Mastering Python for Finance - Second Edition

Newton's method

Newton's method, also known as the Newton-Raphson method, uses an iterative procedure to solve for a root using information about the derivative of a function. The derivative is treated as a linear problem to be solved. The first-order derivation, f′, of the function, f, represents the tangent line. The approximation to the next value of x, given as x₁, is as follows:

Here, the tangent line intersects the x axis at x₁, which produces y=0. This also represents the first-order Taylor expansion about x₁, such that that the new point, , solves the following equation:

This process is repeated with x taking the value of x₁ until ...