# Tag Info

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For historical volatility I actually like this article: http://www.todaysgroep.nl/media/236846/measuring_historic_volatility.pdf it provides several of the better known methods for calculating historical vol, which of course could be done manually. Just being aware of the upsides and downsides of each method. As for implied vol, yes as onlyvix has said it'...

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It comes from options. A common way to do it is from ATM (at the money) put and call and the Black Scholes formula. There are also other ways that use a larger number of options and more complicated maths.

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Thanks to @Quantuple I was able to modify the steps listed above to give a more accurate calculation. I'll run through the modified steps with real numbers all the way to the result. The process is as follows: 60-day IV would be for expiration as of June 28, 2016. Find option series bracketing that date. The June 17 and July 15 series both bracket it. For ...

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IMHO the simplest way would be to: (1) fit a probability distribution to the $T$-period returns you've historically observed. This can be done by moment-matching the sample variance/skewness/kurtosis statistics you've already computed, or using kernel density estimation (2) compute European option prices by numerically integrating the $T$-period returns pdf (...

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At $t=0$, you have a vol surface $(T,K)\to\sigma(t=0,S_t=S_0,T,K)$ the hard question is which dynamics i.e $\sigma$ seen as $\sigma: (t,S_t)\to ((T,K)\to \sigma(t,S_t,T,K))$ and even, if you imagine that behind this, there is a deterministic function, you still have to suppose a dependence with respect to $S_t$ Here are two examples 1) \$\sigma(t=0,S_t=...

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The derivation is in "Managing Smile Risk" by Pat Hagan et al. A copy is here: http://www.math.ku.dk/~rolf/SABR.pdf It is not closed form, but rather an approximation based on expansions.

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It comes from Heat Kernel expansion and differential geometry. See Theorem 6 and Section 8 of http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1717676&download=yes

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