FRANÇOIS-SERGE LHABITAN T 199of course, the most likely candidates to generate model risk, since common
sense is of little use.
10.5 THE MODEL-BUILDING PROCESS AND MODEL
RISK-CREATION
Model risk is somehow similar to a virus: it is relatively easy to catch, and
once in, it becomes extremely contagious. To understand how easy it is
to introduce model risk within an institution, let us focus on the model-
building process, that is, the procedure for the construction and verification
of models for financial derivatives. A typical model-building process can be
split into three steps: (1) model selection or creation; (2) model calibration;
and (3) model usage. Each of these steps is capable of generating model risk.
10.5.1 Model selection/creation
In finance, most models have predictable regular features (deterministic)
and unpredictable ones (stochastic). Since the unpredictable features are
the ones which derivatives target, it is not surprising that the principal
mathematical tool to build derivatives models relies heavily on probabilistic
techniques and the theory of stochastic processes.As an illustration, the stan-
dard approach to option pricing consists of specifying the stochastic process
followed by an underlying asset price and then deriving the option price as
a function of the process parameters. Unfortunately, academic research has
long stressed mathematical elegance as a key to quality.
Since analytic and closed-form solutions were the only noble outputs for
option-pricing models, several researchers carefully selected the stochastic
processes they were using in order to obtain closed-form solutions for their
results. Sometimes, trade-offs were made between mathematical elegance
and realism. Consequently, speculative prices underlying financial deriva-
tives are not necessarily well represented by the few stochastic processes –
and their related probability distributions – that are now commonly used in
finance (for example, essentially normal and log-normal distributions, and
diffusion-like processes). Financial time series exhibit highly non-trivial sta-
tistical features which are hard to model and even harder to explain, for
example, intermittent behavior, volatility clustering (amplitudes of succes-
sive price movements are persistent, but not necessarily their signs), heavy
tailed increments, and subtle dependence structures.
Nowadays, computer power is readily available, and closed-form solu-
tions are considered to be a luxury that most practitioners cannot afford the
time to find, thus preferring crude numerical schemes. Most of the time,
these will work fine. However, numerical and poor semi-analytic methods