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Several resources I saw introduce the notion of bid/ask spread when trying to price options in incomplete market, I don't understand why the notion is introduced since we are interested on the price that will be given by the seller of the option so why considering the bid-ask spread ? To be sure that the $bid\leq ask$ ? Did I miss something ?

Thank you a lot

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    $\begingroup$ I don’t know which resources you refer to but: It allows a bit more flexibility when fitting then requiring that the prices match the mid price? Quoted prices might be preferred over last traded price as the latter could be stale for less liquid contracts. $\endgroup$
    – Bob Jansen ♦
    Jun 6, 2022 at 15:34
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    $\begingroup$ One generalization of equilibrium price is that there are two prices $P_B$ and $P_A$ such that if the market price was above $P_A$ everybody wants to sell it, if the price is below $P_B$ everyone wants to buy it, so these cases are in disequilibrium. But the prices $P_B<=P<=P_A$ are viable and can be considered no-arbitrage prices. In these theories the price is no longer unique. $\endgroup$
    – nbbo2
    Jun 6, 2022 at 16:44
  • $\begingroup$ Oh great ! Thank you I did not see that from this point of view $\endgroup$
    – coboy
    Jun 7, 2022 at 13:20

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It allows a bit more flexibility when fitting then requiring that the prices match the mid price. Quoted prices might be preferred over last traded price as the latter could be stale for less liquid contracts. As pointed out by @nbbo2 this makes all the prices between the bid and the ask no-arbitrage prices.

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