optstockbyfd

Calculate vanilla option prices using finite difference method

Syntax

``````[Price,PriceGrid,AssetPrices,Times] = optstockbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)``````
``````[Price,PriceGrid,AssetPrices,Times] = optstockbyfd(___,Name,Value)``````

Description

example

``````[Price,PriceGrid,AssetPrices,Times] = optstockbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)``` calculates vanilla option prices using the finite difference method. ```

example

``````[Price,PriceGrid,AssetPrices,Times] = optstockbyfd(___,Name,Value)``` adds optional name-value pair arguments. ```

Examples

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Create a `RateSpec`.

```AssetPrice = 50; Strike = 45; Rate = 0.035; Volatility = 0.30; Settle = datetime(2015,1,1); Maturity = datetime(2016,1,1); Basis = 1; RateSpec = intenvset('ValuationDate',Settle,'StartDates',Settle,'EndDates',... Maturity,'Rates',Rate,'Compounding',-1,'Basis',Basis)```
```RateSpec = struct with fields: FinObj: 'RateSpec' Compounding: -1 Disc: 0.9656 Rates: 0.0350 EndTimes: 1 StartTimes: 0 EndDates: 736330 StartDates: 735965 ValuationDate: 735965 Basis: 1 EndMonthRule: 1 ```

Create a `StockSpec`.

`StockSpec = stockspec(Volatility,AssetPrice)`
```StockSpec = struct with fields: FinObj: 'StockSpec' Sigma: 0.3000 AssetPrice: 50 DividendType: [] DividendAmounts: 0 ExDividendDates: [] ```

Calculate the price of a European vanilla call option using the finite difference method.

```ExerciseDates = datetime(2015,5,1); OptSpec = 'Call'; Price = optstockbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)```
```Price = 6.7352 ```

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`

Definition of the option as `'call'` or `'put'`, specified as a character vector or string array with values `'call'` or `'put'`.

Data Types: `char` | `string`

Option strike price value, specified as a nonnegative scalar or vector.

• For a European option, use a scalar of strike price.

• For a Bermuda option, use a `1`-by-`NSTRIKES` vector of strike prices.

• For an American option, use a scalar of strike price.

Data Types: `double`

Settlement or trade date for the barrier option, specified as a scalar datetime, string, or date character vector.

To support existing code, `optstockbyfd` also accepts serial date numbers as inputs, but they are not recommended.

Option exercise dates, specified as a datetime array, string array, or date character vectors:

• For a European option, use a `1`-by-`1` vector of dates. For a Bermuda option, use a `1`-by-`NSTRIKES` vector of dates.

• For an American option, use a `1`-by-`2` vector of dates. The option can be exercised on any date between or including the pair of dates on that row. If only one non-`NaN` date is listed, or if `ExerciseDates` is a `1`-by-`1` vector dates, the option can be exercised between `Settle` and the single listed date in `ExerciseDates`.

To support existing code, `optstockbyfd` also accepts serial date numbers as inputs, but they are not recommended.

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: ```Price = optstockbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'AssetGridSize',1000)```

Size of the asset grid used for a finite difference grid, specified as the comma-separated pair consisting of `'AssetGridSize'` and a positive scalar.

Data Types: `double`

Maximum price for price grid boundary, specified as the comma-separated pair consisting of `'AssetPriceMax'` as a positive scalar.

Data Types: `single` | `double`

Size of the time grid used for a finite difference grid, specified as the comma-separated pair consisting of `'TimeGridSize'` and a positive scalar.

Data Types: `double`

Option type, specified as the comma-separated pair consisting of `'AmericanOpt'` and `NINST`-by-`1` positive integer scalar flags with values:

• `0` — European/Bermuda

• `1` — American

Data Types: `double`

Output Arguments

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Expected prices for vanilla options, returned as a `1`-by-`1` matrix.

Grid containing prices calculated by the finite difference method, returned as a grid that is two-dimensional with size `PriceGridSize*length(Times)`. The number of columns does not have to be equal to the `TimeGridSize`, because ex-dividend dates in the `StockSpec` are added to the time grid. The price for `t = 0` is contained in `PriceGrid(:, end)`.

Prices of the asset defined by the `StockSpec` corresponding to the first dimension of `PriceGrid`, returned as a vector.

Times corresponding to second dimension of the `PriceGrid`, returned as a vector.

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Vanilla Option

A vanilla option is a category of options that includes only the most standard components.

A vanilla option has an expiration date and straightforward strike price. American-style options and European-style options are both categorized as vanilla options.

The payoff for a vanilla option is as follows:

• For a call: $\mathrm{max}\left(St-K,0\right)$

• For a put: $\mathrm{max}\left(K-St,0\right)$

where:

St is the price of the underlying asset at time t.

K is the strike price.