Quantifying the Model Risk Inherent in the Calibration and Recalibration of Option Pricing Models

TL;DR

This paper quantifies two types of model risk in option pricing models—calibration error and recalibration risk—using relative entropy, and analyzes their trade-offs through empirical case studies with Black-Scholes and Heston models.

Contribution

It introduces a unified framework to measure and compare calibration and recalibration risks in option models using relative entropy, highlighting the trade-offs involved.

Findings

Frequent recalibration shifts risk types without reducing total risk.

More complex models may increase risk if robustness is prioritized.

Recalibration frequency impacts the distribution of model risk.

Abstract

We focus on two particular aspects of model risk: the inability of a chosen model to fit observed market prices at a given point in time (calibration error) and the model risk due to recalibration of model parameters (in contradiction to the model assumptions). In this context, we follow the approach of Glasserman and Xu (2014) and use relative entropy as a pre-metric in order to quantify these two sources of model risk in a common framework, and consider the trade-offs between them when choosing a model and the frequency with which to recalibrate to the market. We illustrate this approach applied to the models of Black and Scholes (1973) and Heston (1993), using option data for Apple (AAPL) and Google (GOOG). We find that recalibrating a model more frequently simply shifts model risk from one type to another, without any substantial reduction of aggregate model risk. Furthermore, moving to a more complicated stochastic model is seen to be counterproductive if one requires a high degree of robustness, for example as quantified by a 99 percent quantile of aggregate model risk.