192 MODEL RISK AND FINANCIAL DERIVATIVESstocks or bond traders, derivatives traders cannot sell an option contract,
hedge it, place the paperwork in a drawer and forget about it. Indeed,
there is a need to constantly monitor the corresponding commitments and
adjust the hedge dynamically. Therefore, the need to accurately price and
hedge derivative contracts throughout their life – and, more generally, to
develop models to manage their risks – rapidly became self-evident among
the financial community.
It is therefore not surprising to see that modelling has also significantly
evolved alongside derivatives markets. A few decades ago, the derivatives
industry was lacking sophisticated models, and traders primarily relied
on experience and intuition, with mixed results. Today, there is a prolif-
eration of sophisticated models, which includes well-established models
from academia, proprietary models developed for internal use by leading-
edge financial institutions, and third-party applications intended for sale
or distribution (for example, commercial software). A standard off-the-
shelf financial package typically contains between five and twenty models
to value the same option, whereas a proprietary derivatives pricing soft-
ware in an investment bank might contain several hundred models. As a
result, derivatives traders simultaneously utilize a seemingly disparate col-
lection of models to perform similar or related tasks. These models may
be inconsistent with each other, or even inadequate for the task they are
used for. Nevertheless, their results are often taken for granted, aggregated,
compared and used for making strategic and tactical decisions.
For academics, the abundance of models is clearly unsatisfactory. For
some practitioners, it is simply confusing. For others, it is just a warning
sign of an early developmental stage in the modelling technology. For all,
it should be a signal that a new type of risk has emerged, namely: model
risk. As summarized by Robert C. Merton in his Nobel Prize address, “The
mathematics of financial models can be applied precisely, but the models
are not at all precise in their application to the real world.” The abundance
of models and the imperfect assumptions and hypothetical solutions that
go into them result in model errors becoming more of a probability than
a remote possibility. This hazard is called model risk, and it is generally
categorized as a form of operational risk.
Broadly speaking, model risk encompasses all financial losses directly
attributable to the use of a quantitative model. Derman (1996) lists several
examples of situations associated with model risk, for example, inapplica-
bility of modelling, incorrect model, correct model with incorrect solution,
correct model with inappropriate use, badly approximated solution, soft-
ware and hardware bugs, or unstable data. As illustrated by Green and
Figlewski (1999) or Gibson, Lhabitant, Pistre and Talay (1999), model risk
may lead to a number of problems for financial institutions, such as deriva-
tives trading too low or too high in price, incorrect hedging strategies,
liquidity issues, etc.