Categories of 
Financial risk 

Credit risk 
Market risk 
Liquidity risk 
Operational risk 
Reputational risk 
Volatility risk 
Settlement risk 
Profit risk 
Systemic risk 
In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities.^{[1]} However, model risk is more and more prevalent in activities other than financial securities valuation, such as assigning consumer credit scores, realtime probability prediction of fraudulent credit card transactions, and computing the probability of air flight passenger being a terrorist. Rebonato in 2002 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".
YouTube Encyclopedic

1/5Views:193 97952 12746 96442 531185 034

✪ Introduction to Risk Assessment

✪ Practical Risk Assessment and Mitigation

✪ 4. Stochastic Thinking

✪ Single Index Model

✪ Utility and Risk Preferences Part 1  Utility Function
Transcription
Contents
Types
Burke regards failure to use a model (instead overrelying on expert judgment) as a type of model risk.^{[2]} 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 inaccurate numerical approximations.
Model usage
 Implementation risk.
 Data issues.
 Calibration errors.
Sources
Uncertainty on volatility
Volatility is the most important input in risk management models and pricing models. Uncertainty on volatility leads to model risk. 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."^{[3]} Avellaneda & Paras (1995) proposed a systematic way of studying and mitigating model risk resulting from volatility uncertainty.^{[4]}
Time inconsistency
Buraschi and Corielli 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]}
Correlation uncertainty
Uncertainty on correlation parameters is another important source of model risk. Cont and Deguest propose a method for computing model risk exposures in multiasset equity derivatives and show that options which depend on the worst or best performances in a basket (so called rainbow option) are more exposed to model uncertainty than index options.^{[6]}
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]}
Complexity
Complexity of a model or a financial contract may be a source of model risk, leading to incorrect identification of its risk factors. This factor was cited as a major source of model risk for mortgage backed securities portfolios during the 2007 crisis.
Illiquidity and model risk
Model risk does not only exist 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."^{[8]} Convertible bonds, mortgagebacked 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.^{[9]}
Quantitative approaches
Model averaging vs worstcase approach
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."^{[10]}
Another approach to model risk is the worstcase, or minmax approach, advocated in decision theory by Gilboa and Schmeidler.^{[11]} In this approach one considers a range of models and minimizes the loss encountered in the worstcase scenario. This approach to model risk has been developed by Cont (2006).^{[12]}
Jokhadze and Schmidt (2018) propose several model risk measures using Bayesian methodology. They introduced superposed market risk measures that incorporate model risk and enables consistent market and model risk management. Further, they provide axioms od model risk measures and define several practical examples of superposed model risk measures in the context of financial risk management and contingent claim pricing.
Quantifying model risk exposure
To measure the risk induced by a model, it has to be compared to an alternative model, or a set of alternative benchmark models. The problem is how to choose these benchmark models.^{[13]} In the context of derivative pricing Cont (2006) proposes a quantitative approach to measurement of model risk exposures in derivatives portfolios: first, a set of benchmark models is specified and calibrated to market prices of liquid instruments, then the target portfolio is priced under all benchmark models. A measure of exposure to model risk is then given by the difference between the current portfolio valuation and the worstcase valuation under the benchmark models. Such a measure may be used as a way of determining a reserve for model risk for derivatives portfolios.^{[12]}
Position limits and valuation reserves
Jokhadze and Schmidt (2018) introduce monetary market risk measures that covers model risk losses. Their methodology enables to harmonize market and model risk management and define limits and required capitals for risk positions.
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."^{[14]} Cont (2006) advocates the use of model risk exposure for computing such reserves.
Mitigation
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.
 Avoid letting small issues snowball into large issues later on.
 Independent validation
 Ongoing monitoring and against market
Examples of model risk mitigation
Parsimony
Taleb wrote when describing why most new models that attempted to correct the inadequacies of the Black–Scholes model failed to become accepted:
"Traders are not fooled by the Black–Scholes–Merton 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."^{[15]}
