Documentation

# gapbyls

Determine price of gap digital options using Black-Scholes model

## Syntax

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

## Description

example

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

## Examples

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This example shows how to compute gap option prices 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 of the option if the risk-free rate is 9%, the strike threshold is 50, and the volatility is 20%.

```Settle = 'Jan-1-2008'; Maturity = 'Jul-1-2008'; Compounding = -1; Rates = 0.09; % calculate 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; % calculate the price Pgap = gapbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec,... Strike, StrikeThreshold)```
```Pgap = 2×1 -0.0053 4.4866 ```

## 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 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`

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

Data Types: `double`

## Output Arguments

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Expected prices 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.