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How do traders come up with prices for derivatives?

I always assumed it worked like this: Backoffices continuously collect data and recalibrate the pricing models, for example forward rates or option prices (volatilities) are used to calibrate SABR-Parameters … A trader who wants to sell a swaption uses the bank's pricing library to get an estimate for the fair value of the swaption. The trader adds a few basis points to the NPV from step 2 as a fee. …
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