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Suppose we have the following bid/ask spread for a particular stock: first bid

What is the theoretical value of the stock?

Now suppose we have:

this

What is the theoretical value of the stock?

Now suppose a major event in the market occurs and the particular volume at a price point changes as following:

Here

What is the new theoretical price?

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    $\begingroup$ The term "theoretical price" is not defined in this question, Which makes the question impossible to answer. If you mean "what value should we assign to a small amount (1 share) of stock, then the answer is the midpoint between best bid and best ask. If you mean at what price can I sell a significant amount (thousands) os shares then the answer in another one... $\endgroup$ – Alex C Sep 25 '18 at 17:13
  • $\begingroup$ @AlexC how would you price the security if you're a market maker? (assuming zero ask/bid spread--or if it is bothersome, a 0.01 cent tick) $\endgroup$ – Sameer Lal Sep 26 '18 at 2:35
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It is totally up to the type of use or the type of interpretation that you want to give to the theoretical price and also it depends on what are your belief about the information content of the queue of orders that are currently resting and are visible in the limit order book.

Depending on whether or not you believe that the information displayed in the limit order book adds to your final result for the theoretical price, you could take:

  • the last price at which the security was traded;
  • the mid-price calculated as an unweighted average of the best bid and best ask prices;
  • the mid-price calculated as a weighted average of the best bid and the best ask prices (depending on what is your belief about information content of the depth of the LOB on each side you could decide to include only level 1 information or use the entire depth as in Cao, Hansch, and Wang (2004) 'The Informational Content of an Open Limit Order Book' ).

However, in one of your comments I read that your interested in how a market maker would price that security, and in that case the answer may not be a single number since they are requested to post quotes on both sides of the LOB and therefore they will have a theoretical price at which they believe it is reasonable to sell the security and a theoretical price at which they believe it is reasonable to buy the security and based on that they will post their quotes in the LOB (take also in consideration that they are not obliged to post at the top of the LOB so their theoretical prices may differ from the best bid and ask).

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Well, the price is not changing throughout your examples. The bid/ask price will be the highest buy order and lowest sell order.

If by theoretical price you mean a mid, you would just average the two and maybe say that price is valid up until the min amount between the bid and ask.

Doing some kind of weighted average doesn't really make sense because if you are buying for example , just because the volume went up on the bid, doesn't mean the price has improved for you.

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  • $\begingroup$ Couldn't you argue that since there are more buyers at that tick, the product is more valuable, so the theoretical price should be higher? $\endgroup$ – Sameer Lal Sep 25 '18 at 16:23

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