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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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If the security has negative correlation with other assets that enjoy attractive risk-free rates, then it can be attractive at a return rate under the risk-free level. It would, of course, never be attractive in a single-security portfolio.


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Theoretically, such an asset would not exists with standard deviation less than the risk free rate. You have rightly pointed out that if risk free rate is higher than any rational investor would not invest in the instrument, given lower return along with some amount of risk, when the investor can earn more amount without any risk. In the real world we do ...


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The fact that Implied Vol rises has absolutely nothing to do with riskaversion. If market expects volatility before an upcoming uncertain earnings report, put option prices rise naturally. This is due to the asymmetric payoff profile of options, which always gain from volatility because the downside losses are capped but upside potentially unlimited.



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