# Tag Info

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There seems to be a basic fallacy that someone can come along and learn some machine learning or AI algorithms, set them up as a black box, hit go, and sit back while they retire. My advice to you: Learn statistics and machine learning first, then worry about how to apply them to a given problem. There is no free lunch here. Data analysis is hard work. ...

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My Advice to You: There are several Machine Learning/Artificial Intelligence (ML/AI) branches out there: http://www-formal.stanford.edu/jmc/whatisai/node2.html I have only tried genetic programming and some neural networks, and I personally think that the "learning from experience" branch seems to have the most potential. GP/GA and neural nets seem to be ...

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Google for this paper "Financial applications of random matrix theory: Old laces and new piece" from Marc Potters, Jean-Philippe Bouchaud, and Laurent Laloux. You can also check Prof. Gatheral presentation about Random Matrix Theory http://www.math.nyu.edu/fellows_fin_math/gatheral/RandomMatrixCovariance2008.pdf In R, the package "tawny" has an ...

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Samuelson suggested in 1965 that the stock prices follow a martingale (see P. Samuelson “Proof That Properly Anticipated Prices Fluctuate Randomly”). Assume there is a security with a random payoff $X_T$ at date $T$. Let $..., P_{t–1}, P_t, P_{t+1},...$ be the time series of prices of a security with this payoff. Finally, define the price change $\Delta ... 14 A martingale is a random process$X(t)$which has the following properties:$ E[X(T)|\mathcal{F}_t] = X(t) $for$T > t$and$ E[|X(T)|] < \infty $where$\mathcal{F}_t$is the filtration at time$t$. A martingale is a random walk, but not every random walk is a martingale. A Brownian random walk is a martingale if it does not have drift. Also, a ... 14 Variance ratio tests have been used numerous times to show that financial asset prices do not follow a random walk. You can for example look at -Lo and MacKinlay : Stock market prices do not follow a random walk : http://press.princeton.edu/books/lo/chapt2.pdf (US Stocks) -Hoque, Kim, Pyun: A comparison of variance ratio tests of random walk: A ... 11 Check out page 55 in "Quantitative Equity Investing: Techniques and Strategies," Fabozzi et al. Section is titled "Random Matrix Theory" - very intro. The context pertains to the estimation of a large covariance matrix. Also, see work at Capital Fund Management, filed under: Random Matrix and Finance : correlations and portfolio optimisation 11 If you need a primer covering various domains of math then Dan Stefanica's text will do the job. The text covers multivariable calculus, lagrange multipliers, black scholes PDF, greeks & hedging, newton's method, bootstrapping, taylor series, numerical integration, and risk neutral valuation. It also includes a mathematical appendix. If you want an ... 10 I think there are a lot of different ways to specify this problem. For simplicity, consider independent Garch processes $$r_{1,t} \sim N\left(0,\sigma_{1,t}^{2}\right)$$ $$\sigma_{1,t}^{2} = \beta_{1,1}+\beta_{1,2}\varepsilon_{1,t-1}^{2}+\beta_{1,3}\sigma_{1,t-1}^{2}$$ and $$r_{2,t} \sim N\left(0,\sigma_{2,t}^{2}\right)$$ $$\sigma_{2,t}^{2} = ... 9 The short and brutal answer is: you don't. First, because ML and Statistics is not something you can command well in one or two years. My recommended time horizon to learn anything non-trivial is 10 years. ML not a recipe to make money, but just another ens to observe reality. Second, because any good statistician knows that understanding the data and the ... 8 I doubt you will find one book that covers everything you need, but here are a few that I continually come back to whenever I have some questions on the mathematics. Analysis of Financial Time Series by Ruey Tsay An Introduction to High-Frequency Finance by Dacorogna et al Probability and Statistics by DeGroot and Schervish Statistical Inference by Casella ... 8 I think he was jokingly suggesting to breed top PhD candidates in pure mathematics. I often heard complaints that a lot of PhDs in Mathematical disciplines lack a rigorous base in pure Mathematics. Obviously the hedge fund manager was not suggesting that the proof of the hypothesis will be in any way relevant to trading or financial pricing applications. On ... 8 At the top of this list I still recommend you to seek employment in order to learn from others in QF space. Could you possible work in a quant team within an investment bank where you currently reside? Start to reach out to the quant finance community so you are connected once you decide to locate to where you can practice this discipline.reach out to ... 8 Edit: Freddy's answer is good -- we wrote concurrently. He rightly points out that QF is a broad field, and that it is among other things a community. Here, I describe a practical, down-to-earth path for getting your feet wet in one key piece of it -- software and model development for derivatives analysis, starting with vanilla options. Your best bet ... 