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4

Glassermann et al. have published an approach where the loss distribution is approximated by a quadratic function in the risk factors. Based on this estimation they can apply importance sampling and stratified sampling to reduce the variance of the monte carlo estimate. I have not implemented their technique, but their numerical results look very good. You ...


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The use of kernels to estimate volatility using intraday data is "nothing more" than combining: intraday volatility estimation kernel smoothing Thus you have to take care about the "usual pits" of these two approaches. Intraday volatility estimation. I hope you know the "signature plot" effect. Of course if you use the proper estimation method, it ...


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The answer to the original question is simple: the Chopra-Ziemba paper is highly flawed and unreliable. Note that the framework is in-sample and based on a utility function. It has nothing to do with out-of-sample behavior of the mean vs. the covariance in an optimization. Estimation error grows linearly in the mean but quadratically in the covariance. At ...


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1.Is it correct, that the coefficients are now different to the coefficients of the arima output? It seems right that the ARMA coefficients are different. Indeed, in the second model, the GARCH component will capture fluctuations that the ARMA component will not have to capture, resulting in different ARMA parameter estimates. 2.This is the acf of ...


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Using a realized kernel for calculating volatility will give you results in the same resolution as the data you feed them. So if you feed them minute-by-minute data, then the volatility will be calculated minute-by-minute. What that really means is that only once per minute will you have a good estimate of the volatility of whatever asset you're looking at. ...


2

I don't know what you mean by "any scaling" rule. For the square-root of time I can say that it only needs uncorrelated returns. Assume that the return from time point $1$ to $T$ is called $r_{1,T}$ and that it is given as $r_{1,T} = r_1 + r_2 + \cdots + r_T = \sum_{t=1}^T r_t$ where $r_t, t=1,\ldots,T$ are the one-period (e.g. one day) returns. The ...


2

It could be useful for optimal trading to have accurate estimates of the intraday seasonalities. Seasonalities come from a mix of: rythms (for instance European curves are impacted by US open and news announces) events (news) market design (proximity of fixing auctions) From an estimation viewpoint, you see that the more you can take these effects into ...


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What is your objective? There are many approaches that can accomplish this in broad terms but whether it is sensible depends on your application. For example if you are interested in intraday breaks in the levels process you can look at OLS with a priori indicator function breaks, or perhaps a univariate Kalman filter with a stochastic slope coefficient ...


1

Unfortunately, financial markets are not like physical measures, where you know the "true" value of a physical variable but you just access to it thanks to noised sensors. We do not know the "true" volatility, just because there is not such one value... In statistics you have two kinds of modelling procedures: the ones dedicated to estimate the unknown ...


1

Which realized volatility are you attempting to measure is highly important in order to determine which prices and return series to utilize to compute realized volatility. Here couple ideas: What do you attempt to measure: Bid/Offer spread volatility, traded price variations,...Even if you attempt to measure asset price variations it can make a ...


1

I would suggest writing the joint density as the product of the conditional densities then estimate parameters using an optimization package. The joint density is given by $$f(r_0, \ldots, r_T) = f(r_0) \prod_{t=1}^T f(r_t|r_0, \ldots, r_{t-1})$$ then the log likelihood function is $$L = \log(f(r_0)) + \sum_{t=1}^T \log(f(r_t | r_0, \ldots, r_{t-1}) ...


1

The standard answer to your question would be to do the maximum likelihood estimation. When you say "plug in $\sigma$" you can show that the sample estimate of $\sigma$ is actually the maximum likelihood estimate of $\sigma$ for the normal distribution. If I can assume that your data are IID then what you do is use your distribution with parameters ...


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I have written R code for some time-varying bivariate fat-tailed copula functions (ripped off Patton's Matlab code) and played around with various optimizers. You can then use Rsolnp, nloptr, alabama or DEoptim packages to find an optimisation solution. Here is some R code where I play around with different optimisation algorithms. Note that the data2.csv ...


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One approach which I've encountered in practice is Optimal risk budgeting (ORB). This method is similar to Black Litterman in the sense that it uses active investor views as a starting point. The mean variance optimization is then restricted to those assets for which an active investor view is available, and the allocation is calculated with the constraint ...



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