# Tag Info

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I would offer the distinctions are i) pure statistical approach, ii) equilibrium based approach, and iii) empirical approach. The statistical approach includes data mining. Its techniques originate in statistics and machine learning. In its extreme there is no a priori theoretical structure imposed on asset returns. Factor structure might be identified thru ...

14

I think you have the correct dichotomy here. Things started in the late 1980s and through the 1990s with analytical approaches particularly to derivative pricing (as in "hey, let's create yet another exotic option we can sell to the buy side"). The risk modelling "fashion" of the 1990s (when regulated entities such as banks needed to beef up reporting) ...

14

There are few things to consider. Trading moves the price, to minimize market impact and maximize return it is generally optimal to split an order in several child orders. See the Kyle model. Splitting optimally dependents on specific assumptions that you make. The simplest (and first) approach is that of Berstsimas and Lo (Optimal Control of Execution ...

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Interest rates in general are far from independent and identically distributed. A high interest rate observation is quite likely to be followed by another high observation, and the volatility is likely to be higher as well. Interest rates are also mean reverting, as in most real-world situations (at least for developed markets) interest rates rarely rise ...

9

As far as I know MCMC and also (PMCMC) can be usefull for (bayesian) estimation of parameters of some Hidden process like in the Heston Model case based on observations of the Stock (filtering). But the problem here is that those estimates are not matching those based on calibration of vanilla options of the Risk Neutral measure. So as an econometric tool it ...

9

GARCH will work if volume has memory with some decay. AR will work if volume has mean reversion properties. Both of these are empirical questions and depend on the market. You should also consider if there are seasonal (day-of-week, monthly, quarterly effects) in which case you would want to add dummy variables. MA models will work well if volume behaves ...

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The best paper is probably Relative Volume as a Doubly Stochastic Binomial Point Process - James Mcculloch. In this paper the volume is modelled via a Point Process, and theoretical laws are derived (with confident intervals, etc). And we put elements about this in Market Microstructure in Practice, Chap 2.1. Volume curves are analyzed, not only during the ...

8

There are certainly (short-rate) models which assume bounded interest rates. I suppose I should clarify - the design of the model prohibits negative interest rates. Further, some models asymptotically reach some target, or mean rate which is considered mean reversion, the most famous perhaps the Vasicek. Short rate models where rates cannot go negative: ...

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MCMC can be used for Bayesian inference of other models with hidden variables. Gibbs sampling, for example, is used in Hidden Markov Models. Here is a paper that discuss the differences between MCMC and the more classical approach using the EM algorithm. The question is: Are HMMs a useful model in finance? Some academics argue that they have predictive ...

8

To recover the Black-Scholes pricing equation, you should first express the standard normal cdf in terms of its characteristic function analogous to the Heston solution: $$N(x) = \frac{1}{2} - \frac{1}{\pi} \int_0^{\infty} Re [\frac{e^{-i\phi x} f(\phi)}{i\phi}] d\phi$$ where $f(\phi)$ is the characteristic function of the standard normal distribution: $$... 7 High VIX arguably leads to less predictability of the market factor (i.e. market timing), but high volatility does lead to greater predictability of the cross-section of returns. Indeed, linear risk factor models have higher explanatory power during bear markets. However, your goal is to build a better market timing model where the forecasts (and perhaps ... 7 There is a huge difference between R (and Matlab, SAS, or other statistical languages) and relatively low-level languages such as C/C++/C#/Java in exactly this regard. The latter category is used more often for stable end-products, where speed and performance can be crucial, whereas the former category is used more often for model testing and prototyping. ... 7 The main component of that option premium is (forward-looking) volatility \sigma. The very simplest formula you could use for ATM options is the Bachelier model $$\text{Call}_T = \sigma S \sqrt{\frac{T}{2\pi}}$$ where the time to expiration is T and S is the current underlying price. This formula is "wrong" strictly ... 7 The investor's holdings is a consequence of an investor's utility function interacting with the investor's perceived trading opportunity subject to constraints. (Indeed, the Kelly criterion is also utility maximizing.) We produced trades by re-balancing -- that is to say, we have new expectations of alpha or risk and the optimal portfolio net of these ... 7 Attilio Meucci does some very interesting things with PCA. See e.g. his paper on managing diversification which makes heavy use of it (and explains it very intuitively along the way): Managing Diversification by Attilio Meucci 6 Is your question more about approaches taken on the buy side vs. sell side? If so, you may want to read Attilio Meucci's paper, P vs. Q, on this topic. He breaks down the dichotomy as derivatives pricing (the "Q" world), which uses a lot of very sophisticated modeling involving Ito calculus and PDEs, and portfolio management (the "P" world), which makes ... 6 David Aronson spent 500+ pages detailing this one key idea of multiple comparison problems in searching for trading rules---so have a look at his book called 'Evidence-Based Technical Analysis. 6 I assume you're using returns to compute beta, not the prices. And yes, remove the "jumps", though this should happen automatically since you're looking only at intraday returns. One final piece of advice: you'll get more meaningful results if you smooth the returns via a moving average. 6 Aleš Černý has very simple examples in his book. Alternatively, this paper seems to recap part of the chapter on Fourier series: Introduction to Fast Fourier Transform in Finance - Aleš Černý 6 If at first you don't have a model at all, then geometric Brownian motion is not bad. As others before me said: log-returns are normally distributed in this model. This is debatable and there are times and markets where this is not true. There is more than enough research about this. But why is a model based on Brownian motion not that bad? The reason is ... 6 To provide a straight forward answer: It is not a good model. It never was, it never will be. Until we all do not come up with a better model that provides better modeling accuracy while it is equally intuitive and makes similarly simplifying assumptions the BS model with its geometric brownian motion component is here to stay. It actually does not matter ... 6 Since dW_A and dW_B are already correlated as per the way you construct it, your portfolio being the sum of the two is already correlated. If you want it very explicitity written out, then you could rewrite dW_B = \rho dW_A + \sqrt{1-\rho^2}dW_Z where dW_Z is independent of dW_A. More generally (higher dimensions) you can use Cholesky. Now with ... 5 Have you looked into "noise trader" models? This seems like a market that is mostly noise. A few betters may have some information on or real knowledge of who might win, but certainly nothing like equity markets where there are a lot of people who really know the ins and outs of the firms they're trading. The classic model is Pete Kyle's, which should give ... 5 The model you assume for the interest rate process is a Geometric Brownian Motion. As strimp099 highlights in his comments it is mainly used to model equities because you most of the time want your interest rate models to be positive and mean reverting. A few models have been developed: Vasicek, CIR, HW. You could have a pick in there. As for the ... 5 Since you mention beta, I assume you're familiar with the capital asset pricing model (CAPM). The concept is that an asset's expected returns are linearly correlated with the market's returns. Of course, there are other ways "normalize" returns, as you put it. We can extend CAPM with Fama-French, which adds market cap and relative value to the equation. ... 5 There are many different ways a pricing model can be better : It can allow to reproduce the observed market price (Fit criterion) It takes into account a specific recognized behaviour of the underlying S, say the forward smile dynamic. If you write a product whose value is mostly derived from said behaviour, you dont want to miss that aspect. (Don't fill ... 5 From an academic viewpoint you do not have a lot of choices: The Rosenbaum-Robert approach, the price model with uncertainty zones is a model of trades and duration between trades (implicitly). It is worthwhile to try it. You can also use an Hawkes process, it will have the nice effect of capturing clustering effects on trades. if you want to use ... 5 Yes, there is a software application that you can purchase for 39.99 which stores all your tick data in a highly compressed format while still allowing maximum throughput and lowest latency data queries that I have ever seen. The package provides APIs to all languages under the sun but because they have a special sale going on it comes with the complete ... 5 Let's first restate the formula of the beta of a portfolio P relative to a benchmark B:$$\beta_P=\frac{Cov(r_P,r_B)}{Var(r_B)}  As chrisaycock said in his comment, the key thing to understand is that the beta is a statistical measure computed relative to a benchmark. Hence, I believe that the real question you should be asking is: Which benchmark ...

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