optstocksensbybaw

Calculate American options prices and sensitivities using Barone-Adesi and Whaley option pricing model

Description

PriceSens = optstocksensbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike) calculates American options prices using the Barone-Adesi and Whaley option pricing model.

PriceSens = optstocksensbybaw(___,Name,Value) adds optional name-value pair arguments.

Examples

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Consider an American call option with an exercise price of \$120. The option expires on Jan 1, 2018. The stock has a volatility of 14% per annum, and the annualized continuously compounded risk-free rate is 4% per annum as of Jan 1, 2016. Using this data, calculate the price of the American call, assuming the price of the stock is \$125 and pays a dividend of 2%.

StartDate  = 'Jan-1-2016';
EndDate = 'jan-1-2018';
Basis = 1;
Compounding = -1;
Rates = 0.04;

Define the RateSpec.

RateSpec = intenvset('ValuationDate',StartDate,'StartDate',StartDate,'EndDate',EndDate, ...
'Rates',Rates,'Basis',Basis,'Compounding',Compounding)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: -1
Disc: 0.9231
Rates: 0.0400
EndTimes: 2
StartTimes: 0
EndDates: 737061
StartDates: 736330
ValuationDate: 736330
Basis: 1
EndMonthRule: 1

Define the StockSpec.

Dividend = 0.02;
AssetPrice = 125;
Volatility = 0.14;

StockSpec = stockspec(Volatility,AssetPrice,'Continuous',Dividend)
StockSpec = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.1400
AssetPrice: 125
DividendType: {'continuous'}
DividendAmounts: 0.0200
ExDividendDates: []

Define the American option.

OptSpec = 'call';
Strike = 120;
Settle = 'Jan-1-2016';
Maturity = 'jan-1-2018';

Compute the price and sensitivities for the American option.

OutSpec = {'price';'delta';'theta'};

[Price,Delta,Theta] = optstocksensbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'OutSpec',OutSpec)
Price = 14.5180
Delta = 0.6672
Theta = -3.1861

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

Settlement date for the American option, specified as a NINST-by-1 matrix using a serial date number, a date character vector, or a datetime object.

Data Types: double | char | datetime

Maturity date for the American option, specified as a NINST-by-1 matrix using a serial date number, a date character vector, or a datetime object.

Data Types: double | char | datetime

Definition of the option as 'call' or 'put', specified as a NINST-by-1 cell array of character vectors or string arrays with values 'call' or 'put'.

Data Types: char | string

American option strike price value, specified as a nonnegative scalar or NINST-by-1 matrix of strike price values. Each row is the schedule for one option.

Data Types: single | double

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,Delta,Theta] = optstocksensbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'OutSpec',OutSpec)

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

Output Arguments

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Expected prices or sensitivities for American options, returned as a NINST-by-1 matrix.

Note

All sensitivities are evaluated by computing a discrete approximation of the partial derivative. This means that the option is revalued with a fractional change for each relevant parameter. The change in the option value divided by the increment is the approximated sensitivity value.

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

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

where:

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

K is the strike price.

References

[1] Barone-Aclesi, G. and Robert E. Whaley. “Efficient Analytic Approximation of American Option Values.” The Journal of Finance. Volume 42, Issue 2 (June 1987), 301–320.

[2] Haug, E. The Complete Guide to Option Pricing Formulas. Second Edition. McGraw-Hill Education, January 2007.