impvbybaw

Calculate implied volatility using Barone-Adesi and Whaley option pricing model

Syntax

Volatility = impvbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice)

Volatility = impvbybaw(___,Name,Value)

Description

Volatility = impvbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice) calculates implied volatility using the Barone-Adesi and Whaley option pricing model.

Volatility = impvbybaw(___,Name,Value) adds optional name-value pair arguments.

Examples

Compute the Implied Volatility for an American Option Using the Barone-Adesi and Whaley Option Pricing Model

This example shows how to compute implied volatility using the Barone-Adesi and Whaley option pricing model. Consider three American call options with exercise prices of $100 that expire on July 1, 2017. The underlying stock is trading at $100 on January 1, 2017 and pays a continuous dividend yield of 10%. The annualized continuously compounded risk-free rate is 10% per annum, and the option prices are $4.063, $6.77 and $9.46. Using this data, calculate the implied volatility of the stock using the Barone-Adesi and Whaley option pricing model.

AssetPrice = 100;
Settle = 'Jan-1-2017';
Maturity = 'Jul-1-2017';
Strike = 100;
DivAmount = 0.1;
Rate = 0.05;

Define the RateSpec.

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
'EndDates', Maturity, 'Rates', Rate, 'Compounding', -1, 'Basis', 1)

RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9753
            Rates: 0.0500
         EndTimes: 0.5000
       StartTimes: 0
         EndDates: 736877
       StartDates: 736696
    ValuationDate: 736696
            Basis: 1
     EndMonthRule: 1

Define the StockSpec.

StockSpec = stockspec(NaN, AssetPrice, {'continuous'}, DivAmount)

StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: NaN
         AssetPrice: 100
       DividendType: {'continuous'}
    DividendAmounts: 0.1000
    ExDividendDates: []

Define the American option.

OptSpec = {'call'};
OptionPrice = [4.063;6.77;9.46];

Compute the implied volatility for the American option.

ImpVol =  impvbybaw(RateSpec, StockSpec, Settle, Maturity, OptSpec,...
Strike, OptionPrice)

ImpVol = 3×1

    0.1802
    0.2808
    0.3803

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

serial date number | date character vector | datetime object

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 — Maturity date

serial date number | date character vector | datetime object

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

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: single | double

OptPrice — American option price

nonnegative scalar | nonnegative vector

American option prices from which the implied volatility of the underlying asset is derived, specified as a nonnegative scalar or NINST-by-1 matrix of strike price values.

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: Volatility = impvbybaw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptionPrice)

'Limit' — Lower and upper bound of implied volatility search interval

[0.1 10] (or 10% to 1000% per annum) (default) | positive value

Lower and upper bound of implied volatility search interval, specified as the comma-separated pair consisting of 'Limit' and a 1-by-2 positive vector.

Data Types: double

'Tolerance' — Implied volatility search termination tolerance

1e-6 (default) | positive scalar

Implied volatility search termination tolerance, specified as the comma-separated pair consisting of 'Tolerance' and a positive scalar.

Data Types: double

Output Arguments

Volatility — Expected implied volatility values

matrix

Expected implied volatility values, returned as a NINST-by-1 matrix. If no solution can be found, a NaN is returned.

References

[1] Barone-Adesi, 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.