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You can forecast stock prices thru time-series models, cross-sectional, or panel models. There is considerable variation within these categories. In time-series models you would use an auto-regressive model such as an AR(1) where the independent variable is the dependent variable lagged by one period. Naturally, an AR(2) would consist of 2 lags and so on. ...

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Two ways: Model the returns using an Ornstein-Uhlenbeck process You can control the variance of the residual noise in the process to your desired level of correlation. Conceptually you inject gaussian noise into the synthetic OU process to satisfy your requirement. For example, let's say you have time-series A which is what you are modelling. Time-series ...

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I would reckon this to be a very hard exercise. Unless you know the inner workings of such algorithm and how the news was exactly interpreted you have no idea about what went "wrong" and on which side such opportunities reside. One thing I know for sure is that most all algos that capitalize on news capture primarily the numeric part of the news event. I ...

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I mainly speak as market practitioner when I say that I believe in the end all models that are applied to data and real life pricing issues are discretized. Think about it, even the BS hedge argument is in the end just a "theoretical continuous time overlay" of actual discrete time steps and re-hedges. Thus some of the limiting assumptions re BS. You do not ...

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Wilmott Forums - "How can I simulate correlated random numbers?" Generating correlated normal variates Random Correlated Series Generator (using R) All found with a Google search for "how to generate random correlated series".

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Your equations are for cum-dividend prices, i.e. the price plus dividend today. The paper refers to ex-dividend prices. The correct two equations for investor group $a=1$ are \begin{align} p^1(0) =&\ \frac{3}{4} \left(\frac{1}{2}p^1(0) + \frac{1}{2}(1+p^1(1))\right) \\ p^1(1) =&\ \frac{3}{4} \left(\frac{2}{3}p^1(0) + \frac{1}{3}(1+p^1(1))\right) ...

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Beware, oversimplification ahead! (This means that the following is technically not correct, in fact it is false! But: It gives an intuition what is going on!) If you toss a coin and calculate heads as $-1$ and tails as $1$ you get a mean of $0$ with a variance of $1$. When you add up multiple coin tosses, i.e. create a random process $dz(t)$, the mean ...

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If you want to learn more about price pressure, you should look after market impact of metaorders, which is a more adequate term. Because of the microstructure (i.e. the mix of orderbboks dynamics, trading rules, participants behaviours and habits, etc), the more you buy or sell, the more you influence the price an unfavorable way (for your trades). Just ...

3

Portfolio returns are analyzed to account for risk factors only to determine what the risk factor contributed to the returns, was it the underlying assets or the skill of the portfolio manager. Fama French model explains the returns in terms of principal component such SMB and HML besides the market related returns from CAPM. These links have more detais ...

3

There are a few reasons to use factor models. Most importantly, stocks tend to move together. Stated alternately, the first principal component of the securities in a domestic market tends to explain a large share of the variance. If you're concerned with multiple securities (as in portfolio optimization), then you have to account for this or you will ...

3

What a great question -- it touches on many issues at the core of quantitative finance. This answer might be a lot more than you bargained for, but it's too interesting to pass up. References Mostly, this subject falls somewhere at the intersection of these three highly-interrelated topics: risk-neutral valuation, rational pricing and the fundamental ...

3

You could create a rescaled stochastic indicator from your randomly generated, correlated series. 1) use whatever software/methodology you want to create your random series with 0.85 correlation to the original data. 2) find the maximum and minimum values of this new series and rescale the series to range between 0 and 1 using this formula; (series_value - ...

2

I have seen a technique which uses frequency domain and does pretty much what (I think) you are trying to do. The author does not give the complete details, so you might have to contact him for that, or take a look at the (free) software he has developed. Link here: ...

2

I think the market participants behavior on the micro-level is not different in principle from the behavior on the macro-level. The challenges of better news interpretation, and faster response time are very similar on all levels. There may be a little bit more trading opportunities in HFT, but building HFT strategy and infrastructure is very expensive, ...

