Model risk

Quantitative approaches

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." This approach avoids the "flaw of averages".

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).

Jokhadze and Schmidt (2018) propose several model risk measures using Bayesian methodology. They introduce superposed risk measures that incorporate model risk and enables consistent market and model risk management. Further, they provide axioms of 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. 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

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." Cont (2006) advocates the use of model risk exposure for computing such reserves.

Case studies

• Merrill Lynch (1970s; $70m loss) - for stripped bonds, used a single par yield instead of separate annuity yield-curves and zero-coupon curves for the resultant IO and PO securities.

• NatWest (1997; £90m loss) - incorrect model specification, "a naive volatility input in their systems", for interest rate options and swaptions.

• Bank of Tokyo-Mitsubishi (1997; $83m loss) - a "systematic pricing bias" for out-of-the-money and Bermuda swaptions which had been calibrated to at-the-money vanilla swaptions.

• Barclays de Zoete Wedd (1997; £15m loss) - mispriced currency options.

• LTCM (1998; required $3.65 billion in recapitalization) - risk models had drastically under-estimated the risks of a profound economic crisis, due to an insufficient data-window and a lack of stress testing.

• National Australia Bank (2001; $2.2 Billion AUD loss) - its Homeside interest rate model made inconsistent use of rates.

• 2008 financial crisis – Over-reliance on David X. Li's Gaussian copula model misprices the risk of collateralized debt obligations.

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

Nassim 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 disadvantages 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."