MATLAB FINANCIAL DERIVATIVES TOOLBOX Instrukcja Użytkownika Pobierz pdf (Strona 112)

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• Call a function with the name:

n that implements the Newton

descent algorithm for minimizing the aforementioned function. The

calling syntax of this function should be:

“[MinPoints,xVals] =

n(fun, x, maxIterNum, tol)”

“fun” is the function name “@funToMin”, x is a row vector with the

user’s guess (starting value) about the minimum of the function.

“maxIterNum” is as before the maximum number of iterations that

should be set to 25 if not specified and tol is the tolerance concerning

the norm of the updating component of the point x (stopping criterion)

and should be set to 1e-6 is not specified. The function returns

“MinPoints” that given that the algorithm has converged, it is the

point where the minimum is located, and “xVals” that is an m-by-2

array with the set of the values of x at each iteration of the algorithm

(m is either equal to “maxIterNum” or a smaller number if the

algorithm converges earlier).

This function should call another function with the name:

NumerHessian.m and with the following calling syntax:

“HessVals = NumerHessian(fun,x)”

that takes as input a function and a single coordinate point and

returns the Hessian at that point. Use the finite two sided difference

method explained before. To avoid the calculation of a singular

Hessian that cannot be inverted, after saving the Hessian to a square

matrix, set equal to zero all its off diagonal elements. This is a very

useful rule of thumb that helps the algorithm convergence and

robustness. Use x

=[0 0] as initial estimate for the minimum.

After you have called the function, create a new contour figure of the

function and plot on it the algorithm’s trajectory to the minimum

found in “xVals”. Call once more the function with x0=[-1 -2] and add

the new trajectory to the contour figure. Use

to enter a text that

indicates the trajectory.

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MATLAB FINANCIAL DERIVATIVES TOOLBOX Instrukcja Użytkownika Strona 112