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First of all, may I point out two big misperceptions that you may have: Implied Volatility (IV) is the input to any vanilla option pricing model (not just Black Scholes (BS) that impacts the pricing the most. You can verify this by flipping through the different risk exposures (greeks and higher order sensitivities) and study mean volatilities in such risk ...


4

I suggest you avoid using the VIX for implied vols. Why? One has to consider that the VIX is not simply solely dependant on the dynamics on the S&P 500 anymore because the VIX can be traded via options, etc. Thus many more parameters affect the trajectory of the VIX. The VIX has to equal the ATM option vol because this is where arbitrage assumption ...


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There is a known expansion of implied volatility in moments (I'll find the reference) \begin{equation} \textrm{IV} = \textrm{vol} * (1 + \frac{\textrm{skew}}{6} * \textrm{LMM} + \frac{\textrm{kurt}}{24}*(\textrm{LMM}^2-1)) \end{equation} where log-moneyness is \begin{equation} \textrm{LMM} = ...


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Actually, closing options prices can be downloaded from the exchange, so the data necessary to get the skew is available. If for some reason you don't want to use those closing prices, it is possible to obtain a vol skew from VIX and SKEW. You would need to fit the parameters of a stochastic volatility model (such as Heston's) to the VOL and SKEW data. ...


3

I think you would find the following paper very useful. It compares different pricing models applied to VIX options. You can use it as starting point to apply to VSTOXX options and see where it gets you. The Performance of VIX Option Pricing Models: EmpiricalEvidence Beyond Simulation The following models were tested: Whaley (1993) Grunbichler and ...


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There is another approach to compute Implied Volatility, namely the Model Free Implied Volatility (MFIV). According to this link: "Unlike the traditional concept of implied volatility, where the implied volatility is estimated numerically from an option pricing model, the model free implied volatility (MFIV) is not dependent on any option pricing ...


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The focus on volatility comes about because all price changes "look like" volatility, no matter their source. Improvements in volatility treatment are therefore conflated with improvements in the model, and typically when people consider altered models, they first look to how well the alterations do in providing prices that explain skew for the classical ...


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This article discusses the problem on the German electricity market. They arrive at the following conclusion:"When the B&S model is used to calculate implied volatilities one often obtain different numbers for different values of K and T. In particular, a "smile" or "smirk" shape is often observed in the plot of implied volatility versus strike price. ...



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