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Can anybody explain to me Why should we calculate implied volatility if there is already an implied volatility index where implied volatility is already calculated??? I can't understand the difference

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closed as unclear what you're asking by Daneel Olivaw, skoestlmeier, Helin, LocalVolatility, Attack68 Jan 5 at 19:40

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Assuming that you imply that the corresponding volatility index is VIX, it's value represents the 30day IV using the out-of-the-money puts and calls. However, it doesn't capture the structure of the IV for different strikes and maturities. Secondly, depending on the model, we might extract different IV from the IV implied by the BS formula. For instance, under a jump-diffusion model we would extract different IV if we need to price short-term options.

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  • $\begingroup$ thank you so much for you answer. but if I want to model the IV , is it enough to take volatilities values from the index or should I calculate it taking into consideration different strikes and maturities ? $\endgroup$ – Sawsan Sarita Dec 27 '18 at 19:07
  • $\begingroup$ I assume that you know the Black & Scholes framework. The theoretical European option's price is a function of some parameters, one of them being the volatility of the underlying. Let $P_{BS}=f(parameters,\sigma)$ be the option price as defined by the Black & Scholes equation. Although this price might not equal the observable market prices. I want to find that value of $\sigma$ such that theoretical price equals the market price, given the rest of the parameters fixed. That is the IV for a given option. If you repeat this process for every maturity and strike you will get the volatility surfa $\endgroup$ – Coxswaiiiin Dec 27 '18 at 22:33
  • $\begingroup$ I don’t see how I can make meaningful use of the theoretical options value produced by a model like black scholes that assumes a static implied volatility, which is the biggest and most critical mistake of this model.Therfore, I asked whether I can use any other model or the VDAX itself without going through this model $\endgroup$ – Sawsan Sarita Dec 27 '18 at 22:54
  • $\begingroup$ What is the problem your dealing with? Implied volatility would not be static if you take into consideration different strikes (volatility skew,smirk and smile are some patterns that emerge). Otherwise, do you mean the time series behavior of IV, when talking about statism? $\endgroup$ – Coxswaiiiin Dec 27 '18 at 23:16
  • $\begingroup$ The problem is that I am writing my thesis on 4 volatility models , one of these is implied volatility. However, I can't go through the calculations and consider different strikes ... so I asked whether I can consider only the VDAX(Dax implied volatilities ) which will be much easier for me $\endgroup$ – Sawsan Sarita Dec 28 '18 at 1:01

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