Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now
21

It seems that your question refers to the microstructure noise defined in papers about intraday volatility estimates. Originally, it comes from the bid-ask bounce, i.e. the fact that even if the volatility is zero, you have buyers and sellers at this price and consequently you observe prices at Bid or Ask prices, and not at mid-price. Because of that, if ...


19

The main issue measuring intraday volatility is called "signature plot": when you zoom in, the volatility measure (i.e. empirical quadratic variations) explode. Similarly you have the "Epps effect" for correlations: when you zoom in, the correlations collapse (it is at least a mechanical effect). For the volatility a lot of models can correct this: - first ...


17

The term has a different meaning to different people. to econometricians, microstructure noise is a disturbance that makes high frequency estimates of some parameters (e.g. realized volatility) very unstable. Generally this strand of the literature professes agnosticism as to the its origin; to market microstructure researchers, microstructure noise is a ...


17

Some cynical but functional definitions: It's what you can't model if you're not using tick by tick data It's what proper quant pricing theory doesn't know how to model yet It's information (order book behavior) that reflects momentary fluctuations in the supply/demand of a given contract, rather than its underlying value (eg an arbitrage free price) The ...


14

The expression you have is fine. But more generally, for the intraday volatility, I don't think there "the correct definition". More like, whatever works in the given context. I found the following notes by Almgren pretty useful: http://cims.nyu.edu/~almgren/timeseries/notes7.pdf


13

There are rigorous econometric definitions, as has already been eluded to by others. For practical purposes, microstructure noise is a component of a price process that exhibits mean reversion on some (possibly time-varying) frequency. This reversion is particularly attractive to liquidity provisioners, who seek to profit from this noise component (along ...


7

Very interesting question. I am not an expert on the subject, however, I was able to find a collection of papers on the subject that should get you started. Here is a good and very informative paper that walks you through several tick by tick volatility estimators that seek to reduce the volatility imposed by market micro-structure: Efficient estimation of ...


6

Statistical volatility is the standard deviation of a window of log returns. For example, 30-day statistical volatility is the standard deviation of 30, one-day log returns. The log return comes from the assumption that log stock returns are normally distributed. Statistical volatility differs from implied volatility which is the volatility input to some ...


6

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 ...


6

On a theoretical level and for low frequency data (e.g. daily), your formula seems right. However, since you are talking about one minute bars, things may get a little messy. There is a vast literature on this, and empirically, things are complicated due to market micro-structure noise. Namely, you need to do consider jumps, errors, periods of low volume, ...


6

I think it's alive and well. I don't think there's a specific "decoupling" time, but if you look at e.g. Munnix et al. "Statistical causes for the Epps effect in microstructure noise", it seems that the biased correlation is about 60% of the real value for 1 min data and about 90% for 5 min data, so you could say that 5 min is pretty safe, but 1 min is ...


5

Quick summary: Your model should still be well specified, as long as: 1) You do the analysis on a heavily traded asset, e.g. IBM on NYSE, and 2) You use heteroskedasticity-consistent standard errors in your estimation framework, e.g. White's standard errors. I'm going to start the long answer by re-stating the question to make sure I've got it right. Let ...


5

Your code for volatility seems correct, if you want minute volatility, but is that really what you want? See this recent question on annualizing volatility from intraday data. Also, using first and last tick is what is generally done, but over very short time intervals such as a minute, you will have microstructure issues. Another question here deals with ...


4

The first issue you need to care about using intraday data to compute beta is the Epps effect (collapse of correlation when you zoom in). This effect comes from different parts, the first being that if you try to compute correlations at high frequency, above a given frequency the probability that your 2 secutities move simultaneously is zero. Consequently ...


4

I use Yhang Zhang measure for intraday volatility for timeseries with a rolling 5 or 10 day window. I wrote a C++ and vba implementation which I'm happy to share if you wish. Takes olhc data and gives an 'estimate' of the volatility. For intraday trading (gamma hedging), I found it is a fairly good estimator of the days range. But I would caution on whether ...


3

It is all a matter of frequency. For instance if you want to get annual realized volatility you multiply your last expression by $\sqrt{(N*251)}$ or the second to last expression by $\sqrt{(251)}$. In other words, your last expression is the 5-min realized volatility whereas the second to last expression is the daily realized volatility.


