# The problem of the weighted price

Mid price is so noisy so I try to use the weighted price, which is much better. However I want to define a better price called weighted price

My questions are:

1. How can I get a good weighted price

2. How to judge the weighted-price. How can I define an indicator to judge whether the weighted price is good or bad?

• The best approach depends on your objective. What are you trying to use the microprice for?
– Jase
Apr 27 '20 at 7:50
• There's nothing wrong with being discrete.. You gotta be very careful to concretely distinguish what is actually important in practice vs what is theory/unnecessary niceties for your particular application.
– Jase
Apr 28 '20 at 1:08
• why did the original question change from micro price to weighted price? Apr 28 '20 at 14:59
• Please don’t edit your questions in such a way they become about something else. It’s confusing for others and invalidates existing answers and comments. May 13 '20 at 10:43

Arriving at a good microprice is one of the main preoccupations in the HFT and short-term quantitative trading industry. No answer here will be competitive with these more sophisticated micropricing models.

However if you want something that gives decent predictions (but won't make money after slippage and fees), use either of these two, or some weighted combination of the two:

I know you mentioned bid-ask bounce as a significant problem, but for most applications (and certainly for prediction), it isn't. The last traded price is highly suggestive of future deltas. If you actually measure this, you will see. Either of these will be significantly better than midprice.

Note that these predict deltas in the midprice, $$ln(mid_{t+1}/mid_{t})$$, which is often the most directly actionable in terms of market taking and therefore the most relevant for market taking strategies.

• i think you should be more interested in predicting "micro-returns" not micro-price. would the return simply be calculated as log(micro-price$_t$ / micro-price$_{t-1}$) -1 ? Apr 27 '20 at 11:33
• you said earlier that "I use the mid price to calculate the return". so, once you do get a good micro price, would you calculate its return how i asked? Apr 27 '20 at 17:34
• @develarist I've updated my answer to briefly address the question of what it is that we're predicting
– Jase
Apr 28 '20 at 1:07
• @jimmychou123 To get a more predictive microprice than this requires significant R&D. Often the micropricing model will have several indicators that contribute. You won't find these in the academic literature. Join a HFT firm as a quantitative researcher in a delta one trading team if you want to find out.
– Jase
Apr 28 '20 at 1:11
• @jimmychou123 I can't give more info but you are on the right track.
– Jase
Apr 28 '20 at 4:38

For fixed income trading I acquired a single days worth of iSwap's bid-ask swap data, which is high quality constantly streamed prices of discrete book sizes.

I derived the three standard prices as measures for the mid:

• Mid of Bid and Ask.
• Weighted mid of bid and ask.

All three suffered from the problem of sporadic price jumps when new top level bid or asks were entered into the orderbook (whether it was a signifcant order by volume or not). This you could measure in terms of standard deviation of the absolute prices changes across timespans.

Instead I derived a model for the mid price dependent upon weighted bid-asks at different levels of the orderbook. You can see my answer here: definition of mid price in literature

• Did you look at the link? it gives an example of a model that uses different market depths to derive a weighted mid, then is better than the weighted mid taking only the top level depth.
– Attack68
Apr 27 '20 at 10:36
• You asked what is a good metric to use to define a good price. The standard deviation provides a comparator between methods, it does not provide a way to adjust the price.
– Attack68
Apr 27 '20 at 10:45
• If you had two instruments: apples priced at 1:2 and oranges priced at 5:7, you might say the mid prices are 1.5 and 6. What if there was also an apple/orange spread price at 4.5:5? You now your model is overspecified: 3 prices for 2 instruments: how to derive the mid for all products simultaneously. One way is is using minimum loss fucntion
– Attack68
Apr 27 '20 at 10:50