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

blkxxxblsxxxFinancial Toolbox

I would like to calculate sensitivity to underlying price changes using Black's model.

I see functions to do this using Black-Scholes but not using Black's model.

Best Answer

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).

Related Solutions

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

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

MATLAB: What function do I use to price a Callable Zero Coupon Bond in the Financial Derivatives Toolbox 5.4 (R2009a)

Zero Coupon Callable Bonds are the same as Callable Bonds, with Coupons set zero. Hence, we can use the functions for pricing Callable Bonds (such as OPTEMBNDBYBDT), set the 'Coupons' and 'Periods' parameters to zero, specify Excercise dates and get the price of a Zero Coupon Callable Bond. An example code is attached.

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Related Solutions

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

MATLAB: What function do I use to price a Callable Zero Coupon Bond in the Financial Derivatives Toolbox 5.4 (R2009a)

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