3

First, you should use an exponential moving average, since the amount of state you need to keep is much smaller than for a simple moving average. Second the well known estimator of volatility, $$ \hat{\sigma} = \sqrt{\frac{1}{n}\sum_{i=1}^n (x_i - \bar{x})^2} $$ is not very robust, since the squaring amplifies the contribution of outliers (which is why ...


3

First: once you will have your liquidity indicator, you will need to know if the signal is worth the risk to go faster (or slower if it is a negative signal). Impulse control will tell you that: http://www.ceremade.dauphine.fr/~bouchard/pdf/BML09.pdf Optimal control of trading algorithms: a general impulse control approach, by Bruno Bouchard, Ngoc Minh Dang, ...


3

I'll address your questions in order: 1a) For TSRV constructed using high frequency returns from NYSE market open to market close on a single day, the output should be numbers on the order of magnitude of 1e-4 to 1e-5. In other words, your numbers look about right. I got these number from calculating TSRV for IBM data myself using Kevin Sheppard's MatLab ...


3

In any finite sample, it is always possible for the Zhou estimator to return a negative number, even though we know the unobservable parameter being estimated is non-negative. This is a well known issue in the academic literature. There are several approaches to dealing with this problem: 1) Ignore it. (I don't like this one). It is particularly nefarious ...


3

1) Spurious autocorrelation of non-synchronous trading data was analyzed in this article: http://www.amazon.com/An-econometric-analysis-nonsynchronous-trading/dp/1245789457 During some time intervals a lot of trades occur and during some nothing happens(so prices are stale). So serial correlation of traded prices may be present but this may be due to stale ...


2

The equivalence you are trying to find can only exist in the framework of static volatility. I think the problem is that in the real world, statistical volatility varies a lot with time; and worse off the relative rate at which it varies increases with smaller time increments. So not only does the answer not apply in real-world markets, an estimation of ...


2

Unfortunately for you (but maybe helpful to others) I can only refer to R packages. The R package high-frequency (link) provides rHYCov. The synchrony package (link) provides a whole plethora of methods for temporal, spatial and spatio-temporal statistics. Furthermore, I would personally advise against HY for its boundary artefacts and instead use ...


2

The code you posted is wrong since you do not model the time series behavior of the up/down process (ie if you have 10 up move and consequently 10 down move it is not the same as the opposite ie 10 down and after 10 up..). I would recommend you to use standards Arma Garch models apply on returns instead of modeling the process of up/down. These are (at ...


1

Q1.) Is there anything wrong in principle with this simple sampling strategy? I mean sampling is a valid strategy, it just may not be the best. WOuld a VWAP style price be better? Would just an average be better? Typically when no trade has happened you can model the price as the last, average of the bid/ask spread, etc. The price you want depends on ...


1

I agree with Malick in the sense that an ARMA-GARCH is a better model but I would improve the model by doing a ARFIMA-FIGARCH, the FI stands for Fractional Integrated that are used to deal for long memory processes like HF data. When trying to fit the ARMA the normal approach would be to see the ACF and the PACF which will show a lot of dependency (almost ...


1

This is actually a deceptively good question because, as we all know, estimates of variance are extremely sensitive to sampling frequency, sampling intervals, and lags. This is because not all stock prices perfectly adhere to Brownian Motion (i.e., the variance doesn't adhere strongly to the root time rule). It is also not entirely clear from the paper how ...


1

I'll address things in order as I encountered them in the question. First, your formula for RV only makes sense if $X_{t_i}$ is the log-price, not log-return. If this was just a mistype it would probably be best if you edited the question to correct it. If it is not a mistype, let me know, because then you have bigger problems... Answer 0: I have no idea ...


1

Major measures of liquidity is volume and the spread. I would look for correlation between returns and volume and the bid-ask spread. On each time there is a negative anticipation I would add the stock sizing by the POV target at that point and the difference between arrival price and current price and buy sell imbalances in the order book. The specifics on ...


1

There are waaaaayyy better estimators than $Var(log(Close_{t+1}/Close_{t}))$. This close-close estimator is unbiased, and has a data efficiency defined as $1$. The Parkinson estimator uses high and low prices only (useful when you don't trust your open and close prices, or don't have them). It has a data efficiency of about $4$. The expected variance from "...


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