# optstockbyfd

Calculate vanilla option prices using finite difference method

## Syntax

## Description

`[`

calculates
vanilla option prices using the finite difference method. `Price`

,`PriceGrid`

,`AssetPrices`

,`Times`

]
= optstockbyfd(`RateSpec`

,`StockSpec`

,`OptSpec`

,`Strike`

,`Settle`

,`ExerciseDates`

)

`[`

adds optional name-value pair arguments. `Price`

,`PriceGrid`

,`AssetPrices`

,`Times`

]
= optstockbyfd(___,`Name,Value`

)

## Examples

### Price a Vanilla Call Option Using Finite Difference Method

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

`StockSpec`

— Stock specification for underlying asset

structure

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`

`OptSpec`

— Definition of option

character vector with values `'call'`

or
`'put'`

| string array with values `'call'`

or
`'put'`

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`

`Strike`

— Option strike price value

nonnegative scalar | nonnegative vector

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`

`Settle`

— Settlement or trade date

datetime scalar | string scalar | date character vector

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.

`ExerciseDates`

— Option exercise dates

datetime array | string array | date character vector

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)
```

`AssetGridSize`

— Size of asset grid used for finite difference grid

`400`

(default) | positive scalar

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`

`AssetPriceMax`

— Maximum price for price grid boundary

if unspecified, `StockSpec`

values
are calculated using asset distributions at maturity (default) | positive scalar

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

as a positive scalar.

**Data Types: **`single`

| `double`

`TimeGridSize`

— Size of time grid used for finite difference grid

`100`

(default) | positive scalar

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`

`AmericanOpt`

— Option type

`0`

(European/Bermuda) (default) | scalar with values `[0,1]`

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

`Price`

— Expected prices for vanilla options

scalar

Expected prices for vanilla options, returned as a `1`

-by-`1`

matrix.

`PriceGrid`

— Grid containing prices calculated by finite difference method

grid

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)`

.

`Times`

— Times corresponding to second dimension of `PriceGrid`

vector

Times corresponding to second dimension of the `PriceGrid`

,
returned as a vector.

## More About

### 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: $$\mathrm{max}(St-K,0)$$

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

where:

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

*K* is the strike price.

For more information, see Vanilla Option.

## References

[1] Haug, E. G., J. Haug, and A. Lewis. *"Back to basics:
a new approach to the discrete dividend problem."* Vol.
9, Wilmott magazine, 2003, pp. 37–47.

[2] Wu, L. and Y. K. Kwok. "A front-fixing finite difference method
for the valuation of American options." *Journal of Financial
Engineering.* Vol. 6.4, 1997, pp. 83–97.

## Version History

**Introduced in R2016b**

### R2022b: Serial date numbers not recommended

Although `optstockbyfd`

supports serial date numbers,
`datetime`

values are recommended instead. The
`datetime`

data type provides flexible date and time
formats, storage out to nanosecond precision, and properties to account for time
zones and daylight saving time.

To convert serial date numbers or text to `datetime`

values, use the `datetime`

function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum"); y = year(t)

y = 2021

There are no plans to remove support for serial date number inputs.

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