optstocksensbyfd

Calculate vanilla option prices or sensitivities using finite difference method

Syntax

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

[PriceSens,PriceGrid,AssetPrices,Times] = optstocksensbyfd(___,Name,Value)

Description

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

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

Examples

Calculate the Price and Sensitivities for a Vanilla Call Option Using Finite Difference Method

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

ExerciseDates = 'may-1-2015';
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

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: single | double

Settle — Settlement or trade date

serial date number | date character vector | datetime object

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

ExerciseDates — Option exercise dates

date character vector | nonnegative scalar integer | datetime object

Option exercise dates, specified as a nonnegative scalar integer, date character vector, or 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: PriceSens = optstocksensbyfd(RateSpec,StockSpec,OptSpec,Strike,Settle,ExerciseDates,'OutSpec',{'All'},'AssetGridSize',1000)

'OutSpec' — Define outputs

{'Price'} (default) | character vector with values 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All' | cell array of character vectors with values 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'

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

'AssetGridSize' — Size of asset grid used for finite difference grid

400 (default) | positive scalar

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

'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' and 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

PriceSens — Expected prices or sensitivities for vanilla options

scalar

Expected price or sensitivities (defined by OutSpec) of the vanilla option, returned as a 1-by-1 array.

PriceGrid — Grid containing prices calculated by finite difference method

grid

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).

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.