# Logarithmic price defined as the midpoint of the log bid and ask : Simple Clarification

Guys I would like a simple clarification. The paper by McMillan and Speight (2012) at the data section, defines the logarithmic price as the midpoint of the logarithmic bid and ask. Is that translates to [log(BID)+log(ASK)] / 2 or as log (BID-ASK) ? Thank you very much.

• I reckon its the first - average of log prices - just from simple definition of a midpoint, also it seems sensible enough to do. – Jan Sila Jul 28 '16 at 17:48
• By a quick google search I couldn't clarify it. I proceeded using the first solution but I posted the question just in case. – Greconomist Jul 28 '16 at 17:50
• It also makes sense, say the spread is small, in pennies, then the log would yield a negative value which cannot be taken as a price! – Jan Sila Jul 28 '16 at 17:52

I reckon it's the $\frac{log(ASK)+log(BID)}{2}$, just simple arithmetic average as it makes sense, also considering logarithmic returns, when you can only take a differences from log prices.