 Model risk

In finance, model risk is the risk involved in using models to value financial securities.^{[1]} Rebonato considers alternative definitions including:
 After observing a set of prices for the underlying and hedging instruments, different but identically calibrated models might produce different prices for the same exotic product.
 Losses will be incurred because of an ‘incorrect’ hedging strategy suggested by a model.^{[2]}
Rebonato defines model risk as "the risk of occurrence of a significant difference between the marktomodel value of a complex and/or illiquid instrument, and the price at which the same instrument is revealed to have traded in the market."
Contents
Types of model risk
Burke regards failure to use a model (instead overrelying on expert judgement) as a type of model risk.^{[3]} Derman describes various types of model risk that arise from using a model:^{[1]}
 Wrong model
 Inapplicability of model.
 Incorrect model specification.
 Model implementation
 Programming errors.
 Technical errors.
 Use of numerical approximations.
 Model usage
 Implementation Risk.
 Data issues.
 Calibration errors.
Sources of model risk
 Interest rate modelling
Buraschi and Corelli ^{[4]} formalise the concept of 'time inconsistency' with regards to noarbitrage models that allow for a perfect fit of the term structure of the interest rates. In these models the current yield curve is an input so that new observations on the yield curve can be used to update the model at regular frequencies. They explore the issue of timeconsistent and selffinancing strategies in this class of models. Model risk affects all the three main steps of risk management: specification, estimation and implementation.^{[5]}
 The volatility smile
Derman believes that products whose value depends on a volatility smile are most likely to suffer from model risk. He writes "I would think it’s safe to say that there is no area where model risk is more of an issue than in the modeling of the volatility smile."^{[6]}
 Correlation modelling
Gennheimer investigates the model risk present in pricing basket default derivatives. He prices these derivatives with various copulas and concludes that "... unless one is very sure about the dependence structure governing the credit basket, any investors willing to trade basket default products should imperatively compute prices under alternative copula specifications and verify the estimation errors of their simulation to know at least the model risks they run."^{[7]}
Buraschi, Porchia and Trojani (2010) propose a framework for intertemporal portfolio choice when the covariance matrix of returns is stochastic. An important contribution of this framework is that it allows to derive optimal portfolio implications for economies in which the degree of correlation across different industries, countries, and asset classes is timevarying and stochastic. ^{[8]}
Mitigating model risk
 Theoretical basis
 Considering key assumptions.
 Considering simple cases and their solutions (model boundaries).
 Parsimony.
 Implementation
 Pride of ownership.
 Disseminating the model outwards in an orderly manner.
 Testing
 Stress testing and backtesting.
 Try to simulate model risk.
 Avoid letting small issues snowball into large issues later on.
 Model averaging
Rantala (2006) mentions that "In the face of model risk, rather than to base decisions on a single selected ”best” model, the modeller can base his inference on an entire set of models by using model averaging."^{[9]}
 Position limits and valuation reserves
Kato and Yoshiba discuss qualitative and quantitative ways of controlling model risk. They write "From a quantitative perspective, in the case of pricing models, we can set up a reserve to allow for the difference in estimations using alternative models. In the case of risk measurement models, scenario analysis can be undertaken for various fluctuation patterns of risk factors, or position limits can be established based on information obtained from scenario analysis."^{[10]}
Examples of model risk mitigation
 Parsimony
Taleb wrote when describing why most new models that attempted to correct the inadequacies of the BlackScholes model failed to become accepted:
"Traders are not fooled by the BlackScholesMerton model. The existence of a 'volatility surface' is one such adaptation. But they find it preferable to fudge one parameter, namely volatility, and make it a function of time to expiry and strike price, rather than have to precisely estimate another."^{[11]}
