# dbltouchsensbybls

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

## 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.

Note

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

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

AssetPrice = 105;
Rate = 0.1;
Volatility = 0.2;
Settle = datetime(2018,1,1);
Maturity = datetime(2018,6,1);

Define the RateSpec using intenvset.

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

Define the StockSpec using stockspec.

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 = 6.3082
Delta = -0.2770
Gamma = -0.0311

## Input Arguments

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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

Stock specification for the underlying asset, specified by the StockSpec obtained from 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

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

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

Maturity date for the double touch option, specified as an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

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

• 'DOT' — Double one-touch. The double one-touch option defines two Barrier levels. A double one-touch option provides a Payoff if the underlying asset ever touches either the upper or lower Barrier levels.

• 'DNT' — Double no-touch. The double no-touch option defines two Barrier levels. A double no-touch option provides a Payoff if the underlying asset ever never touches either the upper or lower Barrier levels.

Data Types: char | cell | string

Double barrier value, specified as an NINST-by-2 matrix 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 an NINST-by-1 matrix of numeric values, where each element is a 1-by-2 vector 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 the Barrier value is reached. The payoff is either cash or nothing. If you specify a double no-touch option using BarrierSpec, the payoff is at the Maturity of the option.

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

Define outputs, specified as the comma-separated pair consisting of 'OutSpec' and an NOUT- by-1 or a 1-by-NOUT cell array of character vectors with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'.

OutSpec = {'All'} specifies that the output is Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec to 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 using OutSpec) for double one-touch options, returned as an NINST-by-1 matrix.

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### Double One-Touch and Double No-Touch Options

Double one-touch options and double no-touch options 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 lower Barrier levels. 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.

## Version History

Introduced in R2019b

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