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. However, model risk is more and more prevalent in activities other than financial securities valuation, such as assigning consumer credit scores, real-time probability prediction of fraudulent credit card transactions, and computing the probability of air flight passenger being a terrorist. Rebonato in 2002 considers alternative definitions including:
Contents
- Types of model risk
- Wrong model
- Model implementation
- Model usage
- Model averaging vs worst case approach
- Quantifying model risk exposure
- Position limits and valuation reserves
- Theoretical basis
- Implementation
- Testing
- Parsimony
- Model risk premium
- Case studies
- References
- 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.
Rebonato defines model risk as "the risk of occurrence of a significant difference between the mark-to-model value of a complex and/or illiquid instrument, and the price at which the same instrument is revealed to have traded in the market."
Types of model risk
Burke regards failure to use a model (instead over-relying on expert judgment) as a type of model risk. Derman describes various types of model risk that arise from using a model:
Wrong model
Model implementation
Model usage
Model averaging vs worst-case 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."
Another approach to model risk is the worst-case, or minmax approach, advocated in decision theory by Gilboa and Schmeidler. In this approach one considers a range of models and minimizes the loss encountered in the worst-case scenario. This approach to model risk has been developed by Cont (2006).
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. 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 worst-case valuation under the benchmark models. Such a measure may be used as a way of determining a reserve for model risk for derivatives portfolios.
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." Cont (2006) advocates the use of model risk exposure for computing such reserves.
Theoretical basis
Implementation
Testing
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."
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.
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 pick-up obtained relative to equally rated single obligor instruments is likely to be a direct reflection of model risk."