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

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

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

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

RateSpec — Interest-rate term structure

structure

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

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).

AssetPrices — Prices of asset defined by StockSpec

vector

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

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: $$\max (St-K,0)$$

• For a put: $$\max (K-St,0)$$

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.