# chooserbybls

Price European simple chooser options using Black-Scholes model

## Syntax

``Price = chooserbybls(RateSpec,StockSpec,Settle,Maturity,Strike,ChooseDate)``

## Description

example

````Price = chooserbybls(RateSpec,StockSpec,Settle,Maturity,Strike,ChooseDate)` computes the price for European simple chooser options using the Black-Scholes model.```

## Examples

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Consider a European chooser option with an exercise price of \$60 on June 1, 2007. The option expires on December 2, 2007. Assume the underlying stock provides a continuous dividend yield of 5% per annum, is trading at \$50, and has a volatility of 20% per annum. The annualized continuously compounded risk-free rate is 10% per annum. Assume that the choice must be made on August 31, 2007. Using this data:

```AssetPrice = 50; Strike = 60; Settlement = 'Jun-1-2007'; Maturity = 'Dec-2-2007'; ChooseDate = 'Aug-31-2007'; RiskFreeRate = 0.1; Sigma = 0.20; Yield = 0.05```
```Yield = 0.0500 ```

Define the `RateSpec` and `StockSpec`.

```RateSpec = intenvset('Compounding', -1, 'Rates', RiskFreeRate, 'StartDates',... Settlement, 'EndDates', Maturity); StockSpec = stockspec(Sigma, AssetPrice,'continuous',Yield);```

Price the chooser option.

```Price = chooserbybls(RateSpec, StockSpec, Settlement, Maturity,... Strike, ChooseDate)```
```Price = 8.9308 ```

## Input Arguments

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Annualized zero rate term structure, specified by the `RateSpec` obtained from `intenvset`. For information on the interest-rate specification, see `intenvset`.

Data Types: `struct`

Stock specification for underlying asset, specified using `StockSpec` obtained from `stockspec`. For information on the stock specification, see `stockspec`.

`stockspec` can handle other types of underlying assets. For example, stocks, stock indices, and commodities. If dividends are not specified in `StockSpec`, dividends are assumed to be `0`.

Note

Only dividends of type `continuous` can be considered for choosers.

Data Types: `struct`

Settlement or trade dates, specified using an `NINST`-by-`1` vector of serial date numbers or a cell array of date character vectors. `Settle` must be earlier than `Maturity`.

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

Maturity date, specified as an `NINST`-by-`1` vector using serial date numbers or a cell array of date character vectors.

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

Option strike price value, specified with a `NINST`-by-`1` vector of nonnegative integers.

Data Types: `double`

Choose dates, specified with a `NINST`-by-`1` vector of serial date numbers or cell array of date character vectors.

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

## Output Arguments

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Expected prices, returned as an `NINST`-by-`1` vector.

## References

[1] Rubinstein, Mark. "Options for the Undecided." Risk. Vol 4, 1991.

## Version History

Introduced in R2008b