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optstocksensbyfd

Calculate vanilla option prices or sensitivities using finite difference method

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Syntax

[PriceSens,PriceGrid,AssetPrices,Times] = optstocksensbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates)
[PriceSens,PriceGrid,AssetPrices,Times] = optstocksensbyfd(___,Name,Value)

Description

example

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

example

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

Examples

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Open Live Script

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 and sensitivities for of a European vanilla call option using the finite difference method. 

ExerciseDates = datetime(2015,5,1);
OptSpec = 'Call';
OutSpec = {'price'; 'delta'; 'theta'};
[PriceSens, Delta, Theta] = optstocksensbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,...
ExerciseDates,'OutSpec',OutSpec)
PriceSens = 6.7352

Delta = 0.7765

Theta = -4.9999

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, optstocksensbyfd 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 as follows:

  • 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 cell array of date character vectors, the option can be exercised between Settle and the single listed date in ExerciseDates.

To support existing code, optstocksensbyfd 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: PriceSens = optstocksensbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'OutSpec',{'All'},'AssetGridSize',1000)

Define outputs, specified as the comma-separated pair consisting of 'OutSpec' and a NOUT- by-1 or a 1-by-NOUT cell array of character vectors with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'.

OutSpec = {'All'} specifies that the output is Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec to include each sensitivity.

Example: OutSpec = {'delta','gamma','vega','lambda','rho','theta','price'}

Data Types: char | cell

Size of asset grid used for 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' and 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 price or sensitivities (defined by OutSpec) of the vanilla option, returned as a 1-by-1 array.

Grid containing prices calculated by the finite difference method, returned as a two-dimensional grid 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

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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: 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

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See Also

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