optstocksensbybaw

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

Syntax

PriceSens = optstocksensbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)

PriceSens = optstocksensbybaw(___,Name,Value)

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

Compute an American Option Price and Sensitivities Using the Barone-Adesi and Whaley Option Pricing Model

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  = datetime(2016,1,1);
EndDate = datetime(2018,1,1);
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 = datetime(2016,1,1);
Maturity = datetime(2018,1,1);

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

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

Settle — Settlement date

datetime array | string array | date character vector

Settlement date for the American option, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, optstocksensbybaw also accepts serial date numbers as inputs, but they are not recommended.

Maturity — Maturity date

datetime array | string array | date character vector

Maturity date for the American option, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, optstocksensbybaw also accepts serial date numbers as inputs, but they are not recommended.

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 NINST-by-1 cell array of character vectors or string arrays with values 'call' or 'put'.

Data Types: char | string

Strike — American option strike price value

nonnegative scalar | nonnegative vector

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: double

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

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

Output Arguments

PriceSens — Expected prices or sensitivities for American options

matrix

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.

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] 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.

Version History

Introduced in R2017a

R2022b: Serial date numbers not recommended

Although optstocksensbybaw supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.