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First off, volatility smiles are often drawn over a delta space. Since you're asking, I'll assume you're trying to draw a volatility smile over strike prices, log moneyness, or some similar metric. If you have neither the spot price nor any strike prices associated with your data, I don't believe it's possible to back out both of those values. Not ...


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It really depends what you're trying to achieve! What is the ultimate goal? What are your constraints? Which stocks are you looking at? Without the answers to the above, any partition is just arbitrary: why choose 30th and 70 percentile, vs 10th and 90th? Why choose (-2)*Std.Dev and (+2)*Std.Dev vs just -1 and +1? The selected (and perhaps only correct) ...


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It is a stylized feature that the correlation between SPX and VIX is negative (around -0.7) thus we have an interesting process here. Nothing as simple as driftless Brownian motion. The volatility process jumps up and then fades out which is often modelled as Hawkes process (see e.g. here). Thus conclusions from the simple Gaussian model (with Chi-quared ...


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There are a lot of ways of doing this and what a good way of doing this will be driven by your needs as well. Criteria such as whether the method needs to be (in)sensitive to outliers and whether or not your groups need to be of the same size will influence this. One way to do this would be sorting the volatilities and group them: in groups of equal size ...


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For any normal variable, you have $$aX\sim N(a\mu,a^2\sigma^2).$$ So a linear transformation preserves the distribution type (note that $dW_t\sim N(0,dt)$). When you want to approximate $dS_t$ by setting $dS_t=dS_t$, canceling the $dW_t$ you get: $$\sigma_{ln}S_t=\sigma_n$$


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Usually stockreturns $R$ are assumed normally distributed. If market goes up 1%, the expected stockreturn is $R=\beta\cdot0.01=0.02$ (since $\beta$ being the senstivity to market). Stockprice from $100$ over $103$ requires at least $103/100-1=0.03$ return $R$. As we have now from the question $\sigma=0.02$ and $\mu=0.02$, with $R\sim N(\mu,\sigma)$ we ...


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To avoid confusion (the term futures price could be a type for "future price" or "future's price"), it seems to me that you are talking about the forward price of an asset for which the cost of carry is equal to the interest rate. In that case, indeed, with a fixed interest rate r and an spot S, the forward price F for a time T is given by $F=Se^{r(T-t)}$. ...


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nice point. One way of looking at it, I think, is that you have just two Brownian motions, so in a sense your space is just 2 dimensional. Thus, as long as $V$ and $V_1$ are not "linearly dependent", you're spanning the space, and you're done, and it doesn't really matter what $V_1$ you're choosing. Now, this is of course a very hand-waving argument, in ...


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I have a different solution, which calculates the vol for a list of prices. import math #workout volatility def perc_change(price_list): return [(v / price_list[abs(i-1)])-1 for i, v in enumerate(price_list)] def variance(price_list): perc = perc_change(price_list) avg = average(perc) return [(x - avg)**2 for x in perc] def average(x): return ...


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You can just take the diagonal of the var-cov matrix. This should give you the variance of each stock and then take sqrt of that for std. deviation. sd = sqrt(diag(vcm))


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Do you mean by cross sectional volatility that you take results from the returns of several assets? Of course then volatility is different since you are averaging across returns. For one asset, it is more useful to calculate volatility over time.



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