impvbybls - Determine implied volatility using Black-Scholes option pricing model

Syntax

Volatility = impvbybls(RateSpec, StockSpec, Settle,
Maturity, Strike, OptPrice, 'Name1', Value1...)

Arguments

RateSpec	The annualized continuously compounded rate term structure. For information on the interest rate specification, see intenvset.
StockSpec	Stock specification. See stockspec.
Settle	NINST-by-1 vector of settlement or trade dates.
Maturity	NINST-by-1 vector of maturity dates.
OptSpec	NINST-by-1 cell array of strings 'call' or 'put'.
Strike	NINST-by-1 vector of strike price values.
OptPrice	NINST-by-1 vector of European option prices from which the implied volatility of the underlying asset are derived.
Note   All optional inputs are specified as matching parameter name/parameter value pairs. The parameter name is specified as a character string, followed by the corresponding parameter value. You can specify parameter name/parameter value pairs in any order; names are case-insensitive and partial string matches are allowed provided no ambiguities exist.
Limit	(Optional) Positive scalar representing the upper bound of the implied volatility search interval. Default is 10, or 1000% per annum.
Tolerance	(Optional) Positive scalar implied volatility termination tolerance. Default is 1e-6.

Description

Volatility = impvbybls(RateSpec, StockSpec, Settle, Maturity, Strike, OptPrice, 'Name1', Value1...) computes implied volatility using the Black-Scholes option pricing model.

Volatility is a NINST-by-1 vector of expected implied volatility values. If no solution is found, a NaN is returned.

Examples

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 RateSpec and StockSpec :

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

StockSpec = stockspec(NaN, AssetPrice);

Calculate the implied volatility of the options:

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

ImpvVol =

    0.3175
    0.4878

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

See Also

optstockbybls | optstocksensbybls

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