Title: Quantifying the Model Risk Inherent in the Calibration and Recalibration of Option Pricing Models,
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.