# Documentation

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# cashbybls

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

## Syntax

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

## 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 strike price values. `Payoff` `NINST`-by-`1` vector of payoff values or the amount to be paid at expiration.

## Description

`Price = cashbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,Payoff)` computes cash-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 a European call and put cash-or-nothing options on a futures contract with and exercise strike price of \$90, a fixed payoff of \$10 that expires on October 1, 2008. Assume that on January 1, 2008, the contract trades at \$110, and has a volatility of 25% per annum and the risk-free rate is 4.5% per annum. Using this data, calculate the price of the call and put cash-or-nothing options on the futures contract. First, create the `RateSpec`:

```Settle = 'Jan-1-2008'; Maturity = 'Oct-1-2008'; Rates = 0.045; Compounding = -1; Basis = 1; RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis)```
```RateSpec = struct with fields: FinObj: 'RateSpec' Compounding: -1 Disc: 0.9668 Rates: 0.0450 EndTimes: 0.7500 StartTimes: 0 EndDates: 733682 StartDates: 733408 ValuationDate: 733408 Basis: 1 EndMonthRule: 1 ```

Define the `StockSpec`.

```AssetPrice = 110; Sigma = .25; DivType = 'Continuous'; DivAmount = Rates; StockSpec = stockspec(Sigma, AssetPrice, DivType, DivAmount)```
```StockSpec = struct with fields: FinObj: 'StockSpec' Sigma: 0.2500 AssetPrice: 110 DividendType: {'continuous'} DividendAmounts: 0.0450 ExDividendDates: [] ```

Define the call and put options.

```OptSpec = {'call'; 'put'}; Strike = 90; Payoff = 10;```

Calculate the prices.

```Pcon = cashbybls(RateSpec, StockSpec, Settle,... Maturity, OptSpec, Strike, Payoff)```
```Pcon = 7.6716 1.9965 ```