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3

Well, "mean reversion trading" could mean a lot of things, I am not qualified to describe it in full generality. However, there is a simple model of mean reversion called the Ornstein Uhlenbeck process that is often seen. It has two parameters \lambda and \sigma, where lambda is the strength of the mean reversion (so one over lambda is the mean reversion ...


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For a portfolio you have that the variance is: $$ \sigma^2 = w \Sigma w $$ Thus the volatility is $\sigma^2/\sigma = w \Sigma w/\sigma$. Just focusing on one asset with weight $w_i$ and return $r_i$ we get $$ \sigma^2 = covar(\sum_{i=1}^n w_i r_i, r_P) = \sum_{i=1}^n w_i covar(r_i, r_P), $$ where $r_p$ is the return of the portfolio, and thus $$ \sigma = ...


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Well for real hf stock tick data, i do get negativa volatility. So it can happens for large N


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I think it's ok: the total correction is $\approx -N\eta^2 \sim N^{-1/2},$ which tends to zero for large $N.$ So as long as it is a correction to the estimator $Q > 0$ you are ok.


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Varswap vs volswap would do the trick. Similarly, varswap vs straddle more or less accomplishes the same thing (more local wrt spot), or even a strangle vs straddle (ratio'd vega neut) as the poor mans vol of vol trade.


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The VIX itself is connected to a special strip of options which is sensitive to just the volatility of an underlying in a non model dependent manner. This can be performed for any underlying that has options on it, not just the S&P. There is an excellent white paper regarding it you can find on the CBOE site. VIX White Paper You may not be aware that ...


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This depends on your volatility model. Even for underlying like stocks, many vol models have parameter of vol of vol. And option pricing results from the model obviously have sensitivity to that parameter. Once you hedge out all the other risks (delta, vanna, vega) but leaves out the sensitivity to that parameter, by the model, pnl depends on vol of vol.


3

NN Taleb has some discussion of this in his book Dynamic Hedging. You'll find a lot of criticism of the book out in the aether, and there are certainly a good number of typos, but it is probably the least academic and most experience-based resource out there, and certainly worth considering. Augen is another big experience-based proponent of volatility (e.g. ...


2

The factor $\frac{n}{n-1}$ (Bessel's correction) is used when estimating sample variance. This is because using $n$ in the denominator yields a biased estimator of the variance. That being said, if one assumes that the mean is $0$ (not an unusual assumption), then one doesn't lose a degree of freedom in estimating sample mean, so Bessel's correction isn't ...


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The variable surely should be the percentage volatility. Moreover, it should not be the asset volume, because the volume can be interpreted as liquidity risk proxy measure too, and, so, it should be participated in the TypeLiquidity variable (or variables set). See, for instance, at: Fong, Kingsley YL, Craig W. Holden, and Charles Trzcinka. "What are ...


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Some thoughts about this very interesting question: A long position in a diversified stock index (I would not bet that this is true for all single stocks) quite surely results in a short position in volatility. The correlation here is something like $-0.7$ (as books tell, this is of course just an indication. Therefore I have observed the phenomenon that ...


2

The currency carry trade is generally said to be short volatility. The reason is that when [currency] volatility rises, the carry trade suffers, and when volatility falls, the carry trade does well. You can do a regression of carry trade profits vs volatility [either currency volatility, or even just the VIX as a proxy for all volatility]; or just ...


1

This has been asked many times already. Volatility always refers to a model. And unless stated otherwise this model is the Black-Scholes model. In this model the volatility is the standard deviation of the log-returns divided by the square-root of time: $$ \log(\frac{S_{t}}{S_0}) = (r - \frac{1}{2}\sigma^2)t + \sigma W_t \sim \mathcal{N}\left( (r - ...


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One reason is that implied volatility measures the relative value of the option as the price of an option depends on various parameters. As everyone has its own pricing model, it's insane to quote all parameters. This little simple IV tells you everything you'd need to know for valuation.


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The most common use for implied volatility in valuation is for asseing options or option like postions. A volatile instrument is likley to activate or put an option postion in the money just on the basis of its volatility rather than any fundamental change in the intrinsic or fair market value of the underlying. This needs to be taken into account when ...


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I can't directly answer your question about coding for HAR-RV models, but before you do anything with rolling windows I suggest you look at the paper here. Essentially the paper claims that clustering on time series sequences ( i.e. rolling windows ) is useless, so if your HAR-RV model involves clustering in anyway you'll need to think very carefully about ...


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I don't know of any libraries for this. There is a pretty good literature on the problem you mention though. I suggest https://cs.uwaterloo.ca/~paforsyt/numuncert.pdf as a good paper to follow; they study numerical techniques, document pitfalls, and even prove something about convergence of their preferred approach.


3

It doesn't matter if you use *100 or just pct_change, as long as you are consistent. However, in practice, due to underlying floating point numerical instabilities in the underlying optimization algorithms/default tolerances used in scipy/arch, having the returns expressed in %, i.e. multiplied by 100, will have a better chance of converging during the ...



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