Advances in Risk Management

FRANÇOIS-SERGE LHABITAN T 197

30

25

20

15

10

130

120

110

100 90

80 70

5 Years

2 Years

1 Years

6 Months

2 Months

Time to maturity

Implied volatility

Exercise price

(as a % of market value)

Figure 10.1An example of the volatility surface observed on

the Swiss market index

Black and Scholes assumptions do not hold, then any information implied
by applying their model should by definition be considered suspicious. For a
given option, the single number that we call “implied volatility” is, in some
sense, just an amalgamation of all the unobservable, untradable, omitted
and/or incorrectly specified parameters in the Black and Scholes model.
Nevertheless, most financial institutions and researchers continue to use
implied volatilities and even build more sophisticated models on top of
them.^4

10.4 The role of models for derivatives

Not all derivatives models were created equal. Depending on the role they
are playing, models may be more likely or less likely to generate model risk.
Three different perspectives should be considered.

10.4.1 A model is just shorthand

The first series of models are just convenient mathematical shorthand with
no real meaning. They provide a useful tool to summarize a large amount