MATLAB: Is there any additional information available about the derivative price inputs to the Black-Scholes functions in the Financial Toolbox

blackblsimpvblspricederivativeFinancial Toolboxpricescholes

I am looking for more information about the derivative price inputs to the Black-Scholes functions in the Financial Toolbox. In particular, I would like to know if the derivative price input parameters are yield or discrete. If they are yield, is the yield annualized or is it simply dividend divided by stock price.

Best Answer

The "Q" parameter for the Black-Scholes functions in the Financial Toolbox is the annual dividend rate expressed as a percentage of the price of the security. The equations we use are the Black-Scholes equations from "Options, Futures, & Other Derivatives" by Hull -- you can verify this by opening and viewing the function by entering the command:

edit blsprice

Consider the following example that explains the dividend parameter:

The S&P 100 index currently stands at 696 and has a volatility of 30% per annum. The risk-free rate of interest is 7% per annum and the index provides a dividend yield of 4% per annum. Calculate the value of a three-month European put with strike price 700.

This problem can be solved using the following call to the BLSPRICE function:

[Call, Put] = blsprice(696, 700, .07, .25, .3, .04)

which produces the result:

 Call =
    41.7720
 Put =
    40.5539

Related Solutions

MATLAB: How to calculate sensitivity to underlying price changes using Black’s model in the Financial Toolbox 3.4 (R2008a)

Black's model is a special case of a Black-Scholes model in which the futures/forward contract is the underlying asset and the dividend yield = the risk-free rate. In fact, BLKPRICE , which calculates pricing using Black's model calls BLSPRICE, which is used for pricing using Black-Scholes model.

Hence, you can calculate the sensitivities using the Black's model using the equivalent Black-Scholes function and using appropriate input values. For e.g. to get DELTA , we can use the BLSDELTA as follows:

[C,P] = blsdelta(So, X, R, T, SIGMA, R)

Notice that the last input is really the dividend yield, but is set to the risk-free rate (i.e. the 3rd in input).

MATLAB: What is the difference between IMPVBYBLS and BLSIMPV, and how to I determine the Black-Scholes implied volatility using these functions

Both IMPVBYBLS and BLSIMPV use the Black-Scholes model to compute the implied volatility for a given option price. However, one of the main differences between the two functions is that IMPVBYBLS allows specifying cash dividends as well as continuous dividend yields, while BLSIMPV only allows continuous dividend yields.

If you specify continuous dividend yields for both IMPVBYBLS and BLSIMPV, they produce the same results:

Strike = 29;
AssetPrice = 30;
Sigma = .25;
Rates = 0.05;
Settle = datenum('01-Jan-2008');
Maturity = datenum('01-May-2008');
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, ...
'EndDates',Maturity, 'Rates', Rates, 'Compounding', -1,'Basis',1);
DividendType = {'continuous';'continuous'};
DividendAmounts = [0.05; 0.045];
ExDividendDates = {NaN;NaN};
StockSpec = stockspec(Sigma, AssetPrice, DividendType, DividendAmounts);
OptSpec = {'call'; 'put'};
OptionPrice = optstockbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike);
ImpvVol1 = impvbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, ...
Strike, OptionPrice)
ImpvVol2 = blsimpv(AssetPrice, Strike, Rates, ...
yearfrac(Settle,Maturity,1), OptionPrice, 'Class', OptSpec,'Yield',DividendAmounts)
ImpvVol1 =
0.250000000000000
0.250000000000000
ImpvVol2 =
0.250000000000000
0.250000000000000

Best Answer

Related Solutions

MATLAB: How to calculate sensitivity to underlying price changes using Black’s model in the Financial Toolbox 3.4 (R2008a)

MATLAB: What is the difference between IMPVBYBLS and BLSIMPV, and how to I determine the Black-Scholes implied volatility using these functions

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