Optimization, Modified Duration of Bonds by Edu Pristine

Author of lecture Optimization, Modified Duration of Bonds

Edu Pristine

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... "Application of Derivatives in Finance "Partial Differentiation "Integral ...

... Refers to maximizing or minimizing the function with/without conditions (constraints). Examples: To calculate minimum risk of all given portfolios with/without any constraints. To find the point at which characteristics of return changes. Maxima and Minima of a function 1st derivative test. Step 1: Find stationary points using f (x) =0. Step 2: Find the functional values for all the points on either side in the neighborhood. Step 3: If function value at either side of the point is greater than the value at the stationary point, then it is the local minima. ...

... the stationary point is a local maxima. Step 4: If f  (x) = 0, the second derivative test fails. Example: Find the minimum/ maximum value of using second derivative test. Putting dy/dx =0 we get x=-1/5. Since second derivative at x=-1/5 is positive (10, independent of x in this case) means, local minima Hence x =-1/5 is a local minima. ...

... Step 4: Construct the Hessian matrix. Step 5: if the matrix is negative definite, we have local minima, if the matrix is positive definite, we have local maxima. For functions involving two variables...

... Step 3: solve the equation for x, y and find the functional value. Example: Maximize subject to c onstraint. Solving these three equations we get (1/6, 59/6, 3). Hence, the maximum value is f(1/6, 59/6 ) = 29.92. ...

... V is the present value of all cash payments from the asset (or all expenses from the liability, thus net present value) until maturity. ...