Modelling Extremes in Insurance and Finance: Practical Necessity versus Methodological Challenge Paul Embrechts Department of Mathematics ETH Zurich Switzerland www.math.ethz.ch/~embrechts 28th ICA Paris, May 29, 2006 c P. Embrechts (ETH Zurich) Modelling Extremes in Insurance and Finance 28th ICA Paris 1 / 51
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Modelling Extremes in Insurance and Finance:Practical Necessity versus Methodological
The Committee of European Banking Supervisors on thevalidation and assessment of credit and operational risk
approaches
“If an Extreme Value Theory approach is used, resortingto the stability property of the model (the so-called‘Peaks over Threshold’ stability property) that makes itpossible to compute the highest percentiles of thefrequency and severity distributions from figuresestimated at a lower level (usually at the thresholdlevel).”
Institute of Actuaries and Faculty of Actuaries:A Change Agenda for Reserving
“ Identifying where our Reserving Methods need to beEnhanced:More sophisticated mathematical and statisticalmethodology need not be a priority for actuaries at thisstage. Rather, the focus for enhancement and researchshould be in the following areas:
- ...- Whether extreme value theory has a role to play in
“A natural consequence of the existence of a lender oflast resort is that there will be some sort of allocation ofburden of risk of extreme outcomes. Thus, central banksare led to provide what essentially amounts tocatastrophic insurance coverage ... From the point ofview of the risk manager, inappropriate use of the
normal distribution can lead to an understatement
of risk, which must be balanced against the significantadvantage of simplification. From the central bankscorner, the consequences are even more serious becausewe often need to concentrate on the left tail of thedistribution in formulating lender-of-last-resort policies.Improving the characterization of the distribution ofextreme values is of paramount importance.”
(Alan Greenspan, Joint Central Bank Research Conference, 1995)
“Extreme, synchronized rises and falls in financialmarkets occur infrequently but they do occur. Theproblem with the models is that they did not assign ahigh enough chance of occurrence to the scenario inwhich many things go wrong at the same time - the“perfect storm” scenario”
“Regulators have criticised LTCM and banks for not“stress-testing” risk models against extreme marketmovements... The markets have been through thefinancial equivalent of several Hurricane Andrews hittingFlorida all at once. Is the appropriate response to acceptthat it was mere bad luck to run into such a rare event -or to get new forecasting models that assume morestorms in the future?”
(The Economist, October 1998, after the LTCM rescue)
“... The trading floor is quiet. But this masks theirattempt at picking up the pieces with a new fund, JWMPartners. Now, Mr. Meriwether is preaching new gospel:World financial markets are bound to hit extreme
turbulences again... Mr. Meriwether’s crew, oncebitten, also is betting on more liquid securities: “Withglobalisation increasing, you’ll see more crises,” he says.“Our whole focus is on the extremes now - what’s the
worst that can happen to you in any situation -because we never want to go through that again” ”
(John Meriwether, The Wall Street Journal, 21/8/2000)
“There is always going to bean element of doubt, as one isextrapolating into areas onedoesn’t know about. Butwhat EVT is doing is makingthe best use of whatever datayou have about extremephenomena.”
“The key message is thatEVT cannot do magic – but itcan do a whole lot better thanempirical curve fitting andguesswork. My answer to theskeptics is that if people aren’tgiven well-founded methodslike EVT, they’ll use dubiousones instead.”
“My main concern is that thisvery simple concept might besomething like the emperor’snew clothes because itpromises to solve all problemsof stochastic dependence butit falls short in achieving thegoal.”