194 MODEL RISK AND FINANCIAL DERIVATIVESin fact a patch against model errors – while section 10.4 discusses the role
that financial models play for derivatives contracts. Section 10.5 reviews the
different steps in the model building process where model risk can start.
Section 10.6 presents a short technical study of how things can turn wrong
when an option trader uses the wrong model to hedge his or her book,
while section 10.7 contains a series of (often forgotten) common sense rules
to manage and mitigate model risk. Section 10.8 summarizes our findings
and opens the way to future research.
10.2 From mathematical theory to financial practise
Derivatives pricing finds its roots in the doctoral thesis of Louis Bache-
lier (1900), which developed the first analytical model for the valuation
of financial options. Unfortunately, Bachelier’s theoretical contribution was
too innovative for his time. Consequently, his peers essentially focused on
the weaknesses of his model – normally distributed asset prices allow for
negative security prices and may result in call option prices that exceed the
price of the underlying asset. Therefore, Bachelier was granted his doctoral
degree, but he was only offered a chair in a second-tier university, and his
work remained undiscovered for more than fifty years. In a sense, Bache-
lier became the first publicly known victim of financial model risk, and
quantitative finance went back to sleep.
One has to wait until the late 1960s to see quantitative work laying
again some foundations in finance, with Markowitz’s (1959) and Sharpe’s
(1966) works on portfolio selection and modern portfolio theory. But
the major event was undoubtedly the publication of the option-pricing
model developed by Black and Scholes (1973) and Merton (1973). Though
mathematically complex, their formula was directly applicable, easy to
understand and only required a series of rather straightforward inputs:
the price of the underlying asset, the strike price, the time to maturity, the
volatility of the underlying asset and the risk-free interest rate. Moreover,
their model came out simultaneously with the opening of option trading
at the CBOT. Needless to say, it was an immediate success. Practitioners
and option traders adopted the model as a useful tool for understanding
what the price of an option should be, how to make money from mispriced
options, and how to hedge an option book.
Since then, the interaction between mathematical theory and financial
practice has never ceased. As the mathematical awareness in the financial
research community increased, financial markets became more quantified
and derivatives research actively evolved in three directions in order to
improve the Black, Scholes and Merton framework. The first direction
involved the relaxation of some of the original underlying assumptions,