![]() """A function newton(f, x, feps, maxit) which takes a function f(x) andĪn initial guess x for the root of the function f(x), an allowed toleranceįeps and the maximum number of iterations that are allowed maxit. The first derivative of the function f(x) using central differences.""" """A function derivative(f, x) which computes a numerical approximation of This is what I tried to do but it is totally wrong: def derivative(f, x): In : newton(f, 1.0, 0.2, 15) - math.sqrt(2) Newton Raphson Method In this context: x is (sigma), implied volatility that we are trying to solve f (x) is a function that is the theoretical (BS) option price the actual option price. ![]() If maxit or fewer iterations are necessary for |f(x)| to become smaller than feps, then the value for x should be returned: In : def f(x): Make sure you copy the derivative function definition from training7.py into lab7.py (there are more elegant ways of doing this, but for the purpose of the assessment, this is the most straightforward way we recommend). ![]() You should use the derivative function from the training part of this lab. Where fprime(x) is an approximation of the first derivative (df(x)/dx) at position x. The newton function should use the following Newton-Raphson algorithm: while |f(x)| > feps, do
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