# Documentation

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# optstockbybaw

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

## Syntax

Price = optstockbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)

## Description

example

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

## 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 for the American option.

Price = optstockbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)
Price =

14.5180

## 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 objects with values 'call' or 'put'.

Data Types: char | cell | 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

## Output Arguments

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Expected prices for American options, returned as a NINST-by-1 vector.

## 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.