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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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There are lots of papers online and here are a few I would suggest math.umn riskworx G. Dimitroff, J. de Kock Nowak, Sibetz I you have matlab there is an step step example to calibrate SABR model. Since it uses the financial toolbox of matlab for a few functions I dont think you can replicate it in any other language. There must be C++ code available ...


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There is no skew/smile for forward contracts, but there is for options based on it (caps, floors, swaptions, options on futures). Then it would be the simple Black Formula that should be used in theory (using futures price). The mere existence of the smile is an indicator that the model is fundamentally flawed and it is important to apply a correction.


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I do not agree with nicolas. I think that spot volatility is represented by the front month expiry options while future volatility is represented by e.g. VIX and VSTOXX which are inherently based on a mix with options in further expiries. Please also see the interview in the The Trader Derivatives: "...because they (Volatility futures like VIX) represent ...



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