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There is a qualitative shift in the shape of the density. When V is small it is monotone decaying. When V is large it looks more like a Gaussian. Another reason he uses two schemes is that he wants match two moments of the density. When V is small, the moment matching equations for the quadratic Gaussian are unsolvable. When V is large they are unsolvable ...


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Peter Jaeckel wrote a paper just on how to solve this problem: By Implication (July 2006; Wilmott, pages 60-66, November 2006). Probably the most complicated trivial issue in financial mathematics: how to compute Black's implied volatility robustly, simply, efficiently, and fast downloadable from jaeckel.org In my experience the most important thing is to ...


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Below is the root search algorithm code I wrote in college. This is written in octave. It's simple to understand and re-write in C++. Develop numerical methods algos as a separate module and integrate with your pricing and other code I want to WARN you to re-check for bugs. It always converges for my objective functions First function is Dekker method ...


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Bracketing methods such as Bisection and Regula Falsi are always known to converge but they are very slow. Newton Raphson and secant methods are fast (quadratic convergence) but has convergence problems. Google for Newton Raphson convergence pitfalls. Classical ones such as"Trapped in local minima", "Diverge instead of converge" etc Algorithms such as ...



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