# touchbybls

Price one-touch and no-touch binary options using Black-Scholes option pricing model

Since R2019b

## Syntax

``Price = touchybls(RateSpec,StockSpec,Settle,Maturity,BarrierSpec,Barrier,Payoff)``

## Description

example

````Price = touchybls(RateSpec,StockSpec,Settle,Maturity,BarrierSpec,Barrier,Payoff)` calculates one-touch and no-touch binary options using the Black-Scholes option pricing model. NoteAlternatively, you can use the `Touch` object to price one touch options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments. ```

## Examples

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Compute the price of a one-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 - 0.1; StockSpec = stockspec(Volatility, AssetPrice, DividendType, DividendYield);```

Calculate the price of a one-touch binary option.

```BarrierSpec = "OT"; Barrier = 100; Payoff = 15; Price = touchbybls(RateSpec, StockSpec, Settle, Maturity, BarrierSpec, Barrier, Payoff)```
```Price = 9.4102 ```

## 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. 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`

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

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

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

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

Barrier option type, specified as an `NINST`-by-`1` cell array of character vectors with the following values:

• `'OT'` — One-touch

The one-touch option provides a payoff if the underlying asset ever trades at or beyond the `Barrier` level. Otherwise, the `Payoff` is zero.

• `'NT'` — No-touch

The no-touch option provides a `Payoff` if the underlying asset never trades at or beyond the `Barrier` level. Otherwise, the `Payoff` is zero.

Data Types: `char` | `cell`

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

Data Types: `double`

Payoff value, specified as an `NINST`-by-`1` matrix of numeric values.

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 a no-touch option is specified using the `BarrierSpec`, the payoff is at the `Maturity` of the option.

Data Types: `double`

## Output Arguments

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Expected prices for one-touch options at time 0, returned as an `NINST`-by-`1` matrix.

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### Touch and No-Touch Options

The one-touch and no-touch options provide a payoff if the underlying spot either ever or never trades at or beyond the barrier level. Otherwise, the payoff is zero.

Only two outcomes are possible with a one-touch option if a trader holds the contract all the way through expiration:

• The target price (`Barrier`) is reached and the trader collects the full premium.

• The target price (`Barrier`) is not reached and the trader loses the amount originally paid to open the trade.

## 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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