# gapsensbybls

Determine price or sensitivities of gap digital options using Black-Scholes model

## Syntax

``PriceSens = gapsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold)``
``PriceSens = gapsensbybls(___,Name,Value)``

## Description

example

````PriceSens = gapsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold)` calculates gap European digital option prices or sensitivities using the Black-Scholes option pricing model.```

example

````PriceSens = gapsensbybls(___,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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This example shows how to compute gap option prices and sensitivities using the Black-Scholes option pricing model. Consider a gap call and put options on a nondividend paying stock with a strike of 57 and expiring on January 1, 2008. On July 1, 2008 the stock is trading at 50. Using this data, compute the price and sensitivity of the option if the risk-free rate is 9%, the strike threshold is 50, and the volatility is 20%.

```Settle = datetime(2008,1,1); Maturity = datetime(2008,7,1); Compounding = -1; Rates = 0.09; %create the RateSpec RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', 1); % define the StockSpec AssetPrice = 50; Sigma = .2; StockSpec = stockspec(Sigma, AssetPrice); % define the call and put options OptSpec = {'call'; 'put'}; Strike = 57; StrikeThreshold = 50; % compute the price Pgap = gapbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec,... Strike, StrikeThreshold)```
```Pgap = 2×1 -0.0053 4.4866 ```
```% compute the gamma and delta OutSpec = {'gamma'; 'delta'}; [Gamma ,Delta] = gapsensbybls(RateSpec, StockSpec, Settle, Maturity,... OptSpec, Strike, StrikeThreshold, 'OutSpec', OutSpec)```
```Gamma = 2×1 0.0724 0.0724 ```
```Delta = 2×1 0.2852 -0.7148 ```

## 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 basket option, specified as an `NINST`-by-`1` vector using a datetime array, string array, or date character vectors.

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

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

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

Definition of the option as `'call'` or `'put'`, specified as an `NINST`-by-`1` vector.

Data Types: `char` | `cell`

Pay-off strike value, specified as an `NINST`-by-`1` vector.

Data Types: `double`

Strike values that determine if the option pays off, specified as an `NINST`-by-`1` vector.

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: ```[Gamma,Delta] = gapsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold,'OutSpec',{'gamma'; 'delta'})```

Define outputs, specified as the comma-separated pair consisting of `'OutSpec'` and a `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 or sensitivities (defined using `OutSpec`) for gap option, returned as a `NINST`-by-`1` vector.

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### Gap Option

A gap option is a digital option in which one strike decides if the option is in or out of money and another strike decides the size the size of the payoff.

## Version History

Introduced in R2009a

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