5
$\begingroup$

Is there a consensus on a formula for measuring the market depth of a book at a given point in time? Or a possible proxy for this measurement?

I see so many articles / people discussing market depth but no description on how they calculate it or measure it.

$\endgroup$
  • $\begingroup$ The theoreticians use "Kyle's Lambda" (a single number), the BTC traders use the Market Depth Diagram (a 2-dimensional representation) bitcoincharts.com/charts/bitstampUSD/… . The (absolute value of) the slope of the two sides of the chart is essentially $\frac{1}{\lambda}$ $\endgroup$ – noob2 Jun 9 '17 at 14:14
  • $\begingroup$ I will look into Kyle's lambda as I am looking for a quantitative way to compare one time to another (rather than a heuristic diagram) $\endgroup$ – guy Jun 9 '17 at 14:15
  • 1
    $\begingroup$ I don't know what you're trying to do, but you might also search for liquidity proxies. Eg. this paper has some discussion. $\endgroup$ – Matthew Gunn Jun 9 '17 at 19:56
  • $\begingroup$ I want to compare a trade of size X from one moment in time to another in terms of market impact so i thought normalizing the volume trading at a given time by market depth would be a good way to do this. $\endgroup$ – guy Jun 10 '17 at 1:00
3
$\begingroup$

There is no official definition of market depth (this is only a qualitative concept), only the cost of a roundtrip for a given number of shares of contracts. Take $V$ shares, on average, knowing the shape of the book at time $t$, what is the cost of buying and selling them immediately? You obtain a cost $C(V,t)$. Then you need to average or to choose an adequate $V$ or an adequate $t$.

  • for $t$ there is no reason to choose a specific time, but you can either average on seconds ${\cal T}=(t_1, \ldots, t_K)$ or according to the intraday volume seasonality ${\cal B}=(\tau_1, \ldots,\tau_N)$ (more volume the morning and at the end of the day)
  • for $V$ you can take only a typical volume of interest for you (if you know you will always split your metaorder in chunks of a given size $V^*$)
  • otherwise you can use the average trade size of a day $\bar V$,
  • or you can reuse a typical distribution of trade volumes of the day ${\cal V}=(v_1,\ldots,v_L)$. Be careful when I speak about trades, I have in mind market orders you need to aggregate several trades.

You end up with different measures of market depth, like $$\mathbb{E}(C(V,t)|V\in {\cal V}, t\in {\cal T}),$$ or $$\mathbb{E}(C(V^*,t)|t\in {\cal B}).$$

$\endgroup$
  • 1
    $\begingroup$ "There is not market depth" ? What do you mean? This is what I am referring to. $\endgroup$ – guy Jun 10 '17 at 22:27
  • $\begingroup$ I came across this paper that proposes the measure of the Bid-Ask volume ratio at a particular price level as $ W = \log \frac{\sum \exp(V^b)}{\sum \exp(V^a)}$ where $V^b$ is the volume on the bid side and $V^a$ is the volume on the ask side at the time instant just before a trade comes in. $\endgroup$ – guy Jun 11 '17 at 2:41
  • $\begingroup$ @tbone I mean "there is no official measure of market depth", this is a qualitative definition (I edited my answer). The closest measure is the one I give (the roundtrip), and I add in my answer this idea of averaging. $\endgroup$ – lehalle Jun 11 '17 at 8:09
  • $\begingroup$ @tbone the ZMA paper you talk about is your second comment is about the imbalance that is different from depth. See for instance this one too: arxiv.org/abs/1610.00261 $\endgroup$ – lehalle Jun 11 '17 at 8:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.