2

If you can observe prices at a very high frequency, then "news" is defined as a lot more things than if you are observing prices at a lower frequency. So what you are calling corrections are also news for the high frequency guy because he can observe prices that fast, so do not consider these as corrections to the original news, consider this to be a ...

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I can understand your concerns, but I think you are expecting too much from these theories. We cannot explain aggregate behavior from first principle based on a sound theory of individual decisions under uncertainty and I personally doubt that there will ever be such a Grand Unification in economics. Consumption-based asset pricing models are more related ...

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Another important reason for using risk-adjusted returns is to disentangle "skill" from "risk-taking". Think of a equation for a fund's performance like: $r_{i,t}-r_f=\alpha_i+\epsilon_{i,t}$ where $\alpha_i$ gives you the average excess return of fund $i$. Alpha is often interpreted as measure of a managers' skill in timing the market and selecting ...

2

Let's consider a random process $X$. If $X$ is an adapted process, then we know, without any uncertainty, what its value is at the present time. This idea is formalized with measure theory. For $X$ to be a martingale, it needs to have the following property: at any given time, our best estimate of the value at some point in the future (i.e. forecast), is ...

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Intuitively, because of the central limit theorem: wiener process is a limit of a random walk, and after n steps a random walk moves away from the origin by ~ $\sqrt{n}$ Edit: here is a complete answer. First the formula for the sum. The trick is the following simple observation: if $X_1,.. X_n$ are independent zero mean, then $E(\sum X_i)^2 = ... 1 For a stochastic process$\left(X_{t}\right)$to be adopted to a filtration$\left(\mathcal{F}_{t}\right)_{t\in T}$the random variable$X_{t}$must be$\mathcal{F}_{t}$-measurable for each$t\in T$. A stochastic process is a collection of random variables$X_{t}$, indexed by some set$T\$. Each random variable is a mapping from a probability space into a ...

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A random process that is adapted to a filtration is measurable (ie X_t is F_t-measurable) but not necessarily a martingale. X_t is a martingale if E(X_t | F_s) = X_s for s < t.

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According to the literature in market microstructure, the price pressure is defined as "the change in price when large quantities of a security are traded". Here you can find an example of how price pressure influences the bond market and in which the authors provide a complete definition of the phaenomenon and the relative problem of the information ...

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Consumption-based asset pricing theories are about representative agents, not necessarily about traders and investors in financial institutions. The agents are assumed to follow behaviors based on how people generally would decide whether to invest and how much to invest. The idea is that the average person in the economy does not invest for the joy of ...

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I think in this case no fancy normalization techniques are implied. At least from what I understand from the cited part, they just scale the variables so that they are equal to 100 in the base period (end of preceding year) - something like computing a deflator, commonplace in macro analysis.

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This may or may not be helpful, since I don't have anything to point you to that specifically addresses the high skewness of the distribution you mention. However, this sounds like it is probably an idiosyncratic risk, and that certainly has bearing on whether or not it would be priced. In the standard capital asset pricing model, the marginal investor ...

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Further to my comments to Samik R's answer above, here is the link to my blog post where my attempts to recreate the method linked to in said answer are given. Edit to include more information per Tal Fishman's comment Octave .oct function code #include <octave/oct.h> #include <octave/dColVector.h> #include <octave/CNDArray.h> #include ...

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If you want to make the returns "random", then you will have to generate the whole price paths that meet your correlation criteria and then discard results that don't fit your price criteria. This isn't random. If I know how prices evolve, then I can generate a killer trading rule. I suggest using historical data. These data are easy to obtain with the ...

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Nearly every options trader - and every options marketmaker - will hedge their derivatives exposure by trading the underlying. So even if I buy a set of naked calls, my counterparty (e.g. whoever is writing me the options, usually a hedge fund or a bank) will have negative exposure to the stock and buy it to cancel out their risk. Think of an option as ...

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