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I'm not an equities guy so I don't know anything about volume-weighting, but if I was set this problem the approach that I would take would be to work out the implied volatility of each strike for that day, so that I have a graph of implied volatilty against strike, then interpolate on that graph to get the implied volatility for the ATM strike. Do that for ...

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In index, where the skew is more pronounced, with focus on moves of say 2-3%, when they are down it is more likely they are fast, whereas if they are up, it is more likely that they are slow. For that reason, when you move down you expect the uncertainty (measured by IV) to raise, whereas if you go up you expect it to decrease.

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think of option as an insurance and the cost of the insurance as IV. when the market goes down, investors would buy puts which drives IV up. When market goes up, ppl would exit the puts position, which is a declining demand. IV goes down.

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In my mind volatility (SD) of a stock and implied volatility (IV) are two quite different things: volatility is usually measured backwards looking. The common methods (empirical, GARCH, ..) look into the past. Measuring the risk of owning the stock in the future is often based on these backwards looking observations. We try to measure risk in the real ...

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Well, the implied volatility surface is given by (the Dupire equation) $$\sigma^2(K, T) = 2 \frac{ \frac{\partial C}{\partial T} }{K \frac{\partial^2 C}{\partial K^2}}$$ so at least theoretically if either $K$ or $\frac{\partial^2 C}{\partial K^2}$ becomes very small the implied volatility can tend towards infinity. Whether or not you can find quoted call ...

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There are two approaches. Price call and put options with various strikes. Plot their BS implied volatilities. Find the slope of the graph. Price a call and digital call with the requisite strike. Compute the implied volatility of the call. Use the fact that $DC(model) = DC(BS) - skew \times callvega,$ to solve for the skew. (See eg Section 7.7 of my ...

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All option pricing formulas except this one and this one use some sort of historical volatility . I can't see how you can use the Black Sholes framework and not use some sort of historical volatility uses an order book uses geometric shapes and volume

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If you want to estimate volatility from historical data, the only best linear unbiased estimator (BLUE) is $$\sigma=\sqrt{\frac{1}{T-1}\sum_{i=1}^T (r_i-E(r_i))^2}$$ Any other estimator will hence either be biased or not consistent. Another approach could be to estimate volatility via a GARCH model, which has shown good empirical results in the past. It is ...

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CRR is just a numerical approximation to Black--Scholes. Its main use is in getting American option price. There is no real difference other than slight inaccuracy when using it for Europeans. So no it wouldn't do what you ask. Your questions are philosophical. What is the purpose of the model? if you estimate the volatility from a time series then you can ...

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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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