Coping with model risk

The collapse of the Bretton Woods Agreement, the resulting dollar devaluation and
shift from floating to fixed currency exchange rates, the world oil price crisis and the
explosive increase in interest rates volatility in the late 1970s and early 1980s, the
successive crashes of the stock markets in 1973/4, 1987, 1997 and 1998, the crash
of the bond markets in 1994 – all these events have produced a progressive revolution
in the art and science of risk management and have contributed to the development
of a vast array of financial instruments and quantitative models for eliminating
exposure to risk. These instruments and models have become central to a large
number of practitioners, financial institutions and markets around the world. Indeed,
risk management is certainly the central topic for the management of financial
institutions in the 1990s.

Sophisticated mathematical models and a strong influence on practice were not
always hallmark of finance theory. Finance has long remained a rather descriptive
discipline, based on rules of thumb and experience. The original Bachelier (1900)
work on option pricing remained forgotten for a long time.

The major strides in mathematical modeling came in the area of investments and
capital markets with the Markowitz (1952) portfolio selection model and the Sharpe
(1963) capital asset pricing model. Sharpe’s and Markowitz’s models began a shift
away from the traditional ad-hoc selection of the ‘best’ stock for an investor towards
the concept of a quantified trade-off between risk and return. Both authors were
awarded by the Nobel Prize in Economics in 1990.

The most important development in terms of impact on practice was the publication
of the Black and Scholes (1973) and Merton (1973) model for option pricing just a
month after the Chicago Board Options Exchange started trading the first listed
options in the United States. The simplicity of the model, its analytical tractability
as well as its ease of understanding rapidly seduced practitioners.1 They adopted it.
A new era of mathematical modeling was born.

The extraordinary flow of financial innovations stimulated the further development
of mathematical models. The increasing technical sophistication in financial markets
and the explosion of exotic and over-the-counter instruments induced a concomitant
need for models and, consequently, for analysis and computation. Inexorably, they
led to an escalation in the level of mathematics, including probability theory, statistics,
programming, partial differential equations and numerical analysis. The application
of mathematics to important problems related to derivatives pricing, hedging, or
risk management has expanded rapidly over the past few years, yielding a proliferation
of models.

In the early 1970s, the major problem for financial institutions was the lack of
models. Thirty years later, the problem is now the excessive number of them.
Therefore, a new kind of risk must be considered: model risk. This includes all the
dangers of accepting models without carefully questioning them.