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

16 Pages Posted: 11 Nov 2018

See all articles by Yu Feng

Yu Feng

University of Technology Sydney (UTS) - Faculty of Business

Ralph Rudd

The African Institute of Financial Markets and Risk Management

Christopher Baker

The African Institute for Financial Markets and Risk Management (AIFMRM), University of Cape Town

Qaphela Mashalaba

African Institute of Financial Markets and Risk Management

Melusi Mavuso

University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management

Erik Schlogl

University of Technology Sydney (UTS), Quantitative Finance Research Centre; Financial Research Network (FIRN)

Date Written: October 19, 2018

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) to 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% quantile of aggregate model risk.

Keywords: Model Risk, Relative Entropy, Option Pricing, Model Calibration, Model Recalibration, Stochastic Volatility

JEL Classification: G11, G13, C10

Suggested Citation

Feng, Yu and Rudd, Ralph and Baker, Christopher and Mashalaba, Qaphela and Mavuso, Melusi and Schloegl, Erik, Quantifying the Model Risk Inherent in the Calibration and Recalibration of Option Pricing Models (October 19, 2018). Available at SSRN: https://ssrn.com/abstract=3267775 or http://dx.doi.org/10.2139/ssrn.3267775

Yu Feng

University of Technology Sydney (UTS) - Faculty of Business ( email )

Australia

Ralph Rudd

The African Institute of Financial Markets and Risk Management ( email )

Leslie Commerce Building
Rondebosch
Cape Town, Western Cape 7700
South Africa
+27 21 650 2474 (Phone)

Christopher Baker

The African Institute for Financial Markets and Risk Management (AIFMRM), University of Cape Town ( email )

3rd Floor, leslie Commerce Building
Engineering Mall, Upper Campus
Cape Town, Western Cape 8000
South Africa

Qaphela Mashalaba

African Institute of Financial Markets and Risk Management ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa
0661227589 (Phone)

Melusi Mavuso

University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management ( email )

Leslie Commerce Building
Rondebosch
Cape Town, Western Cape 7700
South Africa

Erik Schloegl (Contact Author)

University of Technology Sydney (UTS), Quantitative Finance Research Centre ( email )

Haymarket
PO Box 123
Sydney, NSW 2007
Australia
+61 2 9514 7785 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.schlogl.com

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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