impvbybls

Determine implied volatility using Black-Scholes option pricing model

Syntax

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

Volatility = impvbybls(___,Name,Value)

Description

Volatility = impvbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice) computes implied volatility using the Black-Scholes option pricing model.

Volatility = impvbybls(___,Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

Examples

Compute the Implied Volatility Using the Black-Scholes Option Pricing Model

This example shows how to compute the implied volatility using the Black-Scholes option pricing model. Consider a European call and put options with an exercise price of $40 that expires on June 1, 2008. The underlying stock is trading at $45 on January 1, 2008 and the risk-free rate is 5% per annum. The option price is $7.10 for the call and $2.85 for the put. Using this data, calculate the implied volatility of the European call and put using the Black-Scholes option pricing model.

AssetPrice = 45;
Settlement = 'Jan-01-2008';
Maturity = 'June-01-2008';
Strike = 40;
Rates = 0.05;
OptionPrice = [7.10; 2.85];
OptSpec = {'call';'put'};

% define the RateSpec and StockSpec
RateSpec = intenvset('ValuationDate', Settlement, 'StartDates', Settlement,...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', -1, 'Basis', 1);

StockSpec = stockspec(NaN, AssetPrice);

ImpvVol =  impvbybls(RateSpec, StockSpec, Settlement, Maturity, OptSpec,...
Strike, OptionPrice,'Method','jackel2016')

ImpvVol = 2×1

    0.3175
    0.4878

The implied volatility is 31.75% for the call and 48.78% for the put.

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

Settlement date, specified as a NINST-by-1 vector of serial date numbers or a date character vectors.

Data Types: double | char

Maturity — Maturity date

serial date number | date character vector

Maturity date for the American option, specified as a NINST-by-1 vector of serial date numbers or a date character vectors.

Data Types: double | char

OptSpec — Definition of option

character vector with values 'call' or 'put'

Definition of the option from which the implied volatility is derived, specified as a NINST-by-1 cell array of character vectors with a value of 'call' or 'put'.

Data Types: char | cell

Strike — Option strike price

nonnegative scalar | nonnegative vector

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

Data Types: double

OptPrice — European option price

nonnegative scalar | nonnegative vector

European option prices from which the implied volatility of the underlying asset is derived, specified as a nonnegative scalar or NINST-by-1 vector.

Data Types: double

Name-Value 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 = impvbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice,'Limit',5,'Tolerance',1e-5)

Limit — Upper bound of implied volatility search interval

10 (1000% per annum) (default) | positive value

Upper bound of implied volatility search interval, specified as the comma-separated pair consisting of 'Limit' and a positive scalar.

Note

If you are using Method with a value of 'jackel2016', the Limit argument is ignored.

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.

Note

If you are using Method with a value of 'jackel2016', the Tolerance argument is ignored.

Data Types: double

Method — Method for computing implied volatility

'jackel2016' (default) | character vector with values 'search' or 'jackel2016' | string with values "search" or "jackel2016"

Method for computing implied volatility, specified as the comma-separated pair consisting of 'Method' and a character vector with a value of 'search' or 'jackel2016' or a string with a value of "search" or "jackel2016".

Data Types: char | string

Output Arguments

Volatility — Expected implied volatility values

vector

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

References

[1] Jäckel, Peter. "Let's Be Rational." Wilmott Magazine., January, 2015 (https://onlinelibrary.wiley.com/doi/pdf/10.1002/wilm.10395).