Fitting model parameters to market prices
Question
What is calibration in quantitative finance?
Short answer
Choosing model parameters so the model reproduces observed prices of liquid instruments (e.g. vanilla options or swaptions). It is usually a least-squares optimisation, or exact fitting through time-dependent parameters. Calibrated models then price exotics consistently with the market. The pitfall is that a good fit today need not mean correct dynamics: parameters often have to be refitted daily, a sign the model is misspecified.
Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 41, p.191; question and answer rewritten by SelfMadeQuant.com.
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