# Documentation

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# assetbybls

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

## Syntax

```Price = assetbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike) ```

## Arguments

 `RateSpec` The annualized continuously compounded rate term structure. For information on the interest rate specification, see `intenvset`. `StockSpec` Stock specification. See `stockspec`. `Settle` `NINST`-by-`1` vector of settlement or trade dates. `Maturity` `NINST`-by-`1` vector of maturity dates. `OptSpec` `NINST`-by-`1` cell array of character vectors with values of `'call'` or `'put'`. `Strike` `NINST`-by-`1` vector of payoff strike price values.

## Description

`Price = assetbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)` computes asset-or-nothing option prices using the Black-Scholes option pricing model.

`Price` is a `NINST`-by-`1` vector of expected option prices.

## Examples

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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 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 price.

`Paon = assetbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike)`
```Paon = 33.7666 26.9662 ```