# assetsensbybls

Determine price or sensitivities of asset-or-nothing digital options using Black-Scholes model

## Syntax

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

## Description

example

````PriceSens = assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)` computes asset-or-nothing European digital options or sensitivities using the Black-Scholes option pricing model.```

example

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

## Examples

collapse all

Consider two asset-or-nothing put options on a nondividend paying stock with a strike of 95 and 93 and expiring on January 30, 2009. On November 3, 2008 the stock is trading at 97.50. Using this data, calculate the price and sensitivity of the asset-or-nothing put options if the risk-free rate is 4.5% and the volatility is 22%. First, create the `RateSpec`.

```Settle = 'Nov-3-2008'; Maturity = 'Jan-30-2009'; Rates = 0.045; Compounding = -1; RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding)```
```RateSpec = struct with fields: FinObj: 'RateSpec' Compounding: -1 Disc: 0.9893 Rates: 0.0450 EndTimes: 0.2391 StartTimes: 0 EndDates: 733803 StartDates: 733715 ValuationDate: 733715 Basis: 0 EndMonthRule: 1 ```

Define the `StockSpec`.

```AssetPrice = 97.50; Sigma = .22; StockSpec = stockspec(Sigma, AssetPrice)```
```StockSpec = struct with fields: FinObj: 'StockSpec' Sigma: 0.2200 AssetPrice: 97.5000 DividendType: [] DividendAmounts: 0 ExDividendDates: [] ```

Define the put options.

```OptSpec = {'put'}; Strike = [95;93];```

Calculate the delta, price, and gamma.

```OutSpec = { 'delta';'price';'gamma'}; [Delta, Price, Gamma] = assetsensbybls(RateSpec, StockSpec, Settle,... Maturity, OptSpec, Strike, 'OutSpec', OutSpec)```
```Delta = 2×1 -3.0833 -2.8337 ```
```Price = 2×1 33.7666 26.9662 ```
```Gamma = 2×1 0.0941 0.1439 ```

## Input Arguments

collapse all

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 of serial date numbers or date character vectors.

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

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

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

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`

### 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] = assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'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

collapse all

Expected prices or sensitivities (defined using `OutSpec`) for asset-or-nothing option, returned as a `NINST`-by-`1` vector.

## Version History

Introduced in R2009a