Decision-Theoretic Calibration of Option Pricing Models

Abstract

We give a decision-theoretic procedure for the calibration of option pricing models. The inspiration behind it comes from the Weighted Monte Carlo (WMC) approach. The procedure incorporates rare-event probability distortion in style of Cumulative Prospect Theory (CPT) by Kahneman and Tversky. We also propose an intertemporal interpolation scheme to use with the probability distortion when more than one option maturity is present in the calibration. We show how the procedure significantly improves the out-of-sample accuracy for the arbitrage models we calibrate compared to the original WMC procedure. To our knowledge, this is the first instance where CPT is used to improve the performance of option pricing models in a practical way.