LO 47.1: Identify and explain errors in modeling assumptions that can introduce

LO 47.1: Identify and explain errors in modeling assumptions that can introduce model risk.
Modeling is a critical component in the risk management of an organization. Models help quantify risk and other exposures as well as potential losses. However, models can be complex and are subject to model risk, which includes input errors, errors in assumptions, and errors in interpretation.
Model Complexity
When quantifying the risk of simple financial instruments such as stocks and bonds, model risk is less of a concern. These simple instruments exhibit less volatility in price and sensitivities relative to complex financial instruments so, therefore, their market values tend to be good indicators of asset values. However, model risk is a significantly more important consideration when quantifying the risk exposures of complex financial instruments, including instruments with embedded options, exotic over-the-counter (OTC) derivatives, synthetic credit derivatives, and many structured products. For these complex instruments, markets are often illiquid and do not provide sufficient price discovery mechanisms, which puts greater emphasis on models to value instruments, typically through a mark-to-model valuation approach. These models are important not only for valuing instruments and assessing risk exposure, but also to determine the proper hedging strategy.
As financial instruments increase in complexity, so do the models used to value them. More complex models, such as the Black-Scholes-Merton option pricing model, increased the
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Topic 47 Cross Reference to GARP Assigned Reading – Crouhy, Galai, and Mark, Chapter 15
threat of model risk, especially for the more complex derivatives such as interest rate caps and floors, swaptions, and credit and exotic derivatives. As technology advanced, so did the complexity of the models created and used. The growth in complexity of the models also increased the reliance on these models. In addition, managers often do not have a solid understanding of the more complex models. When models are difficult to understand, the risk of model errors and the risk of incorrect vetting, interpretation, and oversight increases.
The dangers of relying too heavily on complex models became especially apparent during the 2007-2009 financial crisis. When markets endure a prolonged period of turmoil, models tend to underestimate the volatilities, correlations, and risks of financial instruments, and can overstate values, all of which may lead to sustained losses by market participants. Since models are often used for valuing instruments, a model may show that a strategy is profitable when in fact it is experiencing losses. Following the global credit crisis, model risk became more regulated as the Basel Committee mandated that financial institutions more rigorously assess model risk.
Common Model Errors
Model risk has been apparent over the last several decades through various international crises. A model may be incorrect if it contains incorrect assumptions about a financial instruments price or risk. One example of model error was the remarkable collapse in 1997 of a hedge fund run by Victor Niederhoffer, a well-known Wall Street trader. The funds strategy was to write (sell) deep out-of-money put options on the S&P 500, based on the assumption that the index volatility would not exceed 5% daily, and therefore, the option would expire worthless. In October 1997, the Asian financial crisis created a contagion effect that impacted North American markets. As a result, market volatilities increased significantly above historical levels. This level of volatility was not priced into the advanced mathematical models used by the fund which instead assumed a normal distribution of risk and historical correlations. The fund ultimately experienced substantial losses as its equity was completely wiped out.
Losses from model errors can be due to errors in assumptions, carelessness, fraud, or intentional mistakes that undervalue risk or overvalue profit. The six common model errors are as follows: 1. Assuming constant volatility. One of the most common errors in modeling is the
assumption that the distribution of asset price and risk is constant. The 20072009 financial crisis showed just how incorrect this assumption can be, when market volatilities not predicted by models increased significantly over a short period of time.
2. Assuming a normal distribution o f returns. Market participants frequently make the simplifying assumption in their models that asset returns are normally distributed. Practice has shown, however, that returns typically do not follow a normal distribution, because distributions in fact have fat tails (i.e., unexpected large outliers).
3. Underestimating the number o f risk factors. Many models assume a single risk factor. A
single risk factor may produce accurate prices and hedge ratios for simple products such as a callable bond. For more complex products, including many exotic derivatives (e.g., Bermuda options), models need to incorporate multiple risk factors.
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Topic 47 Cross Reference to GARP Assigned Reading – Crouhy, Galai, and Mark, Chapter 15
4. Assuming perfect capital markets. Models are generally derived with the assumption that
capital markets behave perfectly. Consider a delta hedge strategy that requires active rebalancing based on the assumption that the underlying asset position is continuously adjusted in response to changes in the derivatives price. This strategy will not be effective if capital markets include imperfections, including limitations on short selling, various costs (e.g., fees and taxes), and a lack of continuous trading in the markets.
5. Assuming adequate liquidity. Models often assume liquid markets for long or short
trading of financial products at current prices. During periods of volatility, especially extreme volatility, as seen during the recent financial crisis, liquidity could decline or dry up completely.
6. Misapplying a model. Historically, model assumptions have worked well in most world markets, but tend to break down during periods of greater uncertainty or volatility. For example, traditional models assuming normality did not work well in many countries, including the United States, Europe, and Japan in the post financial crisis period, which has been characterized by low or negative interest rates and unconventional monetary policies including quantitative easing. In these markets, models that include other statistical tools work better. Similarly, models that work well for traditional assets could yield incorrect results when complex factors including embedded options are factored in. Another example of misapplying a model is to use one that was created to value bonds with no embedded options (e.g., a non-callable, non-convertible bond) to now value bonds with embedded options (e.g., a callable, convertible bond).

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