# What exactly is meant by “microstructure noise”?

I see that term tossed around a lot, in articles relating to HFT, and ultra high frequency data.

It says at higher frequencies, smaller intervals, microstructure noise is very dominant.

What is this microstructure noise that they refer to?

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The term has a different meaning to different people.

1. 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;

2. to market microstructure researchers, microstructure noise is a deviation from fundamental value that is induced by the characteristics of the market under consideration, e.g. bid-ask bounce, the discreteness of price change, latency, and asymmetric information of traders. The last example is frequently cited but I don't think it is accurate. Asymmetric information does not have to be a microstructure phenomena, although it can be partly driven by architectural properties of the market.

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I presume the paper I saw clobbered with the term was referring to the first usage. What is the cause of this disturbance which affects HF estimates and not less frequent data? – Palace Chan Nov 11 '11 at 21:07
Group 1 being agnostic means that they can't be bothered, as long as they have a good stochastic model for it, and as long as they can filter it out. If you care about the origin, and want to develop some intuition for it, then read some Group 2 papers. It's a fun read, but it won't help you much with 1. The most typical culprit for HF noise is the so called bid-ask bounce. – Ryogi Jan 26 '12 at 19:06

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 you use the classical quadratic variation estimate for the squared volatility: even with an underlying volatility of zero, you will measure a lot of time $(S_{ask}-S_{bid})^2$. If you model this using an additive noise $\epsilon$, meaning that when the mid-price between $0$ and $T$ follows a discretized Arithmetic Brownian motion ($S_{(k+1)\delta}=S_{k\delta}+\sigma\sqrt{\delta}\xi_{k+1}$), the price you observe at $k\delta$ is $S_{k\delta}+\epsilon_k$ (remember that $\epsilon_k$ is something around half a bid-ask spread, explaining why the traded price is not exactly the mid).

Consequently when you sample $[0,T]$ in $N$ slices (i.e. $\delta=T/N$), the expectation of the quadratic variation, that should be an estimate of $\int_0^T \sigma_t^2 dt$ is:

$$U(N)=\mathbb{E}\left(\sum_{n=1}^{N} (S_{n\delta}+\epsilon_n - (S_{(n-1))\delta} +\epsilon_{n-1}))^2 \right)= \sum_{n=1}^{N} \mathbb{E}(S_{n\delta} - S_{(n-1))\delta} )^2 + \mathbb{E}(\epsilon_n -\epsilon_{n-1})^2$$ since the microstructure noise is assumed to be independent of the price, moroever it is centered and has a variance $v$ so $\mathbb{E}(\epsilon_n -\epsilon_{n-1})^2=2v$.

Our estimate is now: $$U(N)\mathop{\rightarrow}_{N\longrightarrow +\infty}\int_0^T \sigma_t^2 dt+2Nv$$

It means that the estimate of the squared volatility increases linearly with the sampling rate! And technically this comes only from the microstructure noise (with variance $v$).

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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 third is the most accurate but the first is the most useful, IMHO. The second is the most common meaning in academic papers.

Some examples:

• When prices hit certain levels (often round number prices eg multiples of 5), they might move suddenly as a large number of traders have punched in stops at these levels
• In the minutes before a news announcement, spreads widen as some market makers pull their orders in anticipation of upcoming volatility

As you might expect, it is more significant in illiquid markets where there are insufficient players to make efficient market assumptions hold.

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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 with other sources of revenue). In a strict sense, liquidity providers do not want to take directional bets on an asset (though in practice this certainly need not be the case).

Since high-frequency market makers are effectively today's liquidity providers in many electronic markets (replacing the traditional NYSE specialists that had a fiduciary responsibility to provide liquidity), it's quite common to see 'HFT' intrinsically linked to 'microstructure noise'.

Be sure to check out the late Fischer Black's article, 'Noise', from JoF, 1985:

http://www.jstor.org/pss/2328481

Although the paper's direction differs somewhat from your question, it should be of interest.

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Noise is a data anomaly that typically occurs in the absence of signal.

In the context of HFT it may refer to order activity (microstructure) motivated by a competing methodology, such as the rebalancing of a mutual fund portfolio to match the composition of the S&P.

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I wouldn't call an index rebalance "noise" since that's exactly the kind of activity that market makers are looking to provide liquidity for. To me, "noise" implies unpredictability. – chrisaycock Feb 12 '13 at 12:24