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Let me give you an example to show how this can happen. Suppose you invest 0.50 in a coin flip that will pay 1 on heads and 0 on tails a month later. The monthly variance will be .5*(1-.5)^2+.5*(0-.5)^2=.5 so the standard deviation will be .25. This is significantly higher standard deviation than a market index or almost all stocks. So by one measure this is ...

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How about: Barnhart, Scott W. "The effects of macroeconomic announcements on commodity prices." American Journal of Agricultural Economics 71.2 (1989): 389-403. This article analyzes the immediate reaction of a representative sample of commodity prices and two T-bill yields to the unanticipated components of thirteen macroeconomic announcements. ...

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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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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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It might help to look at the solutions of the SDEs that you have there. In the first case $$S_t/S_0 = \exp(-\sigma^2/2 t + \sigma B_t) \quad \quad (1)$$ Thus if you take the log then $\sigma$ is the volatility of the log-returns (assume that $t=1$ time step),. In the second case  S_t = S_0 + \sigma B_t \rightarrow S_t - S_0 = \sigma B_t \quad \quad(2) ...

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