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

Yu Feng (), Ralph Rudd (), Christopher Baker (), Qaphela Mashalaba (), Melusi Mavuso () and Erik Schlogl ()
Additional contact information
Yu Feng: Quantitative Finance Research Centre, University of Technology Sydney, Broadway, NSW 2007, Australia
Ralph Rudd: The African Institute for Financial Markets and Risk Management (AIFMRM), University of Cape Town, Rondebosch 7701, South Africa
Christopher Baker: The African Institute for Financial Markets and Risk Management (AIFMRM), University of Cape Town, Rondebosch 7701, South Africa
Qaphela Mashalaba: The African Institute for Financial Markets and Risk Management (AIFMRM), University of Cape Town, Rondebosch 7701, South Africa
Melusi Mavuso: The African Institute for Financial Markets and Risk Management (AIFMRM), University of Cape Town, Rondebosch 7701, South Africa

Risks, 2021, vol. 9, issue 1, 1-20

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 the recalibration of model parameters (in contradiction to the model assumptions). In this context, we 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 by applying it to the seminal Black/Scholes model and its extension to stochastic volatility, while 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% quantile of aggregate model risk.

Keywords: model risk; option pricing; relative entropy; model calibration; stochastic volatility (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
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Working Paper: Quantifying the Model Risk Inherent in the Calibration and Recalibration of Option Pricing Models (2018) Downloads
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