Some Economically Meaningful Option Model Calibration Performance Measures

Abstract

The desire to more accurately calibrate option pricing models to liquid option prices has been an important driver of the growth of the option pricing literature and practice. However, the most commonly used model calibration accuracy metrics are not designed to reflect the economic consequences of trading based on model prices. To address this shortcoming, we derive, from first principles, in an idealized market setting, new, tractable, and economically meaningful, utility-based, measures of option pricing model calibration performance. We show that when pricing errors are “small,” our measures closely approximate popular percentage pricing error-based metrics. However, our measures can be quite different when model prices are smaller than they ought to be (which can happen when the option pricing model does not properly take into account fat-tailed asset return effects). We compare our measures with widely used metrics and show, via examples using SPX options data, that our new measures better inform us about the economic consequences of model pricing error and thereby better allow us to select among candidate option pricing models.

Keywords: Option Pricing Model, Performance Measure, Model Calibration, Calibration Error, Economic Consequences, Fat-Tailed, Asset Returns, Utility-based

JEL Classification: G13