7 Why don't you try it and report back? Recall, though, that while a random walk is often a rather competitive forecast, realized data is understood to have weak dependence especially in higher moments. Having worked a bit with DieHarder, I'd suspect it to reject a number of series. But the proof is in the pudding... 7 If you asked me for a single book as a starting point I'd probably go for: Frequently Asked Questions in Quantitative Finance by Paul Wilmott 6 Often one will find the argument that a random walk of price changes would be a proof of the efficient market hypothesis, but this is (IMO) a logical fallacy: Only because the EMH does imply random walks in the price changes, the finding of random walks does not imply automagically that the EMH is true. 5 One basic application is predicting financial distress. Get a bunch of data with some companies that have defaulted, and others that haven't, with a variety of financial information and ratios. Use a machine learning method such as SVM to see if you can predict which companies will default and which will not. Use that SVM in the future to short ... 5 Two aspects of statistical learning are useful for trading 1. First the ones mentioned earlier: some statistical methods focused on working on live datasets. It means that you know you are observing only a sample of data and you want to extrapolate. You thus have to deal with in sample and out of sample issues, overfitting and so on... From this viewpoint, ... 5 A martingale can be viewed as a fair game (a game in which there is no arbitrage strategy) A (centered) random walk is a martingale (think of it as the total Gain of the fair game) If EFH is in order, then you can think that all information is in the current price, I think this more comparable to Markov Property than to Martingale property. Hope that ... 5 I have tested lots of forex data for randomness. Some currency pairs are very close to random walk. And the problem is open question, because there is no uniform explanation what the random walk is. According to Mandelbrot, Taleb and some other authors randomness can be different. Even if the data is not random it doesn't mean it can be effectively traded. ... 5 Regarding your first question. You can try to argue in the following manner. Using the fact that E_{Q^t}[P(t,T)|\mathcal{F}_s]P(s,t)=P(s,T), then:$$p(s)=\lim_{T\to\infty}P(s,T)^{\frac{1}{T}}=\lim_{T\to\infty}(P(s,t)E_{Q^t}[P(t,T)|\mathcal{F}_s])^{\frac{1}{T}}=\lim_{T\to\infty}E_{Q^t}[P(t,T)|\mathcal{F}_s]^{\frac{1}{T}}$$as ... 4 When you decide if the performance improvement is worth it you can add these to the downside ow using single precision: the result of your basic B-S pricer will eventually need to be multiplied with a notional and maybe a discount factor; For a sufficiently large notional you will see different results than the one calculated using double precision. Is ... 4 All the ideas above are great ideas. Another kind of test would be an idea borrowed from Random Matrix Theory. Assemble your time-series into a matrix. Evaluate the distribution of the eigenvalues of the matrix vs. the distribution of a random matrix. Turns out that the distribution of eigenvalues in a random matrix conforms to distributions such as the ... 4 The other answers are useful and sensible. I have worked full time in equity research for nearly two decades, so very much a "qualitative" rather than a quantitative approach. However, all the firms for which I have worked had quants and because of my casual interest in the area I've spent a lot of time talking to quant teams over the years, often over a ... 4 The intuitive reason is that an arbitrary payoff in L^0_+ can always throw away wealth to be in L^\infty_+. Strange economically, but it's a common trick whenever a duality argument is going to be used. A bit more formally: Since L^\infty_+ \subset L^0_+, it's clear that Condition 1 implies Condition 2. If Condition 1 doesn't hold, take a ... 4 I can offer you two explanations, one more economical, and the other mathematical. The one based on economics is based on no arbitrage (and probably what you're looking for): You are aware of the "Second" FTAP, which says roughly, that there is precisely one equivalent true/local/\sigma martingale measure if and only if the market is complete, i.e. all ... 4 First question: Looking at the paper, we see that the authors assume, for some \epsilon > 0,$$ \underset{n}{\limsup} P \left(| \widehat{h}(y^n) - \widehat{h}(y) | > \epsilon \right) > \epsilon,$$and from this they wish to deduce$(*)$, or$(3.13)$in their notation, for some$\epsilon$. I claim that if$\left \{ \widehat{h}(y^n) : n \in ...

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An interesting case you present here. What they mean is that for discount bonds modified duration can decrease in value even if bond maturity increases. That's indeed counter-intuitive and not that common. In your example, when you look at modified duration values for coupon rate: 3%, you can see that it's value is rising with longer maturity (going from ...

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I'll throw this in as an "application of RMT" ... EDHEC and FTSE use RMT to decide the optimal number of principal components in their covariance estimation procedure for which they use PCA (Principal Component Analysis). For details look here or here in Appendix C section 4 for details.

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