Risk Management Technology in Financial Services

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122 Risk management technology in financial services

rules presumed to underlie and reflect a given process. This could serve as a model

if the clauses are of a kind that permits to predict further occurrences from those

already experienced – albeit at a confidence level which may not be perfect.

Within the domain defined by the preceding paragraphs, the goal of this chapter

is to present to the reader a comprehensive approach to modelling, with particular

emphasis on models for stress testing (which characterizes also Chapter 11). This

population of models is developed for the long leg of the risk distribution–anew

culture in modelling, and most particularly in financial analysis and experimentation.

Because nearly all current models focus on the high frequency area which is the

bubble part of a normal distribution, the contribution to stress testing of classical

type models is limited. As sections 7.6 and 7.7 will bring to the reader’s attention,

the usual way to stress test is to assume 5, 10, 15 standard deviations from the risk

distribution’s mean. This permits to continue using rich statistical tables developed

for normal distributions, while examining extreme events.

The downside of the solution outlined in the preceding paragraph is that it does

not account for spikes. Yet, spikes which show up at the long leg of a risk distri-

bution are important and costly events. Therefore, we are interested in their origins,

nature, frequency and underlying reasons – which, quite often, tend to change over

time as market conditions evolve. In terms of their analysis, knowledge engineering

(Chapter 9) and genetic algorithms (Chapter 10) might be of help.

7.2 The development of mathematical science

To appreciate the way of mathematical thought accumulated over the ages, we should

turn to the ninth book of Euclid’s Elements. There we find a sequence of propositions

(precisely, 21 to 32) which have no connection whatever with what precedes or

follows them. Such propositions constitute a piece of Pythagorean mathematics, which

predated by centuries Euclid’s work, but still influences present-day science.

Pythagoras, the great philosopher and mathematician of ancient Greece, trans-

formed the science of mathematics, essentially geometry and analytics brought to

Greece from Egypt by Thales, one of the seven sages of antiquity. By all evidence,

the ancient Greeks had learned from the Egyptians the rules for determination of

areas and volumes – just like the Egyptians learned arithmetic from the Babylonians,

who knew how to solve systems of linear and quadratic equations with two or more

unknowns.

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In terms of science and mathematics, the Babylonians, too, had learned a great

deal from other civilizations which preceded their own – particularly from Sumer

and India. This is not surprising because progress in science and technology is based

not only on the research spirit and innovative ideas (see Chapter 1) but also, if not

primarily, on the analytical thinking accumulating during the ages which permits

subsequent generations to leap forward.

An example of knowledge coming from ancient India and benefiting subsequent

generations till the present day is the invention of zero. By all accounts, this has

been the greatest contribution ever to mathematics. It took a real genius to identify

‘nothing’, call it ‘something’ and integrate it into a system of signs and rules.