker for setting up the trade. For example, if the current USD/EUR rate is 1.15, and the trader believes that this rate will change significantly over the next 15 days, the trader can use a double one-touch option with barriers at 1.10 and 1.20. The trader can profit if the rate moves beyond either of the two barriers.

References

[1] Haug, E.The Complete Guide to Option Pricing Formulas.McGraw-Hill Education, 2007.

[2] Wystup, U.FX Options and Structured Products.Wiley Finance, 2007.

版本sion History

Introduced in R2019b

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