Confusion about bid- ask- and last-prices from option prices data

Question

I’m struggling with the interpretation of quoted option prices I obtained from Bloomberg. The call options prices are available for a daily time series with different strikes at a given day. I downloaded the bid-, ask- and last prices (PX_BID, PX_ASK, PX_LAST, where the latter means the last traded price, so I assume that it is either a bid- or ask-price).

Below is an example of the prices (the prices are ordered with increasing strike prices). When comparing the prices, I make some puzzling observations and hope that some of you could clarify this.

PX_BID:  304.87  184.5  106.86  59.61  32.46  17.27   8.6   3.55   0.53   
PX_ASK:  304.87  194.5  116.86  69.61  42.46  27.27  18.6  13.55  10.53    
PX_LAST: 304.87  189.5  111.86  64.61  37.46  22.27  13.6   8.55   5.53   

1. In most of the cases (and in particular for in-the-money options), PX_LAST is exactly the average of the bid- and ask-price. Why is this the case? It could certainly be the case when the market is very liquid, because then bid- and ask-prices are almost the same. This market is however not very liquid.

2. Moreover, the bid-ask spread is almost always identical across the different strikes and across the days for which I observe the prices. Does anyone know what the explanation could be? Is it perhaps the case that there is only one market maker?

3. Occasionally, the bid- and ask-prices for a given option are the same. In the post below, it is written that this might result from the party and counterparty being the same. Can anyone confirm this?

https://money.stackexchange.com/questions/81078/what-happens-when-the-bid-and-ask-are-the-same

4. Sometimes (not in the example above though), prices violate the convexity condition of options, i.e. quotes are not strictly decreasing in the strike price, but e.g. the option at the end of the strike range might be more expensive than the one before. This is irrational. Is that a data error or is it because I consider quotes and not actual prices?

I would appreciate if anyone who knows more about this could respond to the questions. Many thanks in advance!

Answer 1

Sometimes in bloomberg in absense of data the holes might be filled. So the last, bid and ask may be the same item of data.

Sometimes in market making you can have same bid/offer or even backwardation where the market makers cannot see each others prices (i.e. have restricted permission visibility) or cannot deal with each other for credit reasons or business reasons (i.e. preferring clients over interdealer)

Market making of most illiquid products is still done by a human. Pricing consistency/rationality is not always the primary concern. Sometimes it is preferable to get out of position rather than another , even if the cost is increased, and this can be reflected in 'kinks' to what one might term rational pricing. I suspect it will still fall within the bid-offer, however. I.e. the range of uncertainity.