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.^{[16]}
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."^{[17]}
Case studies
 NatWest—Interest rate options and swaptions—incorrect model specification.^{[18]}
 Bank of TokyoMitsubishi—Interest rate options and swaptions.^{[19]}
 LTCM—lack of stress testing—Crouhy, Galai, and Mark.
 Barclays de Zoete Wedd (BZW)—Mispriced currency options.^{[20]}
 National Australia Bank $3 Billion AUD loss on Homeside interest rate model.^{[21]}
 2007–2012 global financial crisis – Overreliance on David X. Li's Gaussian copula model misprices the risk of collateralized debt obligations.^{[22]}
See also
Notes
 ^ ^{a} ^{b} "Model Risk" (pdf). 1996. Retrieved September 10, 2013.
 ^ http://www.siiglobal.org/SII/WEB5/sii_files/Membership/PIFs/Risk/Model%20Risk%2024%2011%2009%20Final.pdf
 ^ Derman, Emanuel (May 26, 2003). "Laughter in the Dark: The Problem of the Volatility Smile".
 ^ Avellaneda, M.; Levy, A.; Parás, A. (1995). "Pricing and hedging derivative securities in markets with uncertain volatilities". Applied Mathematical Finance. 2 (2): 73–88. doi:10.1080/13504869500000005.
 ^ Buraschi, A.; Corielli, F. (2005). "Risk management implications of timeinconsistency: Model updating and recalibration of noarbitrage models". Journal of Banking & Finance. 29 (11): 2883. doi:10.1016/j.jbankfin.2005.02.002.
 ^ Cont, Rama; Romain Deguest (2013). "Equity Correlations Implied by Index Options: Estimation and Model Uncertainty Analysis". Mathematical Finance. 23 (3): 496–530. doi:10.1111/j.14679965.2011.00503.x. SSRN 1592531.
 ^ Gennheimer, Heinrich (2002). "Model Risk in Copula Based Default Pricing Models". CiteSeerX 10.1.1.139.2327. Missing or empty
url=
(help)  ^ Frey, Rüdiger (2000). "Market Illiquidity as a Source of Model Risk in Dynamic Hedging". CiteSeerX 10.1.1.29.6703. Missing or empty
url=
(help)  ^ Black, Keith H. (2004). Managing a Hedge Fund. McGrawHill Professional. ISBN 9780071434812.
 ^ Rantala, J. (2006). "On joint and separate history of probability, statistics and actuarial science". In Liksi; et al. (eds.). Festschrift for Tarmo Pukkila on his 60th Birthday. University of Tampere, Finland. pp. 261–284. ISBN 9514466209.
 ^ Gilboa, I.; Schmeidler, D. (1989). "Maxmin expected utility with nonunique prior". Journal of Mathematical Economics. 18 (2): 141. doi:10.1016/03044068(89)900189.
 ^ ^{a} ^{b} Cont, Rama (2006). "Model uncertainty and its impact on the pricing of derivative instruments" (PDF). Mathematical Finance. 16 (3): 519–547. doi:10.1111/j.14679965.2006.00281.x.
 ^ Sibbertsen; Stahl; Luedtke (November 2008). "Measuring Model Risk" (PDF). Leibnitz University Discussion Paper No. 409.
 ^ Kato, Toshiyasu; Yoshiba, Toshinao (December 2000). "Model Risk and Its Control" (PDF). Monetary and Economic Studies.
 ^ Taleb, Nassim (2010). Dynamic Hedging: Managing Vanilla and Exotic Options. New York: Wiley. ISBN 9780471353478.
 ^ Cherubini, Umberto; Lunga, Giovanni Della (2007). Structured Finance. Hoboken: Wiley. ISBN 9780470026380.
 ^ Fender, Ingo; Kiff, John (2004). "CDO rating methodology: Some thoughts on model and its implications". BIS Working Papers No. 163. SSRN 844225.
 ^ "Model Validation and Backtesting".
 ^ "Controlling Model Risk".
 ^ Simmons, Katerina (1997). "Model Error" (PDF). New England Economic Review: 17–28. Evaluation of various finance models
 ^ "National Australia Bank chief promises review as share price drops".
 ^ "Recipe for Disaster: The Formula That Killed Wall Street". Wired. February 23, 2009.
References
 Avellaneda, M.; Levy, A.; Parás, A. (1995). "Pricing and hedging derivative securities in markets with uncertain volatilities". Applied Mathematical Finance. 2 (2): 73–88. doi:10.1080/13504869500000005.
 Cont, R. (2006). "Model Uncertainty and Its Impact on the Pricing of Derivative Instruments". Mathematical Finance. 16 (3): 519–547. doi:10.1111/j.14679965.2006.00281.x.
 Cont, R.; Deguest, R. (2013). "Equity Correlations Implied by Index Options: Estimation and Model Uncertainty Analysis". Mathematical Finance. 23 (3): 496–530. doi:10.1111/j.14679965.2011.00503.x.
 Cont, R.; Deguest, R.; Scandolo, G. (2010). "Robustness and sensitivity analysis of risk measurement procedures". Quantitative Finance. 10 (6): 593–606. doi:10.1080/14697681003685597.
 Crouhy, Michel; Galai, Dan; Mark, Robert (2000). Risk Management. McGrawHill. ISBN 0071357319.
 Derman, Emanuel (1996). Model Risk (PDF). RISK.
 Jokhadze, Valeriane; Schmidt, Wolfgang M. (2018). "Measuring model in financial risk management and pricing". SSRN. Cite journal requires
journal=
(help)  Lyons, T. J. (1995). "Uncertain volatility and the riskfree synthesis of derivatives". Applied Mathematical Finance. 2 (2): 117–133. doi:10.1080/13504869500000007.
 Rebonato, R. (2001). "Managing Model Risk". Handbook of Risk Management. FTPrentice Hall.
 Taleb, Nassim (2006). Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets. Wiley. ISBN 1400067936.
 US Federal Reserve Policy http://www.federalreserve.gov/bankinforeg/srletters/sr1107a1.pdf SUPERVISORY GUIDANCE ON MODEL RISK MANAGEMENT