How do traders come up with prices for derivatives?

Question

As a follow up to a recent question on why market prices and model prices can sometimes differ substantially, this resulted in a new question.

How do traders come up with prices?

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Example: Let's say someone wants to buy a swaption. I always assumed it worked like this:

1. Backoffices continuously collect data and recalibrate the pricing models, for example forward rates or option prices (volatilities) are used to calibrate SABR-Parameters.
2. 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.
3. The trader adds a few basis points to the NPV from step 2 as a fee.

This does not seem to be the standard approach, so what is actually happening?

Answer 1

You have two main reasons why market prices are not all perfectly aligned with models:

• each bank uses its own model, its own libraries to calibrate, and its own corrected market prices. You can see this reason as the secret sauce of each bank / desk.
• liquidity costs are different from one trade and bank to another: (1) do not forget you have different bid and ask prices for the same product (hence for illiquid products the market prices are transaction prices; they can be different for buys than for sells); (2) when collateralization is needed, the availability and price for collateral can be different from one bank to another; (3) last but not least banks take their inventory into account, if you already sold a lot of risk in one direction, you will now sell it at an higher price (to try to net your inventory back to zero).

To be frank there is a third reason, but I do not like it: some banks / desks may have appetite for risk in given directions. They are ready to take risk. Hence the difference between the "fair price" (in your views: i.e. price that models are telling) and the proposed price can be different. I do not like this third case because banks should be intermediaries (i.e. act as market makers).