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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

## 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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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 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 = 5.6368 ```
```Delta = -0.2536 ```
```Gamma = -0.0275 ```

## 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` matrix using serial date numbers, date character vectors, or datetime objects.

Data Types: `double` | `char` | `datetime`

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

Data Types: `double` | `char` | `cell`

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 Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

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.

## More About

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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.

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

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

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