If I ask a sell-side desk "A" for a "valuation" of a relatively simple OTC product (equity derivative, or 1st generation equity exotic), what are the reasons/main reason why a different sell-side desk "B" (at some other bank) would arrive at a different valuation for exactly the same product?
Pricing these products is subject to different models. One bank might calibrate their vol surfaces slightly differently and have different skews on their respective smiles. Also, one bank might assume a slightly different stochastic process in their model for the pricing - or use the same model, but calibrated with different parameters.
Lastly, If I already am very very long a lot of SPX gamma, I probably don't want to buy a short dated digital near the money from you - I would probably prefer to sell it to you to unload some gamma - and I will show you prices according to my preference - of course if you buy from me immediately, no questions asked, I may suspect that I was a bit low and move the price up a bit afterwards.