How do I get a good mid-price?

I 'm trying to get a mid price for forex data. This answer by alex suggests that I shouldn't simply take ask minus bid. I am not a high frequency trader or market maker. My purpose for the fx mid point data would be to run some pattern recognition algorithms.

My question is how should I get a mid price if not just using ask minus bid?

• Is this for options? Or you have the full smile? – will Jul 5 '16 at 6:50
• not for options @will – lostlostlostlostlost Jul 5 '16 at 8:41

Ask minus bid has nothing to do with the mid price - it is the spread.

Generally you see a collection of bid/offer orders resting on different price levels. In the simplest case, you just see one bid at price $p_b$ and one offer at price $p_a$. In this case the mid price is

$$p_m = \frac{p_a + p_b}{2}$$

That's all there is to it - you don't need to "approximate" the mid price if you know the best bid and offer. The half-way point between them just is the mid price.

Really, the question you should be asking is "what is the fair price?" and not "what is the mid price?". The fair price is the exchange rate at which you would be ambivalent about buying or selling (assuming you don't care about risk).

Most of the time, the fair price $p_f$ satisfies $p_b < p_f < p_a$ and you want to get an accurate value for this, using all the information at your disposal. Just using the mid price i.e. $p_f=p_m$ is not a bad approach, but it can break down -

1. If the spread is wide i.e. $p_a \gg p_b$ then the possible range of values for the fair price is very large. This can happen in illiquid markets. In this case, you may want to use information from previous quotes (for example, what was the mid price the last time you saw a bid-offer spread that was not unreasonably wide).

2. If the quoted volumes on the bid and offer are very different, it may indicate that the fair price is far away from the mid. For example, if the amount bid far exceeds the amount offered, it indicates that demand exceeds supply, so probably $p_f > p_m$, and similarly if the amount offered exceeds the amount bid, you probably have $p_f < p_m$. You can search for "bid ask imbalance" or "liquidity imbalance" to read more about this.

This is an implied mid price.

If an illiquid market and/or quiet time of day to snap bid and ask prices, you may have an implied mid that is skewed (consider the case that a dealer offers at his mid to quickly close a position, but fails to find a buyer unless he hits a bid, crossing full B-A).

A better solution would be weighted implied mid, pick the top five/ten quotes on the orderbook and average. Bloomberg does something very close to this on ALLQ.

p(mid) = [SUM(i=1 to 5){bid(i)(pvol)} + SUM(i=1 to 5){ask(i)(pvol)} ] / {SUM(i=1 to 5){bid(vol)+ask(vol)}}* 1/2