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Yes, you can use Multivariate GARCH model to estimate the volatility of a portfolio. For example, the Constant Conditional Correlation(CCC) GARCH model. In the CCC GARCH model, it says there is a constant correlation between portfolio and the model is defined as: Once you have estimated the correlation matrix, the the composed volatility can be computed by ...

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If you want to use GARCH to estimate past local volatility of the portfolio you can do but, but you'd use GARCH to model the portfolio returns, not prices. Then you will be able to build a range of possible volatilities in the futures given a certain confidence level and you would have a local volatility $\sigma_t$ for each historical point.

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There are many ways to calculate the volatility. timeframe does not metter. it can be monthly quarterly or daily data. You can call them as volatility metrics. Volatility Metrics Volatility is the degree of trading price over a specific time window. Historical volatility is the degree of price changes of past market prices.Volatility indicates the risk ...

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The log likelihood function is indeed rather flat in the $\mu$-direction, for small time horizons (you used $T = 1$ it looks like). As you may have noticed, increasing the number of observations but keeping the time horizon the same DOES NOT IMPROVE the accuracy of the estimate of $\mu$ - this is a bit counterintuitive, if you ask me. But, increasing the ...

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You could just go with a straight confidence interval. I'll explain it in terms of Gaussian/normal distribution, however, for professional use I'd take the extra steps to do bootstrapping and fitted some fat tail distribution. Select some time lag for your data. Calculate the rate of returns for each time step. Calculate the standard deviation and mean of ...

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As far as I know, technical analysis won't work to predict intraday Forex movement. I've done so many backtest using technical analysis but it doesn't have any predictive power. The best way to predict FOREX is to find the difference of interest rates issued by both government of that currency pair. $$Pn = P_0 . e^{(r_{jpy}-r_{usd}) \Delta t }$$ $$... 0 To obtain the vola for the log returns is easy and you don't need itos lemma, since$$ \log S'(t) = \log S_1(t) + \log S_2(t),$$therefore$$ var(S'(t)) = var(\log S_1(t)) + var(\log S_2(t)) + 2covar(\log S_1(t),\log S_2(t))\\ = \sigma_1t+\sigma_2t+2\rho \sigma_1\sigma_2.$$However, to get the vola for the non-log stock price you indeed need to use the ... 1 Use Ito's lemma on the function f(x,y) = xy and then extract out the diffusion term. 5 Note that total implied variance defined as$$ V(T,K) = T\Sigma(T,K)^2 $$should be an increasing function of T. Otherwise you have a calendar arbitrage (sell the call with shorter expiry and buy the cheap longer one). If you interpolate linearly your implied volatility is$$ \Sigma(T,K) = w\Sigma(T_i,K) + (1-w)\Sigma(T_{i+1},K)  with weight $w = ... 2 It implies negative forward variance. I have the book, and went through the section following your quote. In math terms, he is making a proof by contradiction. He first assumes that you can interpolate Iinearly, and comes to the conclusion that it is not a good assumption. The argument does involve some calculus. I don't think I have a better explanation, so ... 1 You're going to have to do a lot of guesswork, obviously, so it's best to keep things mathematically simple. First off, choose a "certainty level" as some quantile$q$, perhaps around 0.9, and the corresponding normal variate$z=N^{-1}(1-q)$. Start by figuring out how much time$T_i$you think each position$N_i\$ will take to liquidate if necessary. Then ...

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Generally if they are missing a completely at random data in few places, you do not have to be worried. I advice you to use one of the technics of imputation: - Previous value - cannot be used in this case - Educated Guessing - you have "knowledge" about the data, you can try to use some interpolation in your mind. - Common-Point Imputation - try to ...

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(1) as AFK says, total remaining variance is somewhat more natural mathematically. Of course it is just a choice of coordinate, and mathematically you can do changes of coordinate so it is for aesthetic rather than hard mathematical reasons. (2) time dependence in SVI-JW parameters is carefully chosen so that if the parameters are held constant across ...

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Financial modeling is often considered as a mixture of art and science. That is a way how you model your data depends on you. You can choose several approaches, for example: calculate max - min price for a given minute data - a very simple approach, calculate the standard deviation of minute-by-minute stock data, calculate GARCH family models for measuring ...

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