# Tag Info

18

It's an interesting question. I particularly agree with the $\mathbb{Q}-\mathbb{P}$ dichotomy mentioned by many. I would add to the other answers that, come to think of it, the Black-Scholes postulated Geometric Brownian Motion could be interpreted as an AR(1) process on the logarithm of the stock price as you discretise the SDE from which it is a ...

11

I think you need to differentiate between Q-quants vs P-quants. The former might not use Econometrics, but P-quants use them a lot.

8

Traditional econometric (time series) models are of little or no value in forecasting market prices for purposes of "making money", i.e, generating excess return over a benchmark in an asset management setting. They have some limited value in strategic and tactical asset allocation. The ineffectiveness of time-series modeling in asset management stems ...

7

Having thought about this I think the following reason is also important and wasn't mentioned so far: When you look at the inner working of this whole class of econometric models it all boils down to the following: It is possible (under some reasonable assumptions) to express any $MA(q)$ model as an $AR(\infty)$ model (and vice-versa for expressing $AR(p)$ ...

6

My answer is very much in the spirit of Kiwiakos' answer. E.g. in this paper (where I am one of the coauthors) we use VMA (vector moving average) models (in the multivariate case) and AR models in the univariate case to calculate proper scaling of volatility or its contributions if there are (cross-) auto-correlations. This happens in the P world due to ...

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 ...

3

Given efficient markets, asset prices should be unpredictable in the sense that any upcoming returns are uncorrelated with current or past returns. Hence for traded assets the price should follow something more similar to a GBM than an O-U process. However, many financial metrics are not prices; for example interest rates or volatility. O-U processes may ...

2

It turns out that GBM with constant drift and constant volatility is not really used in real life. It is well known that volatility as well as drift may vary over time. Hence, if you want to use a model with time-varying parameters, you need to come up with a model to define $\mu_t$ and $\sigma_t$. There are classic models that use some mean-reverting ...

2

Yes of course, credit rates depend on interest rates (i.e. https://en.wikipedia.org/wiki/Libor), which are set by some group of banks in almost every country Going further bankers analyze the market situation and also national interest rates, which are set by central bankers in every country which has a central bank ...

2

Most practitioners think of option prices in terms of implied volatility. It is easier to interpret and to model. One can consider the implied volatility surface as a random field : $\Sigma : \Omega \times \mathbb{R}_+ \times \mathbb{R}_+ \to \mathbb{R}_+$ and apply PCA. The first 3 eigenmodes correspond to absolute level (ATM vol), slope in the strike ...

2

If you have a linear/gaussian state space model and you're using a Kalman Filter, you can use maximum likelihood estimation or the EM algorithm. I personally prefer the former since you don't need to know anything about smoothing. If you use the EM, you do. If your observations are $z_1, \ldots, z_n$, then you can write down an innovations likelihood ...

2

MIDAS is useful when you have a low frequency series and you want to include high frequency data in the regression. So for instance, if you want to forecast quarterly GDP data and want to include daily S&P 500 data as a regressor instead of just using the quarter end value of S&P 500. Usually we assume that the causality runs from S&P 500 to ...

2

Normal distribution makes most sense these days for ratesthat are very low, or even negative, like euribor, chf libor Normal distribution is what is assumed by option brokers impliedvolatility quotes for these currencies

1

auto.arima has many unresolved issues. see: http://www.stat.pitt.edu/stoffer/tsa3/Rissues.htm

1

You can do it manually. Let x be the data series. The code below considers all moving-average lag orders between 0 and max.q and prints out the BIC-minimizing lag order and the corresponding estimated model: m=list() # I will save estimated ARIMA(1,0,q) models here BIC=c() # I will save the corresponding BIC values here max.q=10 # the maximum MA order you ...

1

To address the second question: I've done a couple of different things. When I did not care much about the result, I just took a straight line interpolation or fit a curve to make, for example quarterly into monthly. When I did care, and it was a lot of work, I found a monthly or weekly series similar to the lower frequency series, and used the changes in ...

1

It is very natural to think that why assumption of Normal distribution is made for stochastic process $W_t$ when other more appropriate and valid distribution is available specially for modelling stock price. Before writing answer to your question explicitly, first look at definition of Wiener process: Wiener Process: A Wiener process $W_t$, relative to ...

1

Try modelling samples every 20,000 ticks, instead of 2 hours (or any such number like that). Markets are often less fat tailed in terms of the trade- or volume-clock. See http://www.amazon.ca/Introduction-High-Frequency-Finance-Ramazan-Gen%C3%A7ay/dp/0122796713 and http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2034858

1

I would recommend you the following econometrics textbook Basics Econometrics, with a particular focus on multinomial logit / probit models. I guess the challenging part in your case will consist of specifying the exogenous variables, collecting data, before doing the computations. The latter being quick to perform. As far as I am concerned it's better to ...

1

Continuous time has a so-called elegance, but it is rarely correct. Most Q-measure people rarely care about correctness anyway, since they usually don't root their models in statistics. With no goodness of fit measures, continuous time models are elegant theory. In general, we also see that most ex-ante hedges are rarely good, ex-post. They have large ...

1

Model them individualy and as a group. When you model them as a group you are essentially building a stock index that you can compare the performance of individual stocks to and can then calculate a subgroup beta for each stock. You can also calculate a beta coefficient for the group as a whole to the wider market. Since I assume that you are modeling them ...

1

Quant finance is about finding prices of illiquid assets in terms of more liquid assets. So if you have the the data for liquid small house prices you should be able to come up with a reasonable guess for less liquid larger houses, for example. That's basically what's been done all the time - replication of complicated derivatives wrt more liquid assets. ...

1

1) People usually consider an instantaneous covariance while you are considering a integrated covariance. In a model $$dS_t = S_t \cdot (\alpha(t)dt + A(t)dW_t)$$ the integrated covariance of log-returns is simply the integral over time of the instantaneous covariance:  Cov(R_i(t),R_j(t)) = (i,j)\textrm{-coeff. of} \int_0^t \underbrace ...

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