Why Derivative Quotes Differ from Model Values
Summary
The document explains why a derivative’s quoted market price may differ from a model estimate of fair value. It challenges a simple pricing workflow in which a desk recalibrates a model, obtains a valuation, and adds a fixed fee. The response instead describes several sources of price variation: institutions may use different models, calibration inputs, and adjusted market data; liquidity and transaction costs can differ; and bid and ask prices may diverge, especially for illiquid products.
The discussion also identifies collateral costs and desk inventory as influences on quotes. A bank with substantial exposure in one direction may demand a higher price to encourage trades that reduce that position. The response adds that a desk’s willingness to take risk can also move its proposed price away from its modeled value. These are qualitative explanations, not a pricing formula or measured decomposition. The examples focus on swaptions and bank trading desks, and the document gives no data for estimating the size of any adjustment.
Key ideas
- A model valuation is only one input into a derivative’s market quote.
- Different institutions may use different models, calibration methods, and market data adjustments.
- Bid–ask spreads and liquidity costs can make transaction prices diverge from modeled values.
- Collateral terms and a desk’s existing inventory can influence the price it quotes.
- A desk’s willingness to take on risk may also affect its quote, though the document does not quantify this effect.
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Full text
# How do traders come up with prices for derivatives? # How do traders come up with prices for derivatives? 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? Example: Let's say someone wants to buy a swaption. 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. This does not seem to be the standard approach, so what is actually happening? ## Answer by lehalle (score 4, accepted) https://quant.stackexchange.com/a/29892 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).
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