optstockbyfd

Calculate vanilla option prices using finite difference method

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

collapse all

Create a RateSpec.

AssetPrice = 50;
Strike = 45;
Rate = 0.035;
Volatility = 0.30;
Settle = '01-Jan-2015';
Maturity = '01-Jan-2016';
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 = 'may-1-2015';
OptSpec = 'Call';
Price = optstockbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)
Price = 6.7352

Input Arguments

collapse all

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: single | double

Settlement or trade date for the barrier option, specified as a serial date number, a date character vector, or a datetime object.

Data Types: double | char | datetime

Option exercise dates, specified as a serial date number, a date character vector, or a datetime object:

  • For a European option, use a 1-by-1 vector of dates, specified as a nonnegative scalar integer, a date character vector, or a datetime object. For a Bermuda option, use a 1-by-NSTRIKES vector of dates, specified as a nonnegative scalar integer, date character vector, or datetime object.

  • For an American option, use a 1-by-2 cell array of date character vectors. 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 of serial date numbers or a cell array of date character vectors, the option can be exercised between Settle and the single listed date in ExerciseDates.

Data Types: double | char | cell | datetime

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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

collapse all

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.

More About

collapse all

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(StK,0)

  • For a put: max(KSt,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.

Introduced in R2016b