However Cherubini and Della Lunga describe the disadavantages of parsimony in the context of volatility and correlation modelling. Using an excessive number of parameters may induce overfitting while choosing a severely specified model may easily induce model misspecification and a systematic failure to represent the future distribution.^{[12]}
Model risk properties and implications
 Illiquid product model risk
Model risk does not only exit for complex financial contracts. Frey (2000) presents a study of how market illiquidity is a source of model risk. He writes "Understanding the robustness of models used for hedging and riskmanagement purposes with respect to the assumption of perfectly liquid markets is therefore an important issue in the analysis of model risk in general."^{[13]} Convertible bonds, mortgage backed securities and highyield bonds can often be illiquid and difficult to value. Hedge funds that trade these securities can be exposed to model risk when calculating monthly NAV for its investors.^{[14]}
 Model risk premium
Fender and Kiff (2004) note that holding complex financial instruments such as CDOs "translates into heightened dependence on these assumptions and, thus, higher model risk. As this risk should be expected to be priced by the market, part of the yield pickup obtained relative to equally rated single obligor instruments is likely to be a direct reflection of model risk."^{[15]}
 Difficulty of quantifying model risk
To measure the risk induced by a model it has to be compared to an alternative model. To correctly specify the model risk you have to know an accurate model. However, accurate models are often hard to find. As we cannot always find an accurate model we need a benchmark model giving a close approximation to our data. The problem is how to choose this benchmark model. If we knew the model closest to our data we could easily use this model for risk measurement and model risk would no longer be a problem. Thus, finding a suitable benchmark model is a serious problem. However, it will hardly be possible to overcome this problem when discussing model risk.^{[16]}
Case studies
 Natwest  Interest rate options and swaptions  incorrect model specification.^{[17]}
 Bank of Tokyo/Mitsubushi  Interest rate options and swaptions.^{[18]}
 LTCM  lack of stress testing  Crouhy, Galai and Mark.
 Barclays de Zoete Wedd (BZW)  Mispriced currency options.^{[19]}
See also
Notes
 ^ ^{a} ^{b} http://www.ederman.com/new/docs/gsmodel_risk.pdf Model Risk (1996)
 ^ http://www.quarchome.org/ModelRisk.pdf Theory and Practice of Model Risk Management
 ^ . >http://www.siiglobal.org/SII/WEB5/sii_files/Membership/PIFs/Risk/Model%20Risk%2024%2011%2009%20Final.pdf
 ^ http://www.eco.unipmn.it/eventi/irm/newahead.pdf  Staying Ahead of the Curve: Model Risk and the Term Structure. Andrea Buraschi and Francesco Corielli. (2001)
 ^ Buraschi A, Corielli F, 2005, Risk management implications of timeinconsistency: model updating and recalibration of noarbitrage models, Journal of Banking and Finance 29, Pages: 2883  2907.
 ^ Emanuel Derman  Laughter in the Dark  The Problem of the Volatility Smile (2003)
 ^ Heinrich Gennheimer  Model Risk in Copula Based Default Pricing Models (2002)
 ^ Buraschi A., et al., Correlation Risk and Optimal Portfolio Choice, 2010, The Journal of Finance 65, 393420.
 ^ Rantala, J. (2006): ”On joint and separate history of probability, statistics and actuarial science”, Eds. Liksi et al. Festschrift for Tarmo Pukkila on his 60th Birthday, pp261284, University of Tampere, Finland.
 ^ http://www.imes.boj.or.jp/english/publication/mes/2000/me1825.pdf  Model Risk and Its Control  Toshiyasu Kato and Toshinao Yoshiba, Monetary and Economic Studies/December 2000
 ^ Dynamic Hedging  Wiley. Nassim Taleb
 ^ Structured Finance  Wiley. By Umberto Cherubini, Giovanni Della Lunga
 ^ Frey, Rudiger, 2000, Market illiquidity as a source of model risk in dynamic hedging, Model Risk
 ^ Managing a Hedge Fund, Keith H. Black, McGrawHill Professional (2004) ISBN 9780071434812
 ^ CDO rating methodology: Some thoughts on model and its implications. BIS Working Papers No 163
 ^ Measuring Model Risk  Sibbertsen, Stahl and Luedtke, Leibnitz University (2008)
 ^ http://www.blackswanrisk.com/advisory5.html Model Validation and Backtesting
 ^ http://www.derivativesstrategy.com/magazine/archive/1997/0697fea1.asp Controlling Model Risk
 ^ http://findarticles.com/p/articles/mi_m3937/is_/ai_20414680 Model error  evaluation of various finance models
References
 Rebonato R (2001). ‘Managing Model Risk’ in Handbook of Risk Management. FTPrentice Hall.
 Michel Crouhy, Dan Galai, Robert Mark (2000). Risk Management. McGrawHill. 9780071357319.
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