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impvbybjs

Determine implied volatility using Bjerksund-Stensland 2002 option pricing model

Syntax

Volatility = impvbybjs(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice)
Volatility = impvbybjs(___,Name,Value)

Description

example

Volatility = impvbybjs(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice) computes implied volatility using the Bjerksund-Stensland 2002 pricing model.

    Note:   impvbybjs computes implied volatility of American options with continuous dividend yield using the Bjerksund-Stensland option pricing model.

example

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

Examples

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This example shows how to compute implied volatility using the Bjerksund-Stensland 2002 option pricing model. Consider three American call options with exercise prices of $100 that expire on July 1, 2008. The underlying stock is trading at $100 on January 1, 2008 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 Bjerksund-Stensland 2002 option pricing model.

AssetPrice = 100;
Settle = 'Jan-1-2008';
Maturity = 'Jul-1-2008';
Strike = 100;
DivAmount = 0.1;
Rate = 0.1;

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

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

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

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

    0.1500
    0.2501
    0.3500

The implied volatility is 15% for the first call, and 25% and 35% for the second and third call options.

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

Data Types: double | char

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

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

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

Data Types: double

American 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 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 single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: Volatility = impvbybjs(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice,'Limit',5,'Tolerance',1e-5)

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Upper bound of implied volatility search interval, specified as a positive scalar.

Data Types: double

Implied volatility search termination tolerance, specified as a positive scalar.

Data Types: double

Output Arguments

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

References

Bjerksund, P. and G. Stensland. "Closed-Form Approximation of American Options." Scandinavian Journal of Management. Vol. 9, 1993, Suppl., pp. S88–S99.

Bjerksund, P. and G. Stensland. "Closed Form Valuation of American Options." Discussion paper 2002 (http://www.scribd.com/doc/215619796/Closed-form-Valuation-of-American-Options-by-Bjerksund-and-Stensland#scribd)

Introduced in R2008b

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