198 MODEL RISK AND FINANCIAL DERIVATIVESof information in a few standardized and comparable numbers. This is the
case, for instance, of the yield to maturity of a bond or the implied volatility
of an option. In the latter case, a model (say the Black and Scholes formula)
is a filter that turns quoted dollar values into an indicator of expected future
volatility. As long as the result is taken cautiously, the quality of the model
used plays a limited role. What really matters is the price the shorthand
stands for, not the model itself. As an analogy, measuring and comparing
distance using a biased meter does not matter as long as all distances are
biased by the same factor. With such models, model risk is virtually non-
existent or irrelevant. However, trouble may start if the model output is used
as an input to another model (for example, relying on implied volatility to
implement a hedging strategy).
10.4.2 A model is an approximation too
The second series of models are meant to serve as reasonable approximations
or abstractions of some real-world behavior. They seek to explain relation-
ships between observed phenomena and their generating process in an
idealized way. They are less complicated than reality and hence easier to deal
with. Their simplicity often lies in the fact that only the relevant properties
of reality are represented, so that reasonable and acceptable approxima-
tions of reality are obtained for specific problems in ordinary situations. For
instance, models that provide theoretical values to traders and investors
and/or estimate risk exposures for risk managers enter into this category.
These models are usually popular and do not generate model risk per se.
However, model risk can appear because of self-confidence. When a model
seems to be consistent with the recurrence of similar expected results, we
begintobecomeconfidentaboutitsvalidity, assumethatthemodeliscorrect,
and often start using it as an extrapolation device outside of its definition
range (for example, for rare and unusual situations) to predict and control
the future. As an illustration, consider again the Black and Scholes model.
As illustrated previously, it provides a useful pricing approximation for
most at-the-money options close to expiry, but will give incorrect results for
in-the-money and out-of-the-money options, resulting in the well known
volatility smile.
10.4.3 A model is all that there is
In some extreme cases, a model may be the only tool available for valuation
and/or decision-making. This is the case, for instance, with derivative
instruments traded on OTC markets with only one market-maker, or with
automated quoting and trading machines. Models in this latter category are,