39

The risk-neutral measure $\mathbb{Q}$ is a mathematical construct which stems from the law of one price, also known as the principle of no riskless arbitrage and which you may already have heard of in the following terms: "there is no free lunch in financial markets". This law is at the heart of securities' relative valuation, see this very nice paper by ...


27

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 solution,...


15

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.


13

Upon close reading, this appears to be 3 (interesting) questions, not one. I'm not sure if the mods have the tools needed to split it up, so I'm just going to write down the three questions as I see them and then deal with them one by one. Note, it is simpler for me to talk about variance instead of volatility. This has no material impact on the answer. ...


11

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 ...


11

There is a deeper issue. Frequentist distributions are not probability distributions because they are designed to be minimax distributions rather than actual distributions. This ignores all of the other problems and this also ignores risk-neutral versus any other measure of risk aversion. An even deeper issue is that these models presume that the ...


9

You may want to consider splitting two important, yet very different concepts: Pricing a derivative security with contingent payoff and forecasting an asset. Pricing a derivative can be achieved through setting up a hedge portfolio and track its evolution and "value" at any point in time before the derivative security pays off. Risk-neutral pricing is a ...


8

Chapter 1: Goldilocks is ousted by the bears Once upon a time, the banks used a fixing called LIBOR as a measure of the risk-free interest rate. Then the big hairy crisis came along and ate all our assumptions, leaving just the bones of the fixing (upon which everything else still fixes) and the mantle of risk-free rate proxy was passed on to a family of ...


7

The only "indicators" that I believe add value in academic research are time series smoothing functions. ( I don't call them indicators because they are all lagging thus do not indicate anything into the future). There is clear empirical evidence and a number of academic papers have been published that show that none of the common indicators (common defined ...


7

I think the answer to your question is very dependent on the respective indicators. It can be argued for example that moving averages not only smooth out time series but because they are a shifted version of the original series signals on crossovers make use of the momentum factor. In general you might want to check out the book Evidence Based Technical ...


7

I just made a Genetic Algorithms calculator you can try at http://www.gregthatcher.com/Stocks/GeneticAlgorithmCalculator.aspx I'm not a "quant expert" like all of you (I'm just a programmer), but here is what I've found. 1.) If you set the constraints up correctly, the results are amazing. e.g. you can get portfolios that have very high return and low risk....


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

This is indeed one of the most difficult tasks to do (if not next to impossible). I would say the standard reference is the following: Expected Returns: An Investor's Guide to Harvesting Market Rewards by Antti Ilmanen An abridged (but still about 170 pages long), yet more current - and free (!) version in different formats (pdf, mobi for the Kindle and epub)...


6

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 ...


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

In their book "Counterparty Credit Risk, Collateral and Funding" D. Brigo, M. Morini and A. Pallavicini start with a dialogue between a Physics PhD graduate and an experienced practitioner of Quantitative Finance. The topic of P vs Q is presented in that dialogue in a manner meant to be understandable to a new comer. I would certainly recommend you to have ...


6

Perhaps a case of views based upon theoretical possibilities rather than empirical realities? In theory, $P$ and $Q$ can be extremely different $P$ is the real world, actual probability measure. $Q$ is an artificial probability measure constructed so that security prices are risk neutral expectations (discounted at risk free rate) under measure $Q$. The ...


6

Interest rate futures enable you to build an interest rate projection curve which you can think of as representing the risk neutral expectation of rates in the future, therefore providing you with a "forecast" of rates in the future. Likewise, stock index futures enable you to build a dividend yield and repo cost projection curve which you can think of as ...


6

Basically, you have to choose whether to use a forward-looking or a backward-looking method of forecasting volatility. Let's start with the VIX. The VIX is an implied volatility index. Option pricing models require the volatility of the underlying asset as an input. Volatility is not an observed quantity, so the people who are pricing the options have to ...


5

Speech recognition signal processing is complex and possibly similar to the complexity of financial markets. They are similar as per characterictics the non stationarity, noise types and other aspects such us the existence of a cepstrum etc conceptual frequency and the grammar to construct and articulate concepts is not evenly and randomly distributed; so ...


5

First of all, I must say that it's a very general question, and the answer can vary depending on type of assets you model. In quant finance real world probabilities are generally used for risk management. It can be said, that in order to use real-world probabilities you have to calibrate your models to history. In order to obtain risk-neutral probabilities, ...


5

I am not a physicist, but I thought about some approaches based on physics several months ago. Some of them are easy to implement and some are really hard. The list below is made from the easiest method to the hardest: -          You can start from the basic physics of the movement and measure the velocity of the time series ( based on v = road/ time). You ...


5

Two theoretical explanations regarding the long memory are given by: The mixture of distributions hypothesis of Tauchen and Pitts (1983). Essentially this hypothesis states that trading volume and return are driven by the same information flow process, therefore trading volume and return volatility should share the same long range dependence. ( see ...


5

The main reason is that with interest rate futures interest rates are entering the pricing formula because they are not hedged while with stock index futures the indices are being hedged (while interest rates also enter the pricing formula here!) So with index futures you price the index in a risk-neutral way while with interest rate futures (and index ...


5

I would put it slightly differently. For Stock index futures , the 2019 contract has the same underlying stocks as the spot index. Therefore the futures price can be simply calculated as spot price increased by interest rates and decreased by dividends. The futures price does not contain any interesting new information about stocks that you cannot see in ...


5

I would personally delete those days so you dont change the data distribution. If you really need to fill those blanks, random sample imputation would be the way to go.


4

You might want to have a look at the stochvol vignette (http://cran.r-project.org/web/packages/stochvol/vignettes/article.pdf), where this process is described in detail in Algorithm 1. In particular, if I understand you correctly, what you need is step 4b. Now to your code: 1) It's not really a rolling forecast, because you estimate the model only once. ...


4

You can use Matlab too, that, in my humble opinion, is simpler than R from a syntax point of view. The model you need for is run by the Matlab function arima that can be used with seasonality option to do what you have to do. Here you can find an example and a brief explanation of the model. Type ctrl + F and search for: "Specify a seasonal ARIMA model" ...


4

EDIT : I read more about it and I get some help with someone else, here is the correct answer : The density forecast is the predictive likelihood value of the process estimated at the realized value computed in a one step ahead way. Thus for instance for a standard arma garch process with normal errors: You forecast the mean $u^{f}_{t|t-1}$ and ...


4

The linked to answer does explain it all, but in brief because one set are stationary processes and the others are not. Correlation as a measures gives us the normalized degree of co-movement between process residuals, which assumes stationary processes. With non-constant mean term (ie, non-stationary processes), there's no way to parse out and relate ...


Only top voted, non community-wiki answers of a minimum